Approximate Bayesian computation (ABC) is a popular technique for approximating likelihoods and often used in parameter estimation when the likelihood functions are analytically intractable. In context of Hidden Markov Models (HMMs), we analyze asymptotic behavior posterior distribution ABC based estimation. particular show that Bernstein-von Mises type results still hold but resulting biased s...

In a seminal article, Berger, De Oliveira and Sansó [J. Amer. Statist. Assoc. 96 (2001) 1361–1374] compare several objective prior distributions for the parameters of Gaussian process models with isotropic correlation kernel. The reference distribution stands out among them insofar as it always leads to proper posterior. They prove this result rough kernels: Spherical, Exponential power ρ<2, Ma...

Summary Bayesian inversion generates a posterior distribution of model parameters from an observation equation and prior information both weighted by hyperparameters. The is also introduced for the hyperparameters in fully inversions enables us to evaluate probabilistically joint posterior. However, even linear inverse problem, it unsolved how we should extract useful on This study presents the...

This paper considers the testing of fuzzy hypotheses on the basis of a&nbsp;Bayesian approach. For this, using a notion of prior distribution with&nbsp;interval or fuzzy-valued parameters, we extend a concept of posterior&nbsp;probability of a fuzzy hypothesis. Some of its properties are also put&nbsp;into investigation. The feasibility and effectiveness of the proposed&nbsp;methods are also cla...

For noninformative nonparametric estimation of finite population quantiles under simple random sampling, estimation based on the Polya posterior is similar to estimation based on the Bayesian approach developed by Ericson (1969, JRSSB, 31, 195-233) in that the Polya posterior distribution is the limit of Ericson’s posterior distributions as the weight placed on the prior distribution diminishes...

If the distribution P is considered random and distributed according to , as it is in Bayesian inference, then the posterior distribution is the conditional distribution of P given the observations. The prior is, of course, a measure on some σ-field on and we must assume that the expressions in the display are well defined. In particular, we assume that the map x p → p x is measurable for the p...