# Model choice in separate families: A comparison between the FBST and the Cox test

## TL;DR

This paper compares the Fully Bayesian Significance Test (FBST) and Cox test for selecting among lognormal, gamma, and Weibull models using mixture models and reparametrization, with simulation and real data applications.

## Contribution

The study introduces a reparametrized mixture model approach for model comparison using FBST and compares its performance with the Cox test through simulations and applications.

## Key findings

- FBST effectively discriminates between models in simulated data.
- Reparametrization reduces parameter estimation complexity.
- FBST shows comparable or improved performance over Cox test.

## Abstract

Tests of separate families of hypotheses were initially considered by Cox (1961,1962) In this work, the Fully Bayesian Significance Test, FBST, is evaluated for discriminating between the lognormal, gamma and Weibull models whose families of distributions are separate. Considering a linear mixture model including all candidate distributions, the FBST tests the hypotheses on the mixture weights in order to calculate the evidence measure in favor of each one. Additionally, the density functions of the mixture components are reparametrized in terms of the common parameters, the mean and the variance of the population, since the comparison between the models is based on the same dataset, i.e, on the same population. Reparametrizing the models in terms of the common parameters also allows one to reduce the number of the parameters to be estimated. In order to evaluate the performance of the procedure, some numerical results based on simulated sample points are given. In these simulations, the results of FBST are compared with those of the Cox test. Two applications examples illustrating the procedure for uncensored dataset are also presented. Keywords: Model choice; Separate Models; Mixture model; Significance test; FBST; Cox Test