# A Bayesian ARMA Probability Density Estimator

## TL;DR

This paper introduces a Bayesian method for estimating probability densities using ARMA models, offering advantages like efficiency and parameter uncertainty estimation.

## Contribution

The novel contribution is a Bayesian ARMA-based probability density estimator using MCMC for parameter inference.

## Key findings

- Bayesian ARMA estimators outperform Fourier series in terms of efficiency and parsimony.
- MCMC output provides probability intervals for parameters and the estimated density.
- Simulation studies and a wine attribute example demonstrate the method's effectiveness.

## Abstract

A Bayesian approach for constructing ARMA probability density estimators is proposed. Such estimators are ratios of trigonometric polynomials and have a number of advantages over Fourier series estimators, including parsimony and greater efficiency under common conditions. The Bayesian approach is carried out via MCMC, the output of which can be used to obtain probability intervals for unknown parameters and the underlying density. Finite sample efficiency and methods for choosing the estimator’s smoothing parameter are considered in a simulation study, and the ideas are illustrated with data on a wine attribute.