Abstract: We consider nonparametric Bayesian estimation of a probability density p based on a random sample of size n from this density using a hierarchical prior. The prior consists, for instance, of prior weights on the regularity of the unknown density combined with priors that are appropriate given that the density has this regularity. More generally, the hierarchy consists of prior weights...

In Bayesian analysis of multinomial models, an important assessment task is to elicit an informative joint prior distribution for multinomial probabilities. We start by introducing a method to elicit a univariate beta distribution for the probability of each category using probability quartiles. Three different multivariate priors are introduced using the elicited betas. As a tractable conjugat...

The problem motivating the paper is the determination of sample size in clinical trials under normal likelihoods and at the substantive testing stage of a financial audit where normality is not an appropriate assumption. A combination of analytical and simulation-based techniques within the Bayesian framework is proposed. The framework accommodates two different prior distributions: one is the ...

introduction eccrine poroma is a benign neoplasm thought to derived from eccrine sweat glands. recently, studies have shown wide distribution of eccrine poroma, including acral, face, and abdomen forms. case presentation we reported a 65-years-old woman with rapidly growing 5-cm ulcerative eccrine poroma with active bleeding since one year prior to presentation. conclusions although rapid growt...

Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A Bayesian would assign a data-independent prior probability to “subdivide”, which leads to a prior over infinite(ly many) trees. We derive an exact, fast, and ...