On a New Class of Multivariate Prior Distributions: Theory and Application in Reliability

Abstract

In the context of robust Bayesian analysis for multiparameter distributions, we introduce a new class of priors based on stochastic orders, multivariate total positivity of order 2 (MT P2) and weighted distributions. We provide the new definition, its interpretation and the main properties and we also study the relationship with other classical classes of prior beliefs. We also consider the Hellinger metric and the Kullback-Leibler divergence to measure the uncertainty induced by such a class, as well as its effect on the posterior distribution. Finally, we conclude the paper with a real example about train door reliability.

A Bayesian Model of COVID-19 Cases Based on the Gompertz Curve

“…To conclude, applying our method to the province of Cádiz, located at the South of Spain, we were able to discuss the effectiveness of the first lockdown, the accuracy of the estimates during that lockdown and the beginning of the second and third waves after the lockdown. For future works it would be interesting to apply robust Bayesian techniques as described in [46][47][48][49]. In particular, it would be interesting to consider a band of prior distributions for the parameter a as described in [46].…”

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“…∑ T t=1 𝜆 it ∕T, where T is the total number of iterations and 𝜆 it is the value of the chain for the parameter 𝜆 i at the t-th MCMC step. For any z ∈ R, we estimate the posterior probability of relevance P 1 (z) by interpolating the estimates at the observed z ′ i s. Alternatively, we can first estimate the densities f 0 and f 1 and consequently compute lfdr(z) as defined in (13). The function P1 (z) is then obtained as P1 (z) = 1 − lfdr(z).…”

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