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Statistics Colloquium
Dec. 4 (Fri) 12 noon
2275 Rood Hall

Bayesian Rank Based Methods for Linear and Generalized Linear Models

James Dzikunu
Department of Statistics
Western Michigan University

A Bayesian Rank Based Method for linear models where estimation of the regression coefficients is based on the full conditional distributions is proposed in this research. The data likelihood is based on the asymptotic distribution of the gradient function where the asymptotic linearity of this rank based quantity is utilized. Prior distributions are put on regression coefficients and scale parameter. The effects of different priors on this scale parameter are studied.

We extend this procedure to a Generalized Linear Model where our pseudo-likelihood is a rank based quantity that utilizes Pearson residuals. Our proposed method is robust to outliers in the y-space as far as we specify a link function that is monotone and three times continuously differentiable on a response which is independent and absolutely continuous. A simulation study based on the posterior distribution via Markov Chain Monte-Carlo method is done for inference purposes.

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All statistics students are expected to attend.

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