Approximate Bayesian Inference with the Weighted Likelihood Bootstrap

摘要: We introduce the weighted likelihood bootstrap (WLB) as a way to simulate approximately from posterior distribution. This method is often easy implement, requiring only an algorithm for calculating maximum estimator, such iteratively reweighted least squares. In generic weighting scheme, WLB first order correct under quite general conditions. Inaccuracies can be removed by using source of samples in sampling-importance resampling (SIR) algorithm, which also allows incorporation particular prior information. The SIR-adjusted competitive alternative other integration methods certain models. Asymptotic expansions elucidate second-order properties WLB, generalization Rubin's Bayesian bootstrap. calculation approximate Bayes factors model comparison considered. note that, given sample simulated distribution, required marginal may simulation consistently estimated harmonic mean associated values; modification this estimator that avoids instability noted. These provide simple ways and probabilities very wide class