# Introducing Inner Nested Sampling

## TL;DR

This paper presents Inner Nested Sampling, a Monte Carlo algorithm for estimating moments of functions of Dirichlet distributions within Skilling's Nested Sampling framework.

## Contribution

It introduces a novel Monte Carlo algorithm specifically designed for Dirichlet distributions, expanding the applications of Nested Sampling.

## Key findings

- Efficient estimation of moments for Dirichlet functions.
- Implementation of Inner Nested Sampling within existing frameworks.
- Potential improvements in Bayesian inference methods.

## Abstract

In this paper we will give a Monte Carlo algorithm by which the moments of a functions of Dirichlet probability distributions can be estimated. This algorithm is called Inner Nested Sampling and is an implementation of Skilling's general Nested Sampling framework.