Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1973 · 54 citations · 4 references
Natural SciencesBiostatisticsMathematicsBayesian Data AnalysisProbability TheoryStatisticsBayesian InferenceBayesian ModelingBayesian StatisticsPoisson ProcessesPosterior DistributionsStatistical InferenceBayesian EstimationBayesian Inference For Poisson ProcessesBayesian RegressionBayesian Trend EstimationCompound Poisson ModelsPoisson DistributionPoisson Process EstimationPoisson Regression
Summary This paper is concerned with the problem of testing the existence of a trend in the means θi of Poisson distributions. It is assumed that these means are changing exponentially, that is, log θi = α + βxi. A classical method is reviewed which is used for testing the hypothesis β = 0. The exact Bayesian distribution for β is derived and a Bayesian approximation suggested which proved to be very useful. Finally, a comparison of these three methods by means of numerical examples is made.
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