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This book is intended to be accessible to students with no prior training in econometrics, and only a single course in mathematics e. Stu- dents will find a previous undergraduate course in probability and statistics useful; however Appendix B offers a brief introduction to these topics for those without the prerequisite background. Throughout the book, I have tried to keep the level of mathematical sophistication reasonably low. In contrast to other Bayesian and comparable frequentist textbooks, I have included more computer-related mate- rial.
Modern Bayesian econometrics relies heavily on the computer, and devel- oping some basic programming skills is essential for the applied Bayesian. The required level of computer programming skills is not that high, but I expect that this aspect of Bayesian econometrics might be most unfamiliar to the student xiv Preface brought up in the world of spreadsheets and click-and-press computer packages. Accordingly, in addition to discussing computation in detail in the book itself, the website associated with the book contains MATLAB programs for performing Bayesian analysis in a wide variety of models.
In general, the focus of the book is on application rather than theory. Hence, I expect that the applied economist interested in using Bayesian methods will find it more useful than the theoretical econometrician. In addi- tion, I would like to thank Steve Hardman for his expert editorial advice. Of these, I would like to thank Mark Steel, in particular, for patiently responding to my numerous questions about Bayesian methodology and requests for citations of relevant papers.
Finally, I wish to express my sincere gratitude to Dale Poirier, for his constant support throughout my professional life, from teacher and PhD supervisor, to valued co-author and friend.
This is one of the chief advantages of the Bayesian approach. All of the things that an econometrician would wish to do, such as estimate the parameters of a model, compare different models or obtain predictions from a model, involve the same rules of probability. Bayesian methods are, thus, universal and can be used any time a researcher is interested in using data to learn about a phenomenon. To motivate the simplicity of the Bayesian approach, let us consider two ran- dom variables, A and B.
Alterna- tively, we can reverse the roles of A and B and find an expression for the joint probability of A and B: p. Appendix B provides a brief introduction to probability for the reader who does not have such a background or would like a reminder of this material. However, in economics we typically work with models which depend upon parameters.
For the reader with some previous training in econometrics, it might be useful to have in mind the regression model. In this model interest often centers on the coefficients in the regression, and the researcher is interested in estimating these coefficients.
In this case, the coefficients are the parameters under study. However, Bayesian econometrics is based on a subjective view of probability, which argues that our uncertainty about anything unknown can be expressed using the rules of probability. In this book, we will not discuss such methodological issues see Poirier for more detail.
Rather, we will take it as given that econometrics involves learning about something unknown e. Having established that p. We can then write: p.
At this stage, this may seem a little abstract, and the manner in which priors and likelihoods are developed to allow for the calculation of the posterior may be unclear. Things should become clearer to you in the following chapters, where we will develop likelihood functions and priors in specific contexts. Here we provide only a brief general discussion of what these are.
An Overview of Bayesian Econometrics 3 The prior, p. In many cases, it is reasonable to assume that returns to scale are roughly constant. Prior information is a controversial aspect of Bayesian.
He has published numerous articles in Bayesian econometrics and statistics in journals such as Journal of Econometrics, Journal of the American Statistical Association and the Journal of Business and Economic Statistics. He is an associate editor for several journals, including the Journal of Econometrics and the Journal of Applied Econometrics. Dale J. His professional activities have been numerous, and he has held elected positions in the American Statistical Association and the International Society for Bayesian Analysis.
SGPE: Bayesian Econometrics
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He is interested in building flexible models for large datasets and developing efficient estimation methods. His favorite applications include trend inflation estimation and macroeconomic forecasting. He has co-authored the textbook Statistical Modeling and Computation He received his Ph. His research work in Bayesian econometrics has resulted in numerous publications in top econometrics journals such as the Journal of Econometrics.