6 papers
Central limit theorem for high temperature spin models via martingale embedding
Xiao Fang, Yang Xie, Yi-Kun Zhao
We use martingale embeddings to prove a central limit theorem (CLT) for one-dimensional projections of high-dimensional random vectors in satisfying a Poincaré inequal…
Conditional central limit theorems for exponential random graphs
Xiao Fang, Song-Hao Liu, Zhonggen Su +1
In this paper, we study the Exponential Random Graph Models (ERGMs) conditioning on the number of edges. In subcritical region of model parameters, we prove a conditional Central L…
Normal approximation for exponential random graphs
Xiao Fang, Song-Hao Liu, Qi-Man Shao +1
The question of whether the central limit theorem (CLT) holds for the total number of edges in exponential random graph models (ERGMs) in the subcritical region of parameters has r…
Bernstein von-Mises Theorem for g-prior and nonlocal prior
Xiao Fang, Malay Ghosh
The paper develops Bernstein von Mises Theorem under hierarchical -priors for linear regression models. The results are obtained both when the error variance is known, and also…
Second-order Approximation of Exponential Random Graph Models
Wen-Yi Ding, Xiao Fang
Exponential random graph models (ERGMs) are flexible probability models allowing edge dependency. However, it is known that, to a first-order approximation, many ERGMs behave like…
Posterior Concentration for Gaussian Process Priors under Rescaled and Hierarchical Matérn and Confluent Hypergeometric Covariance Functions
Xiao Fang, Anindya Bhadra
In nonparameteric Bayesian approaches, Gaussian stochastic processes can serve as priors on real-valued function spaces. Existing literature on the posterior convergence rates unde…