distribution function is the p-value and is available numerically by direct calculation or by Markov chain Monte Carlo or by other … Bayesian literature, with many variations and some preference for two versions labelled pppost and pcpred. The bootstrap method … develop: an ancillary based p-value designated panc; a special version of the Bayesian pcpred; and a bootstrap based p …

anti-Bayesian statement appeared on the book of probability theory by mathematician William Feller. It notes that they …

theoreticians that Bayesian methods were absurd—not merely misguided but obviously wrong in principle. We consider several examples …, beginning with Feller's classic text on probability theory and continuing with more recent cases such as the perceived Bayesian … about Bayesian statistics, without aiming at a complete historical coverage of the reasons for this dismissal. …

We consider finite state space stationary hidden Markov models (HMMs) in the situation where the number of hidden … states is unknown. We provide a frequentist asymptotic evaluation of Bayesian analysis methods. Our main result gives …. Using conditions on the prior, we are then able to define a consistent Bayesian estimator of the number of hidden states. It …

We consider finite state space stationary hidden Markov models (HMMs) in the situation where the number of hidden … states is unknown. We provide a frequentist asymptotic evaluation of Bayesian analysis methods. Our main result gives …. Using conditions on the prior, we are then able to define a consistent Bayesian estimator of the number of hidden states. It …

appropriate, most generally via a standard Monte Carlo validation. …The choice of the summary statistics in Bayesian inference and in particular in ABC algorithms is paramount to produce …