By Andrew Gelman, John B. Carlin, Hal S. Stern, Donald B. Rubin, David B. Dunson, Aki Vehtari
Now in its 3rd version, this vintage publication is extensively thought of the top textual content on Bayesian tools, lauded for its obtainable, functional method of studying facts and fixing study difficulties. Bayesian facts research, 3rd variation keeps to take an utilized method of research utilizing up to date Bayesian tools. The authors—all leaders within the facts community—introduce simple options from a data-analytic point of view ahead of featuring complex equipment. during the textual content, various labored examples drawn from actual purposes and study emphasize using Bayesian inference in practice.
New to the 3rd Edition:
● 4 new chapters on nonparametric modeling
● insurance of weakly informative priors and boundary-avoiding priors
● up-to-date dialogue of cross-validation and predictive details criteria
● more desirable convergence tracking and powerful pattern measurement calculations for iterative simulation
● displays of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation
● New and revised software program code
The publication can be utilized in 3 alternative ways. For undergraduate scholars, it introduces Bayesian inference ranging from first ideas. For graduate scholars, the textual content offers potent present methods to Bayesian modeling and computation in information and similar fields. For researchers, it offers an collection of Bayesian tools in utilized information. extra fabrics, together with information units utilized in the examples, options to chose workouts, and software program directions, can be found at the book’s website.
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Extra info for Bayesian Data Analysis (3rd Edition)
Box and Tiao (1973) is an early book on applied Bayesian methods. They give an extensive treatment of inference based on normal distributions, and their first chapter, a broad introduction to Bayesian inference, provides a good counterpart to Chapters 1 and 2 of this book. 1 is discussed at length in the first chapter of Box and Tiao (1973) and also in Box (1980). Cox and Snell (1981) provide a more introductory treatment of these ideas from a less model-based perspective. Many good books on the mathematical aspects of probability theory are available, such as Feller (1968) and Ross (1983); these are useful when constructing probability models and working with them.
Suppose Judy, a brown-eyed child of brown-eyed parents, marries a heterozygote, and they have n children, all brown-eyed. Find the posterior probability that Judy is a heterozygote and the probability that her first grandchild has blue eyes. 4. Probability assignment: we will use the football dataset to estimate some conditional probabilities about professional football games. There were twelve games with point spreads of 8 points; the outcomes in those games were: −7, −5, −3, −3, 1, 6, 7, 13, 15, 16, 20, and 21, with positive values indicating wins by the favorite and negative values indicating wins by the underdog.
Elvis Presley had a twin brother (who died at birth). What is the probability that Elvis was an identical twin? ) 7. Conditional probability: the following problem is loosely based on the television game show Let’s Make a Deal. At the end of the show, a contestant is asked to choose one of three large boxes, where one box contains a fabulous prize and the other two boxes contain lesser prizes. After the contestant chooses a box, Monty Hall, the host of the show, opens one of the two boxes containing smaller prizes.