Bayesian Analysis for the Social Sciences

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.

[1]  Byron Hall.  Bayesian Inference , 2011 .

[2]  I. Grattan-Guinness.  Laplace, Pierre Simon , 2006 .

[3]  K. Fraser.  The Almanac of American Politics 2004 , 2005 .

[4]  Exchangeability and de Finetti’s theorem: from probabilities to quantum‐mechanical states , 2004 .

[5]  P. Diaconis.  Finite forms of de Finetti's theorem on exchangeability , 1977, Synthese.

[6]  Marc Yor.  Weighing the odds: a course in probability and statistics , 2003 .

[7]  S. James Press,et al.  Subjective and Objective Bayesian Statistics , 2002 .

[8]  T. Pham-Gia,et al.  The product and quotient of general beta distributions , 2002 .

[9]  Jeff Gill,et al.  What are Bayesian Methods , 2008 .

[10]  David S. Williams.  Weighing the odds : a course in probability and statistics , 2001 .

[11]  I. Hacking.  An Introduction to Probability and Inductive Logic , 2001 .

[12]  Vic Barnett,et al.  Comparative Statistical Inference , 1974, Technometrics.

[13]  Arto Luoma.  Thomas Bayes , 1999, The Lancet.

[14]  S. Golombok,et al.  Do Parents Influence the Sexual Orientation of Their Children? Findings from a Longitudinal Study of Lesbian Families. , 1996 .

[15]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[16]  N. Turkkan,et al.  Bayesian analysis of the difference of two proportions , 1993 .

[17]  C. Howson,et al.  Scientific Reasoning: The Bayesian Approach , 1989 .

[18]  G. Wood.  Binomial Mixtures and Finite Exchangeability , 1992 .

[19]  B. D. Finetti,et al.  Foresight: Its Logical Laws, Its Subjective Sources , 1992 .

[20]  Steffen L. Lauritzen,et al.  Finite de Finetti theorems in linear models and multivariate analysis , 1992 .

[21]  T. Bayes.  An essay towards solving a problem in the doctrine of chances , 2003 .

[22]  B. M. Hill,et al.  Theory of Probability , 1990 .

[23]  B. Geddes.  How the Cases You Choose Affect the Answers You Get: Selection Bias in Comparative Politics , 1990, Political Analysis.

[24]  Sandy L. Zabell,et al.  The rule of succession , 1989 .

[25]  L. Joseph,et al.  Bayesian Statistics: An Introduction , 1989 .

[26]  S. Zabell.  R. A. Fisher on the history of inverse probability , 1989 .

[27]  C. Howson,et al.  Scientific Reasoning: The Bayesian Approach , 1989 .

[28]  I. J. Good,et al.  The Interface Between Statistics and the Philosophy of Science , 1989 .

[29]  L. Daston.  Classical Probability in the Enlightenment , 1988 .

[30]  S. Zabell.  Buffon, Price, and Laplace: Scientific attribution in the 18th century , 1988, Archive for History of Exact Sciences.

[31]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[32]  C. N. Morris,et al.  The calculation of posterior distributions by data augmentation , 1987 .

[33]  Pertti Mutanen,et al.  Exact Bayesian analysis of two proportions , 1987 .

[34]  Stephen M. Stigler,et al.  The History of Statistics: The Measurement of Uncertainty before 1900 by Stephen M. Stigler (review) , 1986, Technology and Culture.

[35]  S. Stigler.  Laplace's 1774 Memoir on Inverse Probability , 1986 .

[36]  D. Freedman,et al.  On inconsistent Bayes estimates of location , 1986 .

[37]  D. Freedman,et al.  On the consistency of Bayes estimates , 1986 .

[38]  A. F. Smith.  Present Position and Potential Developments: Some Personal Views Bayesian Statistics , 1984 .

[39]  J. Durbin,et al.  Present position and potential developments: some personal views: time series analysis , 1984 .

[40]  M. R. Novick,et al.  The Role of Exchangeability in Inference , 1981 .

[41]  Charalambos D. Aliprantis,et al.  Principles of Real Analysis , 1981 .

[42]  D. Freedman,et al.  Finite Exchangeable Sequences , 1980 .

[43]  David A. Freedman,et al.  De Finetti's generalizations of exchangeability , 1980 .

[44]  P. Diaconis,et al.  Conjugate Priors for Exponential Families , 1979 .

[45]  T. Skocpol,et al.  States and social revolutions : a comparative analysis of France, Russia, and China , 1979 .

[46]  A. Agresti,et al.  Statistical Methods for the Social Sciences , 1979 .

[47]  Edward E. Leamer,et al.  Specification Searches: Ad Hoc Inference with Nonexperimental Data , 1980 .

[48]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[49]  David Heath,et al.  De Finetti's Theorem on Exchangeable Variables , 1976 .

[50]  D. Lindley,et al.  Inference for a Bernoulli Process (a Bayesian View) , 1976 .

[51]  T. Fine,et al.  The Emergence of Probability , 1976 .

[52]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[53]  Herbert I. Weisberg,et al.  Bayesian Comparison of Two Ordered Multinomial Populations , 1972 .

[54]  Alfréd Rényi,et al.  Probability Theory , 1970 .

[55]  P. M. E. Altham,et al.  Exact Bayesian Analysis of a 2 Times 2 Contingency Table, and Fisher's “Exact” Significance Test , 1969 .

[56]  D. J. Finney,et al.  Introduction to Probability and Statistics , 1968 .

[57]  Geoffrey S. Watson,et al.  A Bayesian Study of the Multinomial Distribution , 1967 .

[58]  David Lindley,et al.  Introduction to Probability and Statistics from a Bayesian Viewpoint , 1966 .

[59]  D. Lindley.  The Bayesian Analysis of Contingency Tables , 1964 .

[60]  M. M. Rao,et al.  Bayes Estimation with Convex Loss , 1963 .

[61]  S. Kullback.  Information Theory and Statistics , 1959 .

[62]  F. N. David,et al.  STUDIES IN THE HISTORY OF PROBABILITY AND STATISTICS: I. DICING AND GAMING (A NOTE ON THE HISTORY OF PROBABILITY) , 1955 .

[63]  L. J. Savage,et al.  Symmetric measures on Cartesian products , 1955 .

[64]  Richard Von Mises,et al.  Probability, statistics and truth , 1939 .

[65]  B. D. Finetti.  La prévision : ses lois logiques, ses sources subjectives , 1937 .

[66]  A. Kolmogoroff.  Grundbegriffe der Wahrscheinlichkeitsrechnung , 1933 .

[67]  B. De Finetti,et al.  Funzione caratteristica di un fenomeno aleatorio , 1929 .

[68]  R. Fisher,et al.  On the Mathematical Foundations of Theoretical Statistics , 1922 .

[69]  P. Laplace.  Essai philosophique sur les probabilités , 1921 .

[70]  John Venn,et al.  The Logic Of Chance , 1888 .