Bayesian Inference for Logistic Regression Models using Sequential Posterior Simulation

John Geweke. Current Trends in Bayesian Methodology with Applications (S.K. Upadhyay, U. Singh, D. K. Dey and A. Loganathan, eds.) CRC Press.  Chapter 14, 289-312, 2015.

The logistic speci…fication has been used extensively in non-Bayesian statistics
to model the dependence of discrete outcomes on the values of speci…ed covari-
ates. Because the likelihood function is globally weakly concave estimation by
maximum likelihood is generally straightforward even in commonly arising appli-
cations with scores or hundreds of parameters. In contrast Bayesian inference has
proven awkward, requiring normal approximations to the likelihood or specialized
adaptations of existing Markov chain Monte Carlo and data augmentation meth-
ods. This paper approaches Bayesian inference in logistic models using recently
developed generic sequential posterior simulaton (SPS) methods that require little
more than the ability to evaluate the likelihood function. Compared with exist-
ing alternatives SPS is much simpler, and provides numerical standard errors and
accurate approximations of marginal likelihoods as by-products. The SPS algo-
rithm for Bayesian inference is amenable to massively parallel implementation,
and when implemented using graphical processing units it compares well with the
best existing alternative. The paper demonstrates these points by means of several
examples.

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