Estimating meteor rates using Bayesian inference

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.