ENBIS: European Network for Business and Industrial Statistics

A Bayesian Approach to Model Shifts in Poisson Data

Abstract

Submitted by

Panagiotis Tsiamyrtzis

Authors

Panagiotis Tsiamyrtzis and Douglas M. Hawkins

Affiliation

Dept. of Statistics, Athens University of Economics and Business

Abstract

We consider a process producing count data from a Poisson distribution. Our interest is in detecting on-line whether the Poisson parameter (mean and variance) shifts to either a higher value (causing worst process performance) or to smaller values (good scenario). The necessity for drawing inference sequentially as the observations become available leads us to adopt a Bayesian sequentially updated scheme of mixture of Gamma distributions. Issues regarding inference and prediction will be covered. The developed methodology is very appealing in cases like short runs and/or Phase I count data.

Keywords:
Bayesian SPC by attributes, Change Point, Gamma mixture.

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