Bayesian Analysis via Gibbs Sampling of Susceptibility to Intramammary Infection in Holstein Cattle

S. L. Rodriguez-Zas, D. Gianola, G. E. Shook

Research output: Contribution to journalArticle

Abstract

A Bayesian analysis was undertaken to assess the susceptibility of Holsteins to mastitis from 120 to 305 d in milk. Data included 595 lactations from 267 cows. The response variable was presence or absence of intramammary infection; explanatory vanables were period and season of calving, somatic cell score and cow. The logistic model adopted had period and season of calving and the regression on somatic cell score with vague prior distributions, and cow effects had a normal prior with unknown variance σ2u, which, in turn, had a gamma prior. Implementation was by Gibbs sampling. Posterior densities of location parameters were unimodal and symmetric. The probability of intramammary infection of a sample cow was skewed. The posterior distribution of σ2u was skewed also. Gibbs samples of σ2u had high lag correlations, which gave an effective sample ranging between 47 and 117 from a chain of size 3000. There were differences between estimates of σ2u found using Gibbs sampling and those obtained using approximations. The low information content arising from the small size of the data and the binary nature of the response are reasons for such differences. A sensitivity analysis revealed influences of hyperparameters of the prior distribution of σ2u on inferences about this parameter.

Original languageEnglish (US)
Pages (from-to)2710-2722
Number of pages13
JournalJournal of Dairy Science
Volume81
Issue number10
DOIs
StatePublished - Oct 1998
Externally publishedYes

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Keywords

  • Bayesian
  • Gibbs sampling
  • Priors
  • Somatic cell score

ASJC Scopus subject areas

  • Food Science
  • Animal Science and Zoology
  • Genetics

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