Bayes and empirical Bayes: do they merge?

Bayes and empirical Bayes : Do they merge?

Analysis of Empirical MAP and Empirical Partially Bayes: Can They be Alternatives to Variational Bayes?

Variational Bayesian (VB) learning is known to be a promising approximation to Bayesian learning with computational efficiency. However, in some applications, e.g., large-scale collaborative filtering and tensor factorization, VB is still computationally too costly. In such cases, looser approximations such as MAP estimation and partially Bayesian (PB) learning, where a part of the parameters a...

Empirical Bayes Estimation in Nonstationary Markov chains

Estimation procedures for nonstationary Markov chains appear to be relatively sparse. This work introduces empirical  Bayes estimators  for the transition probability  matrix of a finite nonstationary  Markov chain. The data are assumed to be of  a panel study type in which each data set consists of a sequence of observations on N>=2 independent and identically dis...

Bayes and empirical Bayes changepoint problems

We generalize the approach of Liu and Lawrence (1999) for multiple changepoint problems where the number of changepoints is unknown. The approach is based on dynamic programming recursion for efficient calculation of the marginal probability of the data with the hidden parameters integrated out. For the estimation of the hyperparameters, we propose to use Monte Carlo EM when training data are a...

Empirical Bayes vs. Fully Bayes Variable Selection

For the problem of variable selection for the normal linear model, fixed penalty selection criteria such as AIC, Cp, BIC and RIC correspond to the posterior modes of a hierarchical Bayes model for various fixed hyperparameter settings. Adaptive selection criteria obtained by empirical Bayes estimation of the hyperparameters have been shown by George and Foster [2000. Calibration and Empirical B...