Estimating meteor rates using Bayesian inference

TL;DR

This paper introduces a Bayesian method for estimating true meteor rates from limited observations, using a Poisson likelihood and Jeffreys prior to improve accuracy and confidence interval calculations.

Contribution

It develops a Bayesian framework with a specific prior for more accurate meteor rate estimation from small sample sizes, updating existing activity formulas.

Findings

Provides a Bayesian estimator with expectation E(λ) = n+0.5

Adopts Jeffreys prior for improved inference

Enables calculation of confidence intervals for meteor rates

Abstract

A method for estimating the true meteor rate \lambda\ from a small number of observed meteors n is derived. We employ Bayesian inference with a Poissonian likelihood function. We discuss the choice of a suitable prior and propose the adoption of Jeffreys prior, P(\lambda)=\lambda^{-0.5}, which yields an expectation value E(\lambda) = n+0.5 for any n \geq 0. We update the ZHR meteor activity formula accordingly, and explain how 68%- and 95%-confidence intervals can be computed.