The Effects Of Technology On The Classroom - 1328 Words

On any given day, teens in the United States spend about nine hours using technology, according to a recent report (Common Sense Media). This nine hours is more time than teenagers spend sleeping, completing homework, or interacting with family. In recent years, constant access to the internet and social networking sites has created an addiction- a reliance that today’s youth can’t navigate around. Simultaneous with the greater presence of technology is greater success in the classroom. Over the past decade, the number of students who pass AP exams every year has quintupled (Forbes). But when it comes to basic skills such as holding a conversation, students are falling short. If the same amount of energy being put into teaching BC†¦show more content†¦The teachers who observed positive changes in students’ behavior gave credit to the education program, or some aspect of it, as contributing to the changes. Because of the pertinent lessons being taught in the classroom, the students were able and willing to apply what they learned at school to their daily lives. In the same way, if schools were to make communication curriculum a priority, there would be observable changes in the way students interact and carry themselves. This idea is shared by Sir Ken Robinson, New York Times bestselling author and emeritus professor of arts education at the University of Warwick. In his book Creative Schools, Robinson insists â€Å"The aims of education are to enable students to understand the world around them...so that they can become fulfilled individuals and active, compassionate citizens.† For most students, the classroom is the only place that kids will have the opportunity to learn the necessary skills that they need in order to thrive. With such a great role in teenagers’ lives, schools carry the responsibility of producing the successful citizens that Robinson is referring to. This being said, high school programs should in clude communication education given their significant impact on students’ behaviors and lives. The use of technology has diminished students’ communication skills. This is seen first hand by Paul Barnwell, high school teacher and writer for The Atlantic.Show MoreRelatedThe Effects Of Technology On The Classroom1519 Words   |  7 PagesClassrooms today look almost nothing like the classrooms of past generations. Modern classrooms revolve around technology, every room has either a projector or smart board front and center. A significant amount of homework is submitted digitally, and a computer is often a class requirement. Many studies have shown the positive effects these teaching and learning techniques have, and the results are not often disputed. Technology is helping educate students even at the elementary level, but studiesRead MoreTechnology And Its Effects On The Classroom960 Words   |  4 PagesIPads and all of this new technology is being used more to play Flappy Bird than get any real schoolwork done. With new innovations in technology, schools have decided to incorporate devices like the Smartboard or IPad, but we do not know how to use them effectively to teach. Sure, these devices could be of some help, but the school board has not effectively taught teachers how to fully utilize the very equipment they are using to teach their students. Even with a firewall that can block certainRead MoreThe Effect Of Technology On The Classroom Essay1210 Words   |  5 PagesThere is a growing trend in the use of technology in the classroom. As a teacher, I am always looking for ways to use manipulatives in my lessons to increase meaning and authenticity for students. I would love to keep my students engaged, motivated and interactive in the classroom and still be able to get through the content each day. In order to achieve this, I need to have an arsenal of tools to draw from. That is why I agree with (Tataroglu Erduran, 2010) as stated in the International ElectronicRead MoreThe Effects Of Technology On Our Classroom1166 Words   |  5 Pag esUsing technology in the classroom gives students a much greater advantage in whatever job or lifestyle they decide to pursue after their academic careers. Technology has become so much apart of our daily lives, and routines that we cannot expect the younger generation to be able to keep up unless they are equipped with the tools that are necessary. Some people might argue that inundating kids with too much technology can be harmful. Another argument against technology is that it is putting kids outRead MoreThe Effects Of Educational Technology On The Classroom1345 Words   |  6 PagesResearch Paper: Effects of Educational Technology In the Classroom By: Nicole Ault Computer Science 313 October 1st, 2017 Abstract: This research paper includes several studies on the effects of children’s learning when incorporating technology into their lives. Overall, the studies mentioned can make technology be viewed as an aid or a hinder on a child’s cognitive development. For some people the advances of technology in today’s world can be viewed asRead MoreTechnology And Its Effects On Our Classroom Essay1452 Words   |  6 Pages Technology In Classrooms When people walk into a classroom and a teacher is up front lecturing, all they see are heads down on desks. As they walk around people are sleeping and doodling things like â€Å"I love you†, and writing their names 1000 different ways. The room makes someone feel like they are standing in a funeral home. It is boring and no one pays any attention, and anyone could notice that when there is dried drool on the desks for the next class. Not all classrooms are bland thoughRead MoreThe Positive And Negative Effects Of Technology In The Classroom959 Words   |  4 Pagesthey’ve introduced technology into classrooms. More than anything, people question how much technology helps a student, as well as whether or not it actually hinders their learning. Both positive and negative effects have made themselves present, and both are continuing to grow in number. Whether liked or not, technology is a large part of today’s world, and people will only continue to use it as it grows. In classrooms today, both positives and negatives result from the use of technology, as well as fromRead MoreThe Effects Of Technology On Classroom Practices And Student Outcomes1564 Words   |  7 Pagesall participants should be ensured at all times and the research should be conducted in an ethical manner (National Health and Medical Research Council, 2015, p.5). In the aforementioned research, studying the effects the investment of technology throughout their school was having on classroom practices and student outcomes – specifically in mathematics and science teaching, many ethical considerations must be taken into account. Researchers must have received the appropriate consent from all stakeholdersRead MoreTechnology : Does Technology Help Or Hinder The Student?966 Words   |  4 Pagesviewpoints of today’s generation, and how technology has taken over and welcomed itself into many aspects of our lives. This course paper will take a look at one topi c of interest in particular, which in hopes will shed some light on a heavily discussed topic in the education world: does technology help or hinder the student. This paper will look to prove the point and discover more about the way in which technology has been incorporated into the classroom, both in an elementary context as well asRead MoreHow Personal Computers Affect Student s Learning Processes Essay1691 Words   |  7 Pagescentury, technology like personal computers and tablets have become more accessible and inexpensive. The aim of this research is to inform the public and education institutions on how personal computers affect student’s learning processes in the classroom. Most universities require the access to computers in order to perform task and write assignments. This has manifested in having more computers in a classroom used by the lecturers and students. The massive evolution and consumption of technology have

Feminism Types and Definitions Liberal - 1287 Words

Login Plans Pricing How It Works Courses Degrees Schools Careers | Register Search Courses Lessons Feminism Types and Definitions: Liberal, Socialist, Culture Radical / Sex and Gender in Society / Sociology 101: Intro to Sociology / Social Science / Courses Like? Feminism Types and Definitions: Liberal, Socialist, Culture Radical Video Quiz Congratulations! You ve reached the last video in the chapter. Transcript Start the Next Chapter Race and Ethnicity Definitions: Social Minority vs. Social Majority CREATE YOUR ACCOUNT Show Timeline Share This lesson first provides a general definition of feminism. Then, four specific types of feminism are discussed and defined, including liberal feminism, socialist†¦show more content†¦Radical feminists note that this traditional dichotomy maintains men as economically in power over women, and therefore, the traditional family structure should be rejected. Foreign Language History Humanities Socialist Feminism Math Science Radical feminism is the most extreme form. The second type of feminism, called socialist Social Science feminism, is slightly less extreme but still calls for major social change. Socialist feminism is a movement that calls for an end to capitalism High School Courses through a socialist reformation of our economy. Basically, socialist feminism argues that capitalism AP strengthens and supports the sexist status quo because men are the ones who currently have Socialist feminism calls for an end to capitalism Common Core power and money. Those men are more willing to share their power and money with other men, which GED means that women are continually given fewer opportunities and resources. This keeps women under the High School control of men. In short, socialist feminism focuses on economics and politics. They might point out the fact that in the United States women are typically paid only $0.70 for the exact same job that a man would be paid a Other Courses dollar for. Why are women paid less than men for the same work? Socialist feminists point out that this difference is based on a capitalist system.Show MoreRelatedDoes Feminism Create Equality?1037 Words   |  5 PagesDoes Feminism Create Equality? Feminism is an umbrella term for people who think there is something wrong with the idea that gender has the capability to limit an individual’s social and political right. Even if there is inequality between men and women, feminism has never been the main reason to give women their civil rights. Feminism started among European activists in the 19th century, when women were not treated equally and were not elected to high positions of power. Indeed, it sought to eliminateRead MoreFeminism : The Second Wave Of Feminism1222 Words   |  5 PagesWhat is feminism? Feminism is a definition to philosophy in which women and their contributions are valued. It is based on a social political and economical which is an equality for women. It’s a revolution that includes women and men who who wish the world to be equal without boundaries. The evolution of the rights of women in Australia owes much to successive waves of feminism, or the women s movement. The first of these took pl ace in the late 19th century and was concerned largely with gainingRead MorePolitical Feminism and its Misrepresentation1163 Words   |  5 Pagesthere is not just one kind of feminism, there are hundreds in each aspect of our life (Tavaana, 2014). The most under represented group within feminism is the kind that is in the government. Not all have the same theories, and therefore, do not have the same beliefs. However what we do know is that, whatever theory they have, or agenda they follow, they are all fierce promoters of gender equality. One theory of feminism that exists is the world is â€Å"Second Wave feminism† (Mandle, 2014). This is theRead MoreFeminism : A Social, Economic, And Social Equality Of The Sexes1465 Words   |  6 PagesFeminism. This seemingly harmless word can ruin or heighten a person’s reputation, it can give someone new views on the world, it can destroy relationships, it can build new ones; this single word can change lives. Most people categorize â€Å"feminism† as a code for women that tells them to hate men, not shave, burn bras, be vegan, and if there is any time left over maybe, just maybe, to fight for women’s rights. Now, there are definitely feminists that fulfill this stereotype but the vast majority ofRead MoreFeminism : The First Wave Of Feminism1267 Words   |  6 PagesFeminism is a movement calling for social change, holding to a belief that women are oppressed by American society due to patriarchy’s inherent sexism. This social movement explained quite simply started in the 19th century when women fought for the right to vote, sought to improve workplace conditions for women as well as increase working opportunities. From this initial movement, called first wa ve feminism, stemmed other waves that though somewhere in the same vein, they held many differing goalsRead MoreFeminism Theory : Who Want Women Equality, They Should Look Into Feminism1552 Words   |  7 PagesShelby Milinovich Mrs. Almack English 4 AP September 21, 2014 Feminism Theory To those who want women equality, they should look into feminism. To be a feminist you don’t have to be a woman, you just need to support women in their fight to be legally equal to men in social and economical situations. This means women deserve equal pay, equal access to education, make decisions about their own body, ending job sex segregation, better working conditions, for women to be able to hold a public officeRead MoreFeminism And The World Of The 2016 Election884 Words   |  4 PagesFeminism and Intersectionality are at the forefront of the 2016 election. While feminism is still viewed in somewhat limited terms of promoting the equality and status of women, Intersectionality is defined in much broader language, as the interconnection of race, gender, ability, and class in the social world. Moreover, all of these intersecting categories overlap and cannot be separated. Thus, the traditional view of feminism, that promotes the equality of women first and foremost, is often pittedRead MoreWomen During The 19th Century Essay1107 Words   |  5 Pagesdecades after, pants would be allowed, introducing scandalous shorts along with it. Although heavily criticized, the stigma of shorts lessened, showing us more familiar styles. Dress reform went full force in this era. Fashion during the second-wave feminism was marked the increase of more comfortable clothing. Women were primarily working in factories for the war effort, so their dress was consisted mainly of pants and high collared shirts []. Fashion in this era would eventually go towards flashy paddedRead MoreFeminism1121 Words   |  5 PagesFEMINISM Introduction to Sociology Feminism Belief in the social, political, and economic equality of the sexes. The movement organized around this belief. Feminism Feminist Theory is an outgrowth of the general movement to empower women worldwide. Feminism can be defined as a recognition and critique of male supremacy combined with efforts to change it. Feminism The goals of feminism are: To demonstrate the importance of women To reveal that historically women have been subordinate to menRead MoreFeminism And Gender And Ethnic Studies1172 Words   |  5 PagesMy Interpretation of Feminism Feminism has had a deep impact on me since I was infantile. Though she never mentioned it, my mother was an active feminist. I grew up playing with toys considered to belong to either sex. I was taught to be strong and to let my emotions out, and I was given freedom to make my own identity. This was my first experience of social feminism, followed years later by learning the definition of feminism and learning to also see discrimination politically and economically

Bayesian Inference Free Essays

string(34) " in the context of a binary GLMM\." Biostatistics (2010), 11, 3, pp. 397–412 doi:10. 1093/biostatistics/kxp053 Advance Access publication on December 4, 2009 Bayesian inference for generalized linear mixed models YOUYI FONG Downloaded from http://biostatistics. We will write a custom essay sample on Bayesian Inference or any similar topic only for you Order Now oxfordjournals. org/ at Cornell University Library on April 20, 2013 Department of Biostatistics, University of Washington, Seattle, WA 98112, USA ? HAVARD RUE Department of Mathematical Sciences, The Norwegian University for Science and Technology, N-7491 Trondheim, Norway JON WAKEFIELD? Departments of Statistics and Biostatistics, University of Washington, Seattle, WA 98112, USA jonno@u. ashington. edu S UMMARY Generalized linear mixed models (GLMMs) continue to grow in popularity due to their ability to directly acknowledge multiple levels of dependency and model different data types. For small sample sizes especially, likelihood-based inference can be unreliable with variance components being particularly difficult to estimate. A Bayesian approach is appealing but has been hampered by the lack of a fast implementation, and the difficulty in specifying prior distributions with variance components again being particularly problematic. Here, we briefly review previous approaches to computation in Bayesian implementations of GLMMs and illustrate in detail, the use of integrated nested Laplace approximations in this context. We consider a number of examples, carefully specifying prior distributions on meaningful quantities in each case. The examples cover a wide range of data types including those requiring smoothing over time and a relatively complicated spline model for which we examine our prior specification in terms of the implied degrees of freedom. We conclude that Bayesian inference is now practically feasible for GLMMs and provides an attractive alternative to likelihood-based approaches such as penalized quasi-likelihood. As with likelihood-based approaches, great care is required in the analysis of clustered binary data since approximation strategies may be less accurate for such data. Keywords: Integrated nested Laplace approximations; Longitudinal data; Penalized quasi-likelihood; Prior specification; Spline models. 1. I NTRODUCTION Generalized linear mixed models (GLMMs) combine a generalized linear model with normal random effects on the linear predictor scale, to give a rich family of models that have been used in a wide variety of applications (see, e. g. Diggle and others, 2002; Verbeke and Molenberghs, 2000, 2005; McCulloch and others, 2008). This flexibility comes at a price, however, in terms of analytical tractability, which has a ? To whom correspondence should be addressed. c The Author 2009. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals. permissions@oxfordjournals. rg. 398 Y. F ONG AND OTHERS number of implications including computational complexity, and an unknown degree to which inference is dependent on modeling assumptions. Likelihood-based inference may be carried out relatively easily within many software platforms (except perhaps for binary responses), but inference is dependent on asymptotic sampling distributions of estimato rs, with few guidelines available as to when such theory will produce accurate inference. A Bayesian approach is attractive, but requires the specification of prior distributions which is not straightforward, in particular for variance components. Computation is also an issue since the usual implementation is via Markov chain Monte Carlo (MCMC), which carries a large computational overhead. The seminal article of Breslow and Clayton (1993) helped to popularize GLMMs and placed an emphasis on likelihood-based inference via penalized quasi-likelihood (PQL). It is the aim of this article to describe, through a series of examples (including all of those considered in Breslow and Clayton, 1993), how Bayesian inference may be performed with computation via a fast implementation and with guidance on prior specification. The structure of this article is as follows. In Section 2, we define notation for the GLMM, and in Section 3, we describe the integrated nested Laplace approximation (INLA) that has recently been proposed as a computationally convenient alternative to MCMC. Section 4 gives a number of prescriptions for prior specification. Three examples are considered in Section 5 (with additional examples being reported in the supplementary material available at Biostatistics online, along with a simulation study that reports the performance of INLA in the binary response situation). We conclude the paper with a discussion in Section 6. 2. T HE G ENERALIZED LINEAR MIXED MODEL GLMMs extend the generalized linear model, as proposed by Nelder and Wedderburn (1972) and comprehensively described in McCullagh and Nelder (1989), by adding normally distributed random effects on the linear predictor scale. Suppose Yi j is of exponential family form: Yi j |? i j , ? 1 ? p(†¢), where p(†¢) is a member of the exponential family, that is, p(yi j |? i j , ? 1 ) = exp yi j ? i j ? b(? i j ) + c(yi j , ? 1 ) , a(? 1 ) Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 for i = 1, . . . , m units (clusters) and j = 1, . . , n i , measurements per unit and where ? i j is the (scalar) ? canonical parameter. Let ? i j = E[Yi j |? , b i , ? 1 ] = b (? i j ) with g(? i j ) = ? i j = x i j ? + z i j b i , where g(†¢) is a monotonic â€Å"link† function, x i j is 1 ? p, and z i j is 1 ? q, with ? a p ? 1 vector of fixed ? Q effects and b i a q ? 1 vector of random ef fects, hence ? i j = ? i j (? , b i ). Assume b i |Q ? N (0, Q ? 1 ), where ? the precision matrix Q = Q (? 2 ) depends on parameters ? 2 . For some choices of model, the matrix Q is singular; examples include random walk models (as considered in Section 5. ) and intrinsic conditional ? autoregressive models. We further assume that ? is assigned a normal prior distribution. Let ? = (? , b ) denote the G ? 1 vector of parameters assigned Gaussian priors. We also require priors for ? 1 (if not a constant) and for ? 2 . Let ? = (? 1 , ? 2 ) be the variance components for which non-Gaussian priors are ? assigned, with V = dim(? ). 3. I NTEGRATED NESTED L APLACE APPROXIMATION Before the MCMC revolution, there were few examples of the applications of Bayesian GLMMs since, outside of the linear mixed model, the models are analytically intractable. Kass and Steffey (1989) describe the use of Laplace approximations in Bayesian hierarchical models, while Skene and Wakefield Bayesian GLMMs 399 (1990) used numerical integration in the context of a binary GLMM. You read "Bayesian Inference" in category "Papers" The use of MCMC for GLMMs is particularly appealing since the conditional independencies of the model may be exploited when the required conditional distributions are calculated. Zeger and Karim (1991) described approximate Gibbs sampling for GLMMs, with nonstandard conditional distributions being approximated by normal distributions. More general Metropolis–Hastings algorithms are straightforward to construct (see, e. g. Clayton, 1996; Gamerman, 1997). The winBUGS (Spiegelhalter, Thomas, and Best, 1998) software example manuals contain many GLMM examples. There are now a variety of additional software platforms for fitting GLMMs via MCMC including JAGS (Plummer, 2009) and BayesX (Fahrmeir and others, 2004). A large practical impediment to data analysis using MCMC is the large computational burden. For this reason, we now briefly review the INLA computational approach upon which we concentrate. The method combines Laplace approximations and numerical integration in a very efficient manner (see Rue and others, 2009, for a more extensive treatment). For the GLMM described in Section 2, the posterior is given by m Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 ? y ? ? ? ?(? , ? |y ) ? ?(? |? )? (? ) i=1 y ? p(y i |? , ? ) m i=1 1 ? ? Q ? ? b ? ?(? )? (? )|Q (? 2 )|1/2 exp ? b T Q (? 2 )b + 2 y ? log p(y i |? , ? 1 ) , where y i = (yi1 , . . . , yin i ) is the vector of observations on unit/cluster i. We wish to obtain the posterior y y marginals ? (? g |y ), g = 1, . . . , G, and ? (? v |y ), v = 1, . . . , V . The number of variance components, V , should not be too large for accurate inference (since these components are integrated out via Cartesian product numerical integration, which does not scale well with dimension). We write y ? (? g |y ) = which may be evaluated via the approximation y ? (? g |y ) = K ? ? y ? ?(? g |? , y ) ? ?(? |y )d? , ? ? y ? ?(? g |? , y ) ? ? (? |y )d? ? y ? ? (? g |? k , y ) ? ? (? k |y ) ? k, ? (3. 1) k=1 here Laplace (or other related analytical approximations) are applied to carry out the integrations required ? ? for evaluation of ? (? g |? , y ). To produce the grid of points {? k , k = 1, . . . , K } over which numerical inte? y gration is performed, the mode of ? (? |y ) is located, and the Hessian is approximated, from which the grid is created and exploited in (3. 1). The output of INLA consists of posterior marginal distributions, which can be summarized via means, variances, and quantiles. Importantly for model comparison, the normaly izing constant p(y ) is calculated. The evaluation of this quantity is not straightforward using MCMC (DiCiccio and others, 1997; Meng and Wong, 1996). The deviance information criterion (Spiegelhalter, Best, and others, 1998) is popular as a model selection tool, but in random-effects models, the implicit approximation in its use is valid only when the effective number of parameters is much smaller than the number of independent observations (see Plummer, 2008). 400 Y. F ONG AND OTHERS 4. P RIOR DISTRIBUTIONS 4. 1 Fixed effects Recall that we assume ? is normally distributed. Often there will be sufficient information in the data for ? o be well estimated with a normal prior with a large variance (of course there will be circumstances under which we would like to specify more informative priors, e. g. when there are many correlated covariates). The use of an improper prior for ? will often lead to a proper posterior though care should be taken. For example, Wakefield (2007) shows that a Poisson likelihood with a linea r link can lead to an improper posterior if an improper prior is used. Hobert and Casella (1996) discuss the use of improper priors in linear mixed effects models. If we wish to use informative priors, we may specify independent normal priors with the parameters for each component being obtained via specification of 2 quantiles with associated probabilities. For logistic and log-linear models, these quantiles may be given on the exponentiated scale since these are more interpretable (as the odds ratio and rate ratio, respectively). If ? 1 and ? 2 are the quantiles on the exponentiated scale and p1 and p2 are the associated probabilities, then the parameters of the normal prior are given by ? = ? = z 2 log(? 1 ) ? z 1 log(? 2 ) , z2 ? 1 Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 log(? 2 ) ? log(? 1 ) , z2 ? z1 where z 1 and z 2 are the p1 and p2 quantiles of a standard normal random variable. For example, in an epidemiological context, we may wish to specify a prior on a relative risk parameter, exp(? 1 ), which has a median of 1 and a 95% point of 3 (if we think it is unlikely that the relative risk associated with a unit increase in exposure exceeds 3). These specifications lead to ? 1 ? N (0, 0. 6682 ). 4. 2 Variance components We begin by describing an approach for choosing a prior for a single random effect, based on Wakefield (2009). The basic idea is to specify a range for the more interpretable marginal distribution of bi and use this to drive specification of prior parameters. We state a trivial lemma upon which prior specification is based, but first define some notation. We write ? ? Ga(a1 , a2 ) for the gamma distribution with un? normalized density ? a1 ? 1 exp(? a2 ? ). For q-dimensional x , we write x ? Tq (? , , d) for the Student’s x x t distribution with unnormalized density [1 + (x ? ? )T ? 1 (x ? )/d]? (d+q)/2 . This distribution has location ? , scale matrix , and degrees of freedom d. L EMMA 1 Let b|? ? N (0, ? ?1 ) and ? ? Ga(a1 , a2 ). Integration over ? gives the marginal distribution of b as T1 (0, a2 /a1 , 2a1 ). To decide upon a prior, we give a range for a generic random effect b and specify the degrees of freev d dom, d, and then solve for a1 and a2 . For the range (? R, R) , we use the relationship  ±t1? (1? q)/2 a2 /a1 = d  ±R, where tq is the 100 ? qth quantile of a Student t random variable with d degrees of freedom, to give d a1 = d/2 and a2 = R 2 d/2(t1? (1? q)/2 )2 . In the linear mixed effects model, b is directly interpretable, while for binomial or Poisson models, it is more appropriate to think in terms of the marginal distribution of exp(b), the residual odds and rate ratio, respectively, and this distribution is log Student’s t. For example, if we choose d = 1 (to give a Cauchy marginal) and a 95% range of [0. 1, 10], we take R = log 10 and obtain a = 0. 5 and b = 0. 0164. Bayesian GLMMs 401 ?1 Another convenient choice is d = 2 to give the exponential distribution with mean a2 for ? ?2 . This leads to closed-form expressions for the more interpretable quantiles of ? o that, for example, if we 2 specify the median for ? as ? m , we obtain a2 = ? m log 2. Unfortunately, the use of Ga( , ) priors has become popular as a prior for ? ?2 in a GLMM context, arising from their use in the winBUGS examples manual. As has been pointed out many times (e. g. Kelsall and Wakefield, 1999; Gelman, 2006; Crainiceanu and others, 2008), this choice pl aces the majority of the prior mass away from zero and leads to a marginal prior for the random effects which is Student’s t with 2 degrees of freedom (so that the tails are much heavier than even a Cauchy) and difficult to justify in any practical setting. We now specify another trivial lemma, but first establish notation for the Wishart distribution. For the q ? q nonsingular matrix z , we write z ? Wishartq (r, S ) for the Wishart distribution with unnormalized Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 Q Lemma: Let b = (b1 , . . . , bq ), with b |Q ? iid Nq (0, Q ? 1 ), Q ? Wishartq (r, S ). Integration over Q b as Tq (0, [(r ? q + 1)S ]? 1 , r ? q + 1). S gives the marginal distribution of The margins of a multivariate Student’s t are t also, which allows r and S to be chosen as in the univariate case. Specifically, the kth element of a generic random effect, bk , follows a univariate Student t distribution with location 0, scale S kk /(r ? q + 1), and degrees of freedom d = r ? q + 1, where S kk d is element (k, k) of the inverse of S . We obtain r = d + q ? 1 and S kk = (t1? (1? q)/2 )2 /(d R 2 ). If a priori b are correlated we may specify S jk = 0 for j = k and we have no reason to believe that elements of S kk = 1/Skk , to recover the univariate specification, recognizing that with q = 1, the univariate Wishart has parameters a1 = r/2 and a2 = 1/(2S). If we believe that elements of b are dependent then we may specify the correlations and solve for the off-diagonal elements of S . To ensure propriety of the posterior, proper priors are required for ; Zeger and Karim (1991) use an improper prior for , so that the posterior is improper also. 4. 3 Effective degrees of freedom variance components prior z z z z density |z |(r ? q? 1)/2 exp ? 1 tr(z S ? 1 ) . This distribution has E[z ] = r S and E[z ? 1 ] = S ? 1 /(r ? q ? 1), 2 and we require r q ? 1 for a proper distribution. In Section 5. 3, we describe the GLMM representation of a spline model. A generic linear spline model is given by K yi = x i ? + k=1 z ik bk + i , where x i is a p ? 1 vector of covariates with p ? 1 associated fixed effects ? , z ik denote the spline 2 basis, bk ? iid N (0, ? b ), and i ? iid N (0, ? 2 ), with bk and i independent. Specification of a prior for 2 is not straightforward, but may be of great importance since it contributes to determining the amount ? b of smoothing that is applied. Ruppert and others (2003, p. 77) raise concerns, â€Å"about the instability of automatic smoothing parameter selection even for single predictor models†, and continue, â€Å"Although we are attracted by the automatic nature of the mixed model-REML approach to fitting additive models, we discourage blind acceptance of whatever answer it provides and recommend looking at other amounts of smoothing†. While we would echo this general advice, we believe that a Bayesian mixed model approach, with carefully chosen priors, can increase the stability of the mixed model representation. There has been 2 some discussion of choice of prior for ? in a spline context (Crainiceanu and others, 2005, 2008). More general discussion can be found in Natarajan and Kass (2000) and Gelman (2006). In practice (e. g. Hastie and Tibshirani, 1990), smoothers are often applied with a fixed degrees of freedom. We extend this rationale by examining the prior degrees of freedom that is implied by the choice 402 Y. F ONG AND OTHERS ?2 ? b ? Ga(a1 , a2 ). For the general linear mixed model y = x ? + zb + , we have x z where C = [x |z ] is n ? ( p + K ) and C y = x ? + z b = C (C T C + 0 p? p 0K ? p )? 1 C T y , = 0 p? K 2 cov(b )? 1 b ? )? 1 C T C }, Downloaded from http://biostatistics. xfordjournals. org/ at Cornell University Library on April 20, 2013 (see, e. g. Ruppert and others, 2003, Section 8. 3). The total degrees of freedom associated with the model is C df = tr{(C T C + which may be decomposed into the degrees of freedom associated with ? and b , and extends easily to situations in which we have additional random effects, beyond those associated with the spline basis (such an example is considered in Section 5. 3). In each of these situations, the degrees of freedom associated C with the respective parameter is obtained by summing the appropriate diagonal elements of (C T C + )? C T C . Specifically, if we have j = 1, . . . , d sets of random-effect parameters (there are d = 2 in the model considered in Section 5. 3) then let E j be the ( p + K ) ? ( p + K ) diagonal matrix with ones in the diagonal positions corresponding to set j. Then the degrees of freedom associated with this set is E C df j = tr{E j (C T C + )? 1 C T C . Note that the effective degrees of freedom changes as a function of K , as expected. To evaluate , ? 2 is required. If we specify a proper prior for ? 2 , then we may specify the 2 2 joint prior as ? (? b , ? 2 ) = ? (? 2 )? (? b |? 2 ). Often, however, we assume the improper prior ? (? 2 ) ? 1/? 2 since the data provide sufficient information with respect to ? 2 . Hence, we have found the substitution of an estimate for ? 2 (for example, from the fitting of a spline model in a likelihood implementation) to be a practically reasonable strategy. As a simple nonspline demonstration of the derived effective degrees of freedom, consider a 1-way analysis of variance model Yi j = ? 0 + bi + i j 2 with bi ? iid N (0, ? b ), i j ? iid N (0, ? 2 ) for i = 1, . . . , m = 10 groups and j = 1, . . . , n = 5 observa? 2 tions per group. For illustration, we assume ? ? Ga(0. 5, 0. 005). Figure 1 displays the prior distribution for ? , the implied prior distribution on the effective degrees of freedom, and the bivariate plot of these quantities. For clarity of plotting, we exclude a small number of points beyond ? 2. 5 (4% of points). In panel (c), we have placed dashed horizontal lines at effective degrees of freedom equal to 1 (c omplete smoothing) and 10 (no smoothing). From panel (b), we conclude that here the prior choice favors quite strong smoothing. This may be contrasted with the gamma prior with parameters (0. 001, 0. 001), which, in this example, gives reater than 99% of the prior mass on an effective degrees of freedom greater than 9. 9, again showing the inappropriateness of this prior. It is appealing to extend the above argument to nonlinear models but unfortunately this is not straightforward. For a nonlinear model, the degrees of freedom may be approximated by C df = tr{(C T W C + where W = diag Vi? 1 d? i dh 2 )? 1 C T W C }, and h = g ? 1 denotes the inverse link function. Unfortunately, this quantity depends on ? and b , which means that in practice, we would have to use prior estimates for all of the parameters, which may not be practically possible. Fitting the model using likelihood and then substituting in estimates for ? and b seems philosophically dubious. Bayesian GLMMs 403 Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 Fig. 1. Gamma prior for ? ?2 with parameters 0. 5 and 0. 005, (a) implied prior for ? , (b) implied prior for the effective degrees of freedom, and (c) effective degrees of freedom versus ? . 4. 4 Random walk models Conditionally represented smoothing models are popular for random effects in both temporal and spatial applications (see, e. g. Besag and others, 1995; Rue and Held, 2005). For illustration, consider models of the form ? (m? r ) Q u 2 exp ? p(u |? u ) = (2? )? (m? r )/2 |Q |1/2 ? u 1 T u Qu , 2 2? u (4. 1) 404 Y. F ONG AND OTHERS where u = (u 1 , . . . , u m ) is the collection of random effects, Q is a (scaled) â€Å"precision† matrix of rank Q m ? r , whose form is determined by the application at hand, and |Q | is a generalized determinant which is the product over the m ? r nonzero eigenvalues of Q . Picking a prior for ? u is not straightforward because ? u has an interpretation as the conditional standard deviation, where the elements that are conditioned upon depends on the application. We may simulate realizations from (4. 1) to examine candidate prior distributions. Due to the rank deficiency, (4. 1) does not define a probability density, and so we cannot directly simulate from this prior. However, Rue and Held (2005) give an algorithm for generating samples from (4. 1): 1. Simulate z j ? N (0, 1 ), for j = m ? r + 1, . . . , m, where ? j are the eigenvalues of Q (there are j m ? r nonzero eigenvalues as Q has rank m ? r ). 2. Return u = z m? r +1 e n? r +1 + z 3 e 3 + †¢ †¢ †¢ + z n e m = E z , where e j are the corresponding eigenvectors of Q , E is the m ? (m ? ) matrix with these eigenvectors as columns, and z is the (m ? r ) ? 1 vector containing z j , j = m ? r + 1, . . . , m. The simulation algorithm is conditioned so that samples are zero in the null-space of Q ; if u is a sample and the null-space is spanned by v 1 and v 2 , then u T v 1 = u T v 2 = 0. For example, suppose Q 1 = 0 so that the null-space is spanned by 1, and the rank defici ency is 1. Then Q is improper since the eigenvalue corresponding to 1 is zero, and samples u produced by the algorithm are such that u T 1 = 0. In Section 5. 2, we use this algorithm to evaluate different priors via simulation. It is also useful to note that if we wish to compute the marginal variances only, simulation is not required, as they are available as the diagonal elements of the matrix j 1 e j e T . j j 5. E XAMPLES Here, we report 3 examples, with 4 others described in the supplementary material available at Biostatistics online. Together these cover all the examples in Breslow and Clayton (1993), along with an additional spline example. In the first example, results using the INLA numerical/analytical approximation described in Section 3 were compared with MCMC as implemented in the JAGS software (Plummer, 2009) and found to be accurate. For the models considered in the second and third examples, the approximation was compared with the MCMC implementation contained in the INLA software. 5. 1 Longitudinal data We consider the much analyzed epilepsy data set of Thall and Vail (1990). These data concern the number ? of seizures, Yi j for patient i on visit j, with Yi j |? , b i ? ind Poisson(? i j ), i = 1, . . . , 59, j = 1, . . . , 4. We concentrate on the 3 random-effects models fitted by Breslow and Clayton (1993): log ? i j = x i j ? + b1i , (5. 1) (5. 2) (5. 3) Downloaded from http://biostatistics. oxfordjournals. rg/ at Cornell University Library on April 20, 2013 log ? i j = x i j ? + b1i + b2i V j /10, log ? i j = x i j ? + b1i + b0i j , where x i j is a 1 ? 6 vector containing a 1 (representing the intercept), an indicator for baseline measurement, a treatment indicator, the baseline by treatment interaction, which is the parameter of interest, age, and either an indicator of the fourth visit (models (5. 1) an d (5. 2) and denoted V4 ) or visit number coded ? 3, ? 1, +1, +3 (model (5. 3) and denoted V j /10) and ? is the associated fixed effect. All 3 models 2 include patient-specific random effects b1i ? N 0, ? , while in model (5. 2), we introduce independent 2 ). Model (5. 3) includes random effects on the slope associated with â€Å"measurement errors,† b0i j ? N (0, ? 0 Bayesian GLMMs 405 Table 1. PQL and INLA summaries for the epilepsy data Variable Base Trt Base ? Trt Age V4 or V/10 ? 0 ? 1 ? 2 Model (5. 1) PQL 0. 87  ± 0. 14 ? 0. 91  ± 0. 41 0. 33  ± 0. 21 0. 47  ± 0. 36 ? 0. 16  ± 0. 05 — 0. 53  ± 0. 06 — INLA 0. 88  ± 0. 15 ? 0. 94  ± 0. 44 0. 34  ± 0. 22 0. 47  ± 0. 38 ? 0. 16  ± 0. 05 — 0. 56  ± 0. 08 — Model (5. 2) PQL 0. 86  ± 0. 13 ? 0. 93  ± 0. 40 0. 34  ± 0. 21 0. 47  ± 0. 35 ? 0. 10  ± 0. 09 0. 36  ± 0. 04 0. 48  ± 0. 06 — INLA 0. 8  ± 0. 15 ? 0. 96  ± 0. 44 0. 35  ± 0. 23 0. 48  ± 0. 39 ? 0. 10  ± 0. 09 0. 41  ± 0. 04 0. 53  ± 0. 07 — Model (5. 3) PQL 0. 87  ± 0. 14 ? 0. 91  ± 0. 41 0. 33  ± 0. 21 0. 46  ± 0. 36 ? 0. 26  ± 0. 16 — 0. 52  ± 0. 06 0. 74  ± 0. 16 INLA 0. 88  ± 0. 14 ? 0. 94  ± 0. 44 0. 34  ± 0. 22 0. 47  ± 0. 38 ? 0. 27  ± 0. 16 — 0. 56  ± 0. 06 0. 70  ± 0. 14 Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 visit, b2i with b1i b2i ? N (0, Q ? 1 ). (5. 4) We assume Q ? Wishart(r, S ) with S = S11 S12 . For prior specification, we begin with the bivariate S21 S22 model and assume that S is diagonal. We assume the upper 95% point of the priors for exp(b1i ) and exp(b2i ) are 5 and 4, respectively, and that the marginal distributions are t with 4 degrees of freedom. Following the procedure outlined in Section 4. 2, we obtain r = 5 and S = diag(0. 439, 0. 591). We take ? 2 the prior for ? 1 in model (5. 1) to be Ga(a1 , a2 ) with a1 = (r ? 1)/2 = 2 and a2 = 1/2S11 = 1. 140 (so that this prior coincides with the marginal prior obtained from the bivariate specification). In model (5. 2), ? 2 ? 2 we assume b1i and b0i j are independent, and that ? 0 follows the same prior as ? , that is, Ga(2, 1. 140). We assume a flat prior on the intercept, and assume that the rate ratios, exp(? j ), j = 1, . . . , 5, lie between 0. 1 and 10 with probability 0. 95 which gives, using the approach described in Section 4. 1, a normal prior with mean 0 and variance 1. 172 . Table 1 gives PQL and INLA summaries for models (5. 1–5. 3). There are some differences between the PQL and Bayesian analyse s, with slightly larger standard deviations under the latter, which probably reflects that with m = 59 clusters, a little accuracy is lost when using asymptotic inference. There are some differences in the point estimates which is at least partly due to the nonflat priors used—the priors have relatively large variances, but here the data are not so abundant so there is sensitivity to the prior. Reassuringly under all 3 models inference for the baseline-treatment interaction of interest is virtually y identical and suggests no significant treatment effect. We may compare models using log p(y ): for 3 models, we obtain values of ? 674. 8, ? 638. 9, and ? 665. 5, so that the second model is strongly preferred. 5. Smoothing of birth cohort effects in an age-cohort model We analyze data from Breslow and Day (1975) on breast cancer rates in Iceland. Let Y jk be the number of breast cancer of cases in age group j (20–24,. . . , 80–84) and birth cohort k (1840–1849,. . . ,1940–1949) with j = 1, . . . , J = 13 and k = 1, . . . , K = 11. Following Breslow and Clayton (1993), we assume Y jk |? jk ? ind Poisson(? jk ) with log ? jk = log n jk + ? j + ? k + vk + u k (5. 5) and where n jk is the person-years denominator, exp(? j ), j = 1, . . . , J , represent fixed effects for age relative risks, exp(? is the relative risk associated with a one group increase in cohort group, vk ? iid 406 Y. F ONG AND OTHERS 2 N (0, ? v ) represent unstructured random effects associated with cohort k, with smooth cohort terms u k following a second-order random-effects model with E[u k |{u i : i k}] = 2u k? 1 ? u k? 2 and Var(u k |{u i : 2 i k}) = ? u . This latter model is to allow the rates to vary smoothly with cohort. An equivalent representation of this model is, for 2 k K ? 1, 1 E[u k |{u l : l = k}] = (4u k? 1 + 4u k+1 ? u k? 2 ? u k+2 ), 6 Var(u k |{u l : l = k}) = 2 ? . 6 Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 The rank of Q in the (4. 1) representation of this model is K ? 2 reflecting that both the overall level and the overall trend are aliase d (hence the appearance of ? in (5. 5)). The term exp(vk ) reflects the unstructured residual relative risk and, following the argument in Section 4. 2, we specify that this quantity should lie in [0. 5, 2. 0] with probability 0. 95, with a marginal log Cauchy ? 2 distribution, to obtain the gamma prior ? v ? Ga(0. 5, 0. 00149). The term exp(u k ) reflects the smooth component of the residual relative risk, and the specification of a 2 prior for the associated variance component ? u is more difficult, given its conditional interpretation. Using the algorithm described in Section 4. 2, we examined simulations of u for different choices of gamma ? 2 hyperparameters and decided on the choice ? u ? Ga(0. 5, 0. 001); Figure 2 shows 10 realizations from the prior. The rationale here is to examine realizations to see if they conform to our prior expectations and in particular exhibit the required amount of smoothing. All but one of the realizations vary smoothly across the 11 cohorts, as is desirable. Due to the tail of the gamma distribution, we will always have some extreme realizations. The INLA results, summarized in graphical form, are presented in Figure 2(b), alongside likelihood fits in which the birth cohort effect is incorporated as a linear term and as a factor. We see that the smoothing model provides a smooth fit in birth cohort, as we would hope. 5. 3 B-Spline nonparametric regression We demonstrate the use of INLA for nonparametric smoothing using O’Sullivan splines, which are based on a B-spline basis. We illustrate using data from Bachrach and others (1999) that concerns longitudinal measurements of spinal bone mineral density (SBMD) on 230 female subjects aged between 8 and 27, and of 1 of 4 ethnic groups: Asian, Black, Hispanic, and White. Let yi j denote the SBMD measure for subject i at occasion j, for i = 1, . . . , 230 and j = 1, . . . , n i with n i being between 1 and 4. Figure 3 shows these data, with the gray lines indicating measurements on the same woman. We assume the model K Yi j = x i ? 1 + agei j ? 2 + k=1 z i jk b1k + b2i + ij, where x i is a 1 ? vector containing an indicator for the ethnicity of individual i, with ? 1 the associated 4 ? 1 vector of fixed effects, z i jk is the kth basis associated with age, with associated parameter b1k ? 2 2 N (0, ? 1 ), and b2i ? N (0, ? 2 ) are woman-specific random effects, finally, i j ? iid N (0, ? 2 ). All random terms are assumed independent. Note that the spline model is assumed common to all ethnic groups and all women , though it would be straightforward to allow a different spline for each ethnicity. Writing this model in the form y = x ? + z 1b1 + z 2b 2 + = C ? + . Bayesian GLMMs 407 Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 Fig. 2. (a) Ten realizations (on the relative risk scale) from the random effects second-order random walk model in which the prior on the random-effects precision is Ga(0. 5,0. 001), (b) summaries of fitted models: the solid line corresponds to a log-linear model in birth cohort, the circles to birth cohort as a factor, and â€Å"+† to the Bayesian smoothing model. we use the method described in Section 4. 3 to examine the effective number of parameters implied by the ? 2 ? 2 priors ? 1 ? Ga(a1 , a2 ) and ? 2 ? Ga(a3 , a4 ). To fit the model, we first use the R code provided in Wand and Ormerod (2008) to construct the basis functions, which are then input to the INLA program. Running the REML version of the model, we obtain 2 ? = 0. 033 which we use to evaluate the effective degrees of freedoms associated with priors for ? 1 and 2 . We assume the usual improper prior, ? (? 2 ) ? 1/? 2 for ? 2 . After some experimentation, we settled ? 2 408 Y. F ONG AND OTHERS Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 Fig. 3. SBMD versus age by ethnicity. Measurements on the same woman are joined with gray lines. The solid curve corresponds to the fitted spline and the dashed lines to the individual fits. ?2 2 on the prior ? 1 ? Ga(0. 5, 5 ? 10? 6 ). For ? 2 , we wished to have a 90% interval for b2i of  ±0. 3 which, ? 2 with 1 degree of freedom for the marginal distribution, leads to ? 2 ? Ga(0. 5, 0. 00113). Figure 4 shows the priors for ? 1 and ? 2 , along with the implied effective degrees of freedom under the assumed priors. For the spline component, the 90% prior interval for the effective degrees of freedom is [2. 4,10]. Table 2 compares estimates from REML and INLA implementations of the model, and we see close correspondence between the 2. Figure 4 also shows the posterior medians for ? 1 and ? 2 and for the 2 effective degrees of freedom. For the spline and random effects these correspond to 8 and 214, respectively. The latter figure shows that there is considerable variability between the 230 women here. This is confirmed in Figure 3 where we observe large vertical differences between the profiles. This figure also shows the fitted spline, which appears to mimic the trend in the data well. 5. 4 Timings For the 3 models in the longitudinal data example, INLA takes 1 to 2 s to run, using a single CPU. To get estimates with similar precision with MCMC, we ran JAGS for 100 000 iterations, which took 4 to 6 min. For the model in the temporal smoothing example, INLA takes 45 s to run, using 1 CPU. Part of the INLA procedure can be executed in a parallel manner. If there are 2 CPUs available, as is the case with today’s prevalent INTEL Core 2 Duo processors, INLA only takes 27 s to run. It is not currently possible to implement this model in JAGS. We ran the MCMC utility built into the INLA software for 3. 6 million iterations, to obtain estimates of comparable accuracy, which took 15 h. For the model in the B-spline nonparametric regression example, INLA took 5 s to run, using a single CPU. We ran the MCMC utility built into the INLA software for 2. 5 million iterations to obtain estimates of comparable accuracy, the analysis taking 40 h. Bayesian GLMMs 409 Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 Fig. 4. Prior summaries: (a) ? 1 , the standard deviation of the spline coefficients, (b) effective degrees of freedom associated with the prior for the spline coefficients, (c) effective degrees of freedom versus ? , (d) ? 2 , the standard deviation of the between-individual random effects, (e) effective degrees of freedom associated with the individual random effects, and (f) effective degrees of freedom versus ? 2 . The vertical dashed lines on panels (a), (b), (d), and (e) correspond to the posterior medians. Table 2. REML and INLA summaries for spinal bone data. Intercept corresponds to Asian group Vari able Intercept Black Hispanic White Age ? 1 ? 2 ? REML 0. 560  ± 0. 029 0. 106  ± 0. 021 0. 013  ± 0. 022 0. 026  ± 0. 022 0. 021  ± 0. 002 0. 018 0. 109 0. 033 INLA 0. 563  ± 0. 031 0. 106  ± 0. 021 0. 13  ± 0. 022 0. 026  ± 0. 022 0. 021  ± 0. 002 0. 024  ± 0. 006 0. 109  ± 0. 006 0. 033  ± 0. 002 Note: For the entries marked with a standard errors were unavailable. 410 Y. F ONG AND OTHERS 6. D ISCUSSION In this paper, we have demonstrated the use of the INLA computational method for GLMMs. We have found that the approximation strategy employed by INLA is accurate in general, but less accurate for binomial data with small denominators. The supplementary material available at Biostatistics online contains an extensive simulation study, replicating that presented in Breslow and Clayton (1993). There are some suggestions in the discussion of Rue and others (2009) on how to construct an improved Gaussian approximation that does not use the mode and the curvature at the mode. It is likely that these suggestions will improve the results for binomial data with small denominators. There is an urgent need for diagnosis tools to flag when INLA is inaccurate. Conceptually, computation for nonlinear mixed effects models (Davidian and Giltinan, 1995; Pinheiro and Bates, 2000) can also be handled by INLA but this capability is not currently available. The website www. r-inla. rg contains all the data and R scripts to perform the analyses and simulations reported in the paper. The latest release of software to implement INLA can also be found at this site. Recently, Breslow (2005) revisited PQL and concluded that, â€Å"PQL still performs remarkably well in comparison with more elaborate procedures in many practical situations. † We believe that INLA provides an attractive alter native to PQL for GLMMs, and we hope that this paper stimulates the greater use of Bayesian methods for this class. Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 S UPPLEMENTARY MATERIAL Supplementary material is available at http://biostatistics. oxfordjournals. org. ACKNOWLEDGMENT Conflict of Interest: None declared. F UNDING National Institutes of Health (R01 CA095994) to J. W. Statistics for Innovation (sfi. nr. no) to H. R. R EFERENCES BACHRACH , L. K. , H ASTIE , T. , WANG , M. C. , NARASIMHAN , B. AND M ARCUS , R. (1999). Bone mineral acquisition in healthy Asian, Hispanic, Black and Caucasian youth. A longitudinal study. The Journal of Clinical Endocrinology and Metabolism 84, 4702–4712. B ESAG , J. , G REEN , P. J. , H IGDON , D. AND M ENGERSEN , K. 1995). Bayesian computation and stochastic systems (with discussion). Statistical Science 10, 3–66. B RESLOW, N. E. (2005). Whither PQL? In: Lin, D. and Heagerty, P. J. (editors), Proceedings of the Second Seattle Symposium. New York: Springer, pp. 1–22. B RESLOW, N. E. AND C LAYTON , D. G. (1993). Approximate inference in generalized linear mixed models. Journal of th e American Statistical Association 88, 9–25. B RESLOW, N. E. AND DAY, N. E. (1975). Indirect standardization and multiplicative models for rates, with reference to the age adjustment of cancer incidence and relative frequency data. Journal of Chronic Diseases 28, 289–301. C LAYTON , D. G. (1996). Generalized linear mixed models. In: Gilks, W. R. , Richardson, S. and Spiegelhalter, D. J. (editors), Markov Chain Monte Carlo in Practice. London: Chapman and Hall, pp. 275–301. Bayesian GLMMs 411 C RAINICEANU , C. M. , D IGGLE , P. J. AND ROWLINGSON , B. (2008). Bayesian analysis for penalized spline regression using winBUGS. Journal of the American Statistical Association 102, 21–37. C RAINICEANU , C. M. , RUPPERT, D. AND WAND , M. P. (2005). Bayesian analysis for penalized spline regression using winBUGS. Journal of Statistical Software 14. DAVIDIAN , M. AND G ILTINAN , D. M. (1995). Nonlinear Models for Repeated Measurement Data. London: Chapman and Hall. D I C ICCIO , T. J. , K ASS , R. E. , R AFTERY, A. AND WASSERMAN , L. (1997). Computing Bayes factors by combining simulation and asymptotic approximations. Journal of the American Statistical Association 92, 903–915. Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 D IGGLE , P. , H EAGERTY, P. , L IANG , K. -Y. Oxford: Oxford University Press. AND Z EGER , S. (2002). Analysis of Longitudinal Data, 2nd edition. FAHRMEIR , L. , K NEIB , T. AND L ANG , S. (2004). Penalized structured additive regression for space-time data: a Bayesian perspective. Statistica Sinica 14, 715–745. G AMERMAN , D. (1997). Sampling from the posterior distribution in generalized linear mixed models. Statistics and Computing 7, 57–68. G ELMAN , A. (2006). Prior distributions for variance parameters in hierarchical models. Bayesian Analysis 1, 515–534. H ASTIE , T. J. AND T IBSHIRANI , R. J. (1990). Generalized Additive Models. London: Chapman and Hall. H OBERT, J. P. AND C ASELLA , G. (1996). The effect of improper priors on Gibbs sampling in hierarchical linear mixed models. Journal of the American Statistical Association 91, 1461–1473. K ASS , R. E. AND S TEFFEY, D. (1989). Approximate Bayesian inference in conditionally independent hierarchical models (parametric empirical Bayes models). Journal of the American Statistical Association 84, 717–726. K ELSALL , J. E. AND WAKEFIELD , J. C. (1999). Discussion of â€Å"Bayesian models for spatially correlated disease and exposure data† by N. Best, I. Waller, A. Thomas, E. Conlon and R. Arnold. In: Bernardo, J. M. , Berger, J. O. , Dawid, A. P. and Smith, A. F. M. (editors), Sixth Valencia International Meeting on Bayesian Statistics. London: Oxford University Press. M C C ULLAGH , P. AND N ELDER , J. A. (1989). Generalized Linear Models, 2nd edition. London: Chapman and Hall. M C C ULLOCH , C. E. , S EARLE , S. R. AND N EUHAUS , J. M. (2008). Generalized, Linear, and Mixed Models, 2nd edition. New York: John Wiley and Sons. M ENG , X. AND W ONG , W. (1996). Simulating ratios of normalizing constants via a simple identity. Statistical Sinica 6, 831–860. NATARAJAN , R. AND K ASS , R. E. (2000). Reference Bayesian methods for generalized linear mixed models. Journal of the American Statistical Association 95, 227–237. N ELDER , J. AND W EDDERBURN , R. (1972). Generalized linear models. Journal of the Royal Statistical Society, Series A 135, 370–384. P INHEIRO , J. C. AND BATES , D. M. (2000). Mixed-Effects Models in S and S-plus. New York: Springer. P LUMMER , M. (2008). Penalized loss functions for Bayesian model comparison. Biostatistics 9, 523–539. P LUMMER , M. (2009). Jags version 1. 0. 3 manual. Technical Report. RUE , H. AND H ELD , L. (2005). Gaussian Markov Random Fields: Thoery and Application. Boca Raton: Chapman and Hall/CRC. RUE , H. , M ARTINO , S. AND C HOPIN , N. (2009). Approximate Bayesian inference for latent Gaussian models using integrated nested laplace approximations (with discussion). Journal of the Royal Statistical Society, Series B 71, 319–392. 412 RUPPERT, D. R. , WAND , M. P. University Press. AND Y. F ONG AND OTHERS C ARROLL , R. J. (2003). Semiparametric Regression. New York: Cambridge S KENE , A. M. AND WAKEFIELD , J. C. (1990). Hierarchical models for multi-centre binary response studies. Statistics in Medicine 9, 919–929. S PIEGELHALTER , D. , B EST, N. , C ARLIN , B. AND VAN DER L INDE , A. (1998). Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society, Series B 64, 583–639. S PIEGELHALTER , D. J. , T HOMAS , A. AND B EST, N. G. (1998). WinBUGS User Manual. Version 1. 1. 1. Cambridge. T HALL , P. F. AND VAIL , S. C. (1990). Some covariance models for longitudinal count data with overdispersion. Biometrics 46, 657–671. V ERBEKE , G. V ERBEKE , G. AND AND Downloaded from http://biostatistics. oxfordjournals. org/ at Cornell University Library on April 20, 2013 M OLENBERGHS , G. (2000). Linear Mixed Models for Longitudinal Data. New York: Springer. M OLENBERGHS , G. (2005). Models for Discrete Longitudinal Data. New York: Springer. WAKEFIELD , J. C. (2007). Disease mapping and spatial regression with count data. Biostatistics 8, 158–183. WAKEFIELD , J. C. (2009). Multi-level modelling, the ecologic fallacy, and hybrid study designs. International Journal of Epidemiology 38, 330–336. WAND , M. P. AND O RMEROD , J. T. (2008). On semiparametric regression with O’Sullivan penalised splines. Australian and New Zealand Journal of Statistics 50, 179–198. Z EGER , S. L. AND K ARIM , M. R. (1991). Generalized linear models with random effects: a Gibbs sampling approach. Journal of the American Statistical Association 86, 79–86. [Received September 4, 2009; revised November 4, 2009; accepted for publication November 6, 2009] How to cite Bayesian Inference, Papers

Three Reasons Browsers Difficult To Secure â€Myassignmenthelp.Com

Question: Discuss About The Three Reasons Browsers Difficult To Secure? Answer: Introduction Today everyone knows about the web browser and its usage. To use web browser no need to do so much by a user. After installing web browser through its executable file, an icon appears on the screen and by clicking on that icon browser will open and user can use that accordingly. While using web browsers, a user has to face some security related issues that are critical enough to control. In next segment of report, I will discuss main challenges, problems, appropriate technologies to resolve issues and unclear areas of web browser attacks. Discussion The very popular web browsers are Mozilla Firefox, Internet Explorer, Google Chrome, Opera and Safari. These all browsers have to encounter problem of web attacks and these attacks are conducted by using social engineering, cross-site scripting and client-side exploits. Due to these attacks of web browsers, following challenges have to face by users. Challenges of Web Browser Attacks According to analysis, it is found that near about 45% of people those are surfing internet are not using most secure version of web browser and facing following challenges. The first challenge is of security patches applied to web browsers. If a web browser is not equipped with appropriate security patches than web browsers can result in vulnerable attacks. Moreover, security patches cannot work without proper patching of browser plug-ins (Zeltser.com, 2017). Another challenging factor is poor coding of web applications and vulnerabilities that are found in software solutions connected with web browsers. These weak factors of web browsers are necessary to overcome at developers end because hackers are taking advantage from these weak factors. Therefore, these above discussed challenges of web browsers attacks are required to control by developers by using advanced techniques at priority basis. Otherwise, issues of data lost and virus attacks will be increased. Problems of Web Browsers Attacks Due to above challenging factors of web browser attacks, various problems have raised for people who use web browsers that are listed as below: The first problem is that due to lack of security on web browsers, hackers can easily hack them and can access information about saved login, cookies, cache and visited websites. Another problem is of addition of harmful programming scripts into browsers by hackers. These scripts are vulnerable enough and redirect the users automatically to unknown websites without any knowledge of users (Shema, 2012). Those websites may have some malicious programs that can enter into computers system of user and can cause damage. Another problem is related to alteration of web browsers by malicious attacks from hackers side. These alternations lead to weird activities of web browsers that users are unable to understand (Lifewire, 2017). Relevant Technologies Web browsers can be protected from vulnerabilities by using appropriate technologies. Following are some relevant technologies that can be used to manage web browser attacks: The configuration of web browser should be done properly. While configuring browser, it is necessary to follow-up every instruction and security patches and plug-ins should also be installed properly. These plug-ins are helpful to protect web browsers from unknown entities (Us-cert.gov, 2017) Another relevant technology is to update browser regularly and also install third party solutions like ad-blocker to restrict harmful online advertisements to enter into the system. The advertisements so much injurious for system that these can slow down the system and can corrupt its boot files. Ad blockers are useful enough to stop these types of advertisements and other unknown entities. Web browsers have security and privacy options and with the help of these options web browsers can become more secure. For example, by hiding saved login passwords, by clearing caches and cookies that are not required at regular basis and by clicking checkbox options those are related to privacy of web browser content and its display. Application of Relevant Technologies The application area of these technologies is wide enough and these can be used to protect different versions of web browsers. Most of the web browser developers are using these relevant technologies to protect their browsers from unknown vulnerabilities (Howtogeek.com, 2017). Unclear Areas of Web Browser Attacks Web browser attacks are common among people but there are some vague areas about which people must have knowledge. The first thing that is not yet cleared about web browser attacks is that why programming languages are not so strong to restrict vulnerable browser attacks. At developers end this thing must be cleared that how programming languages can be more protective and strong to stop hackers to mischief web browser. Moreover, an appropriate solution for protect web browsers from hackers is also not properly found yet (Thorpe, 2017). Research Questions While analyzing problem of web browser attacks, some common research questions are found that are required to discuss here in this report. Question 1: What is the best way to get prevention from Web Browser Attacks? Answer: The most appropriate way to get prevention from web browser attacks is its periodical updates. Regular updates provides strength to browser to cope up with vulnerable objects (Computing Browser, 2017). Question 2: What is the main reason of Web Browser Attack? Answer: The entrance of any third party application or any other entity into web browser without knowledge but with permission of users, is the main reason of web browser attacks (Its.ucsc.edu, 2017). Described Issues in the Forum To know about the main issues of Web browser attacks I have selected a forum and according to that forum the main issues of web browser attacks are violation of security of users information such as cookies and login information, entrance of virus into system through web browser and slow performance of web browser as well as computer system. These issues put bad impact on users activities that they perform by using web browsers. This available information in forum is accurate and users of web browsers must have knowledge about these issues and must use appropriate security techniques to resolve these problems (SearchMidmarketSecurity, 2017). Issue that is addressed the in Forum All the mentioned issues in selected forum about web browser attacks are relevant. But another issue that is not addressed in this forum is that downloading content from different websites by using web browsers can also be harmful for users if it will not be scanned properly before downloading into system (Adams, 2017). This content may have some attached virus entities that enters into web browser easily and also try to corrupt the main files of browser. Due to this, browser does not work properly and also becomes slower than its normal speed. This issue is important to discuss here because nowadays, downloading rate of movies, audio and other content have become so higher and people do not care while downloading content and click on links that are harmful (Happyhamstercomputers.com, 2017). Impact of Issues of Real World The above discussed issues and challenges of web browser attacks have bad impacts on users of web browsers. This is because due to these attacks their computer systems, its content and web browser related information are at high risk. From the first day after installation, it has become essential for them to protect their web browsers by using secure software solutions that are especially made to get prevention from web browser attacks. If these software solutions will not be used then overall problem of web browser attacks can get worse. At developers end, due to improper management of security and privacy of web browsers, hackers are trying to get into browsers to violate them (Searchsecurity.techtarget.com, 2017). Most important Lesson Learnt from Discussions First of all I got to know that security and privacy of web browser is mandatory to maintain at users and as well as developers end. Moreover, users must not allow any unknown entity to enter into system through browser and to do this, appropriate third party software solutions should be used. On other side, while developing web browsers, developers must use secure programming languages and all security patches and plugins should be configured properly (Google, 2017). Conclusion In conclusion, it is right to say that without web browsers it is difficult to access data from different websites and to explore other internet sources. But security should be maintained at priority basis and everyone should have knowledge about possible challenges and risk factors of using web browsers and how these can be overcome by using security tools. References Securing Your Web Browser. (2017). Us-cert.gov. Retrieved 28 September 2017, from https://www.us-cert.gov/publications/securing-your-web-browser How to avoid attacks that exploit a Web browser vulnerability. (2017). SearchMidmarketSecurity. Retrieved 28 September 2017, from https://searchmidmarketsecurity.techtarget.com/tip/How-to-avoid-attacks-that-exploit-a-Web-browser-vulnerability Three Web Attack Vectors Using the Browser. (2017). Zeltser.com. Retrieved 28 September 2017, from https://zeltser.com/web-browser-attack-vectors/ Computing, H., Browser, W. (2017). What is a Web Browser?. WhatIsMyIPAddress.com. Retrieved 28 September 2017, from https://whatismyipaddress.com/web-browser Thorpe, E. (2017). Three reasons why browsers are so difficult to secure. IT PRO. Retrieved 28 September 2017, from https://www.itpro.co.uk/security/29077/three-reasons-why-browsers-are-so-difficult-to-secure Do You Know What a Web Browser Actually Is?. (2017). Lifewire. Retrieved 28 September 2017, from https://www.lifewire.com/what-is-a-browser-446234 7 Ways to Secure Your Web Browser Against Attacks. (2017). Howtogeek.com. Retrieved 28 September 2017, from https://www.howtogeek.com/228828/7-ways-to-secure-your-web-browser-against-attacks/ Web browser security news, help and research - SearchSecurity. (2017). Searchsecurity.techtarget.com. Retrieved 28 September 2017, from https://searchsecurity.techtarget.com/resources/Web-Browser-Security Google, i. (2017). 20 Things I Learned About Browsers and the Web. 20thingsilearned.com. Retrieved 28 September 2017, from https://www.20thingsilearned.com/en-GB/all/print Shema, M. (2012). Hacking web apps. Amsterdam [u.a.]: Elsevier/Syngress. Web Browser Secure Settings. (2017). Its.ucsc.edu. Retrieved 28 September 2017, from https://its.ucsc.edu/software/release/browser-secure.html Adams, D. (2017). 11 steps to reduce the risk of web attacks - Patriot Technologies, Inc.. Patriot Technologies, Inc.. Retrieved 28 September 2017, from https://patriot-tech.com/blog/2011/02/04/11-steps-to-reduce-the-risk-of-web-attacks/ Understanding Web Browser Attacks | Get Certified Get Ahead. (2017). Get Certified Get Ahead. Retrieved 28 September 2017, from https://blogs.getcertifiedgetahead.com/understanding-web-browser-attacks/ The 2 Main Types of Web Browser Attacks | Happy Hamster Computers. (2017). Happyhamstercomputers.com. Retrieved 28 September 2017, from https://happyhamstercomputers.com/computer-repair-tips/the-2-main-types-of-web-browser-atta