# The variation of the posterior variance and Bayesian sample size determination

## TL;DR

This paper investigates Bayesian sample size determination using the first two moments of the expected posterior variance, showing that a new criterion improves success rates and provides asymptotic insights, with applications to real datasets.

## Contribution

It introduces a novel Bayesian sample size criterion based on the first two moments of the expected posterior variance, enhancing success rates over traditional methods.

## Key findings

- Proposed criterion increases required sample size.
- Significantly improves success rate for bounding posterior variance.
- Provides asymptotic expressions and phase transition insights.

## Abstract

We consider Bayesian sample size determination using a criterion that utilizes the first two moments of the expected posterior variance. We study the resulting sample size in dependence on the chosen prior and explore the success rate for bounding the posterior variance below a prescribed limit under the true sampling distribution. Compared with sample size determination based on the expected average of the posterior variance the proposed criterion leads to an increase in sample size and significantly improved success rates. Generic asymptotic properties are proven, such as an asymptotic expression for the sample size and a sort of phase transition. Our study is illustrated using two real world datasets with Poisson and normally distributed data. Based on our results some recommendations are given.