Posterior properties of the Weibull distribution for censored data

05/17/2020
by   Eduardo Ramos, et al.
0

The Weibull distribution is one of the most used tools in reliability analysis. In this paper, assuming a Bayesian approach, we propose necessary and sufficient conditions to verify when improper priors lead to proper posteriors for the parameters of the Weibull distribution in the presence of complete or right-censored data. Additionally, we proposed sufficient conditions to verify if the obtained posterior moments are finite. These results can be achieved by checking the behavior of the improper priors, which are applied in different objective priors to illustrate the usefulness of the new results. As an application of our theorem, we prove that if the improper prior leads to a proper posterior, the posterior mean, as well as other higher moments of the scale parameter, are not finite and, therefore, should not be used.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/01/2023

Necessary and sufficient conditions for posterior propriety for generalized linear mixed models

Generalized linear mixed models (GLMMs) are commonly used to analyze c...
research
07/05/2021

Analyzing Relevance Vector Machines using a single penalty approach

Relevance vector machine (RVM) is a popular sparse Bayesian learning mod...
research
05/15/2020

Power laws distributions in objective priors

The use of objective prior in Bayesian applications has become a common ...
research
12/28/2020

Objective Bayesian Analysis for the Differential Entropy of the Gamma Distribution

The use of entropy related concepts goes from physics, such as in statis...
research
02/13/2023

Transcendence Certificates for D-finite Functions

Although in theory we can decide whether a given D-finite function is tr...
research
08/19/2016

A Strongly Quasiconvex PAC-Bayesian Bound

We propose a new PAC-Bayesian bound and a way of constructing a hypothes...
research
08/01/2020

Posterior Impropriety of some Sparse Bayesian Learning Models

Sparse Bayesian learning models are typically used for prediction in dat...

Please sign up or login with your details

Forgot password? Click here to reset