Abstract
We examine whether it is worthwhile eliciting subjective judgements to account for dependency in a multivariate Poisson-Gamma probability model. The challenge of estimating reliability during product design motivated the choice of model class. For the multivariate Poisson-Gamma model we adopt an empirical Bayes methodology to present an estimator with improved accuracy. A simulation study investigates the estimation error of this estimator for different degrees of dependency and examines the impact of dependency being mis-specified when assessed by subjective judgement. Our theoretical and simulation findings give analysts insights about the value of eliciting dependency.
Highlights
Probability modelling is an established means of representing and analysing uncertainties associated with risk and reliability problems
Consider a problem that can be characterised by multiple uncertain variables, dependency will arise if information for one variable provides information about other variables
First we present an estimator for the multivariate Poisson-Gamma model that pools data from correlated processes and should result in reduced model estimation error
Summary
Probability modelling is an established means of representing and analysing uncertainties associated with risk and reliability problems. Dependencies between uncertain variables expressed probabilistically require appropriate modelling to provide meaningful results. Consider a problem that can be characterised by multiple uncertain variables, dependency will arise if information for one variable provides information about other variables. The conditional expectation of a variable differs from its unconditional expectation. Some modelling classes explicitly capture dependency within the probabilistic structure. Bayesian belief networks (BBN) reported in a range of contexts[1,2,3] as well as multivariate distributions for risk and reliability problems.[4,5,6,7]
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