DNA methylation is a defining feature of mammalian cellular identity and essential for normal development 1,2 . Most cell types, except germ cells and pre-implantation embryos 3–5 , display relatively stable DNA methylation patterns with 70–80% of all CpGs being methylated 6 . Despite recent advances we still have a too limited understanding of when, where and how many CpGs participate in genomic regulation. Here we report the in depth analysis of 42 whole genome bisulfite sequencing (WGBS) data sets across 30 diverse human cell and tissue types. We observe dynamic regulation for only 21.8% of autosomal CpGs within a normal developmental context, a majority of which are distal to transcription start sites. These dynamic CpGs co-localize with gene regulatory elements, particularly enhancers and transcription factor binding sites (TFBS), which allow identification of key lineage specific regulators. In addition, differentially methylated

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Charting a dynamic DNA methylation landscape of the human genome

List of Figures. List of Tables. Preface. Acknowledgments. Introduction. Part I: Introducing Bayesian Analysis. 1. The foundations of Bayesian inference. 1.1 What is probability? 1.2 Subjective probability in Bayesian statistics. 1.3 Bayes theorem, discrete case. 1.4 Bayes theorem, continuous parameter. 1.5 Parameters as random variables, beliefs as distributions. 1.6 Communicating the results of a Bayesian analysis. 1.7 Asymptotic properties of posterior distributions. 1.8 Bayesian hypothesis testing. 1.9 From subjective beliefs to parameters and models. 1.10 Historical note. 2. Getting started: Bayesian analysis for simple models. 2.1 Learning about probabilities, rates and proportions. 2.2 Associations between binary variables. 2.3 Learning from counts. 2.4 Learning about a normal mean and variance. 2.5 Regression models. 2.6 Further reading. Part II: Simulation Based Bayesian Analysis. 3. Monte Carlo methods. 3.1 Simulation consistency. 3.2 Inference for functions of parameters. 3.3 Marginalization via Monte Carlo integration. 3.4 Sampling algorithms. 3.5 Further reading. 4. Markov chains. 4.1 Notation and definitions. 4.2 Properties of Markov chains. 4.3 Convergence of Markov chains. 4.4 Limit theorems for Markov chains. 4.5 Further reading. 5. Markov chain Monte Carlo. 5.1 Metropolis-Hastings algorithm. 5.2 Gibbs sampling. 6. Implementing Markov chain Monte Carlo. 6.1 Software for Markov chain Monte Carlo. 6.2 Assessing convergence and run-length. 6.3 Working with BUGS/JAGS from R. 6.4 Tricks of the trade. 6.5 Other examples. 6.6 Further reading. Part III: Advanced Applications in the Social Sciences. 7. Hierarchical Statistical Models. 7.1 Data and parameters that vary by groups: the case for hierarchical modeling. 7.2 ANOVA as a hierarchical model. 7.3 Hierarchical models for longitudinal data. 7.4 Hierarchical models for non-normal data. 7.5 Multi-level models. 8. Bayesian analysis of choice making. 8.1 Regression models for binary responses. 8.2 Ordered outcomes. 8.3 Multinomial outcomes. 8.4 Multinomial probit. 9. Bayesian approaches to measurement. 9.1 Bayesian inference for latent states. 9.2 Factor analysis. 9.3 Item-response models. 9.4 Dynamic measurement models. Part IV: Appendices. Appendix A: Working with vectors and matrices. Appendix B: Probability review. B.1 Foundations of probability. B.2 Probability densities and mass functions. B.3 Convergence of sequences of random variabales. Appendix C: Proofs of selected propositions. C.1 Products of normal densities. C.2 Conjugate analysis of normal data. C.3 Asymptotic normality of the posterior density. References. Topic index. Author index.

Bayesian Analysis for the Social Sciences

In this article, we propose two asymmetry measures for stock returns. Unlike the popular skewness measure, our measures are based on the distribution function of the data rather than just the third central moment. We present empirical evidence that the greater upside asymmetries calculated using our new measures imply lower average returns in the cross section of stocks. In contrast, when using the skewness measure, the relationship between asymmetry and returns is inconclusive.

Stock Return Asymmetry: Beyond Skewness

The general beta distribution in 4 parameters, denoted gbeta (α, β; c, d), defined on the interval (c,d) is one of the most useful distributions in statistical applications and in related fields such as Operations Research and Management Science. We give here the exact expressions of the densities of X1X2 and of X1/X2, where X1 and X2 are independent general beta variables, and discuss the relationships between the new results with those already obtained. Applications in Reliability and Bayesian Quality Control are given. A computer program, developed for hypergeometric functions in general, can be used to carry out the precise computation of these densities.

The product and quotient of general beta distributions

We derive the exact expression of the density of the linear combination of two independent general beta variables Applications to some statistical problems are presented and a classification of the various forms of the generalized beta available in the literature is also given

Distribution of the linear combination of two general beta variables and applications

In this article we give the expression of the prior distribution of p1-P2, where P1 and P2 and independent proportions with a beta prior each. The expression derived for the posterior distribution of P1-P2 then shows the closure of the beta-difference family for independent dual Bernoulli samples. Other bayesian results are also presented.

Bayesian analysis of the difference of two proportions

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Bayesian analysis of the difference of two proportions