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ON ASSESSING THE POTENTIAL SEVERITY OF AN OUTBREAK OF A RARE INFECTIOUS DISEASE: A BAYESIAN APPROACH
Author(s) -
Heyde C. C.
Publication year - 1979
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1979.tb01145.x
Subject(s) - outbreak , poisson distribution , bayesian probability , statistics , population , mathematics , distribution (mathematics) , econometrics , demography , biology , virology , mathematical analysis , sociology
Summary In this paper an infective population, during the early stages of the outbreak of a disease, is approximated by a Galton‐Watson process. Attention is focused on the threshold theorem which assesses an epidemic as major if the associated Galton‐Watson process is supercritical (i.e. the mean μ of the offspring distribution is greater than one). A Bayesian formulation is adopted together with the assumption of a power series offspring distribution and an approximate form is found for P(μ >1) computed from the posterior distribution of μ. Exact results are given for the case of a Poisson offspring distribution. The results are illustrated with applications to three sets of data on smallpox outbreaks. The Bayesian approach has a number of advantages over classical methods and in particular allows the cases μ < 1, μ > 1 to be treated without distinction.