Calibrating the prior distribution for a normal model with conjugate prior

Bayesian Fuzzy Hypothesis Testing with Imprecise Prior Distribution

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

Prior distribution

A Nonparametric Conjugate Prior Distribution for the Maximizing Argument of a Noisy Function

We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step procedure of first, doing inference over the function space and second, finding the extrema of these functions. Here we skip the representation step and direct...

A Nonparametric Conjugate Prior Distribution for the Maximizing Argument of a Noisy Function

We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step procedure of first, doing inference over the function space and second, finding the extrema of these functions. Here we skip the representation step and direct...

Misinformation in the conjugate prior for the linear model with implications for free-knot spline modelling.

In the conjugate prior for the normal linear model, the prior variance for the coefficients is a multiple of the error variance parameter. However, if the prior mean for the coefficients is poorly chosen, the posterior distribution of the model can be seriously distorted because of prior dependence between the coefficients and error variance. In particular, the error variance will be overestima...