In Bayesian inference, uncertainty is expressed in terms of probability. More important, in Bayesian inference, probability is subjective: it is belief. Bayesian inference starts when we formulate a model that we believe is a good...
moreIn Bayesian inference, uncertainty is expressed in terms of probability. More important, in Bayesian inference, probability is subjective: it is belief. Bayesian inference starts when we formulate a model that we believe is a good representation of the situation that holds our interest. We then construct a distribution over the parameters of the model-which are unknown-where that distribution represents our prior beliefs about the situation before we observe data. According to Baye's Law, the posterior distribution for these parameters given the data we have observed is proportional to the product of our prior beliefs and the joint probability of the observed variables, given the parameters. These are the components of Bayesian inference: model, prior beliefs, data, and posterior beliefs. Perhaps no other recent development in modern statistics has attracted more attention than the renaissance in Bayesian methods. Researchers from many fields including political science have turned to Bayesian methods and Bayesian posterior simulation to expand their toolkit and engage new research questions. In support of these goals, a number of texts have been published to aid students and practitioners, and they have enabled the expansion of political science questions to Bayesian methods. Social science monographs, however, are notably scarce. One of the signal contributions of Bayesian Methods: A Social and Behavioral Sciences Approach is to reintroduce Bayesian inference and computing to a general social sciences audience. This is an important contribution-one that will make demand for this book high. Rather than limit this contribution to the reintroduction of Bayesian inference, though, Jeff Gill has gone some way toward reinventing the graduate-level methodology textbook. On the one hand, Bayesian Methods covers all the basics necessary for students and practitioners with moderate statistics training to apply Bayesian methods to traditional regression-type problems. Discussion of the foundations of Bayesian inference, the generalized linear model, and the choice of priors provide a firm foundation for those wanting to expand their research to new methods. Even though other texts review this material in greater detail, Gill expands the material by providing computational guidance for those wishing to estimate these models in R, and exhaustive references for those wishing to reinforce their understanding of the theory presented. Once the reader is comfortable