Bayesian inference for generalized linear model with linear inequality constraints

Bayesian statistical inference for Generalized Linear Models (GLMs) with parameters lying on a constrained space is of general interest (e.g., in monotonic or convex regression), but often constructing valid prior distributions supported subspace spanned by set linear inequality constraints can be challenging, especially when some the might binding leading to lower dimensional subspace. For case canonical link, it shown that generalized truncated multivariate normal desired used. Moreover, such distribution facilitates construction purpose product slice sampling method obtain (approximate) samples from corresponding posterior distribution, making inferential computationally efficient wide class GLMs an arbitrary constraints. The proposed sampler uniformly ergodic, having geometric convergence rate under mild regularity conditions satisfied many popular logistic and Poisson regressions coefficients). One primary advantages estimation over classical methods uncertainty parameter estimates easily quantified using simulated path Markov Chain sampler. Numerical illustrations data sets are presented illustrate superiority compared existing terms bias variances. In addition, real studies fertilizer-crop production estimating SCRAM nuclear power plants.