A Compendium of Conjugate Priors
نویسنده
چکیده
This report reviews conjugate priors and priors closed under sampling for a variety of data generating processes where the prior distributions are univariate, bivariate, and multivariate. The effects of transformations on conjugate prior relationships are considered and cases where conjugate prior relationships can be applied under transformations are identified. Univariate and bivariate prior relationships are verified using Monte Carlo methods.
منابع مشابه
THE EMPIRICAL BAYES METHOD OF ANALYSIS OF A SERIES OF EXPERIMENTS
The classical method of analysis of a series of experiments is somewhat involved in being conditional on various, occasionally unrealistic, assumptions such as homogeneity of variances of experimental error, lack of interactions of treatments and places,etc. In this work, we adopt a Bayesian view to account for such heterogeneities. Our appoach is illustrated by a real series of experiment...
متن کاملGibbs Sampling, Conjugate Priors and Coupling
We give a large family of simple examples where a sharp analysis of the Gibbs sampler can be proved by coupling. These examples involve standard statistical models – exponential families with conjugate priors or location families with natural priors. Many of them seem difficult to succesfully analyze using spectral or Harris recurrence techniques.
متن کاملBayesian approach to cubic natural exponential families
For a natural exponential family (NEF), one can associate in a natural way two standard families of conjugate priors, one on the natural parameter and the other on the mean parameter. These families of conjugate priors have been used to establish some remarkable properties and characterization results of the quadratic NEF’s. In the present paper, we show that for a NEF, we can associate a class...
متن کاملGero Walter A Technical Note on the Dirichlet - Multinomial Model
This short note contains an explicit proof of the Dirichlet distribution being the conjugate prior to the Multinomial sample distribution as resulting from the general construction method described, e.g., in Bernardo and Smith (2000). The well-known Dirichlet-Multinomial model is thus shown to fit into the framework of canonical conjugate analysis (Bernardo and Smith 2000, Prop. 5.6, p. 273), w...
متن کاملInvariant conjugate analysis for exponential families
There are several ways to parameterize a distribution belonging to an exponential family, each one leading to a different Bayesian analysis of the data under standard conjugate priors. To overcome this problem, we propose a new class of conjugate priors which is invariant with respect to smooth reparameterization. This class of priors contains the Jeffreys prior as a special case, according to ...
متن کامل