Noninformative Prior Weights for Dirichlet PDFs*

Audun Jøsang, Jin-Hee Cho, Feng Chen

Abstract: The noninformative prior weight W of a Dirichlet PDF (Probability Density Function) determines the balance between the prior probability and the influence of new observations on the posterior probability distribution. In this work, we propose a method for dynamically converging the weight W in a way that satisfies two constraints. The first constraint is that the prior Dirichlet PDF (i.e. in the absence of evidence) must always be uniform, which dictates that W = k where k is the cardinality of the domain. The second constraint is that the prior weight of large domains must not be so heavy that it prevents new observation evidence from having the expected influence over the shape of the Dirichlet PDF, which dictates that W quickly converges to a low constant C <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W</inf> in the presence of observation evidence, where typically C <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W</inf> = 2. In the case of a binary domain, the noninformative prior weight is normally set to W = 2, irrespective of the amount of evidence. In the case of a multidimensional domain with arbitrarily large cardinality k, the noninformative prior weight is initially equal to the domain cardinality k, but rapidly decreases to the constant convergence factor C <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W</inf> as the amount of evidence increases.