2020/05/01 by Debashis Chatterjee, Chatterjee, Debashis, Sourabh Bhattacharya +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #Statistical Mechanics and Entropy #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2005.00234
openalex publication_date 2020/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we investigate posterior convergence of nonparametric binary\nand Poisson regression under possible model misspecification, assuming general\nstochastic process prior with appropriate properties. Our model setup and\nobjective for binary regression is similar to that of Ghosal and Roy (2006)\nwhere the authors have used the approach of entropy bound and exponentially\nconsistent tests with the sieve method to achieve consistency with respect to\ntheir Gaussian process prior. In contrast, for both binary and Poisson\nregression, using general stochastic process prior, our approach involves\nverification of asymptotic equipartition property along with the method of\nsieve, which is a manoeuvre of the general results of Shalizi (2009), useful\neven for misspecified models. Moreover, we will establish not only posterior\nconsistency but also the rates at which the posterior probabilities converge,\nwhich turns out to be the Kullback-Leibler divergence rate. We also investgate\nthe traditional posterior convergence rates. Interestingly, from subjective\nBayesian viewpoint we will show that the posterior predictive distribution can\naccurately approximate the best possible predictive distribution in the sense\nthat the Hellinger distance, as well as the total variation distance between\nthe two distributions can tend to zero, in spite of misspecifications.\n