The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting

多元正态概率的线性成本Vecchia近似

Linear-Cost Vecchia Approximation of Multivariate Normal Probabilities

本文提出了一种基于Vecchia近似的线性成本方法，用于高效估计多元正态概率及截断分布采样，同时保持与MET方法相同的收敛速率。

Bayesian inference and prediction for mean-mixtures of normal distributions

We study frequentist risk properties of predictive density estimators for mean mixtures of multivariate normal distributions, involving an unknown location parameter $θ\in \mathbb{R}^d$, and which include multivariate skew normal distributions. We provide explicit representations for Bayesian posterior and predictive densities, including the benchmark minimum risk equivariant (MRE) density, which is minimax and generalized Bayes with respect to an improper uniform density for $θ$. For four dimensions or more, we obtain Bayesian densities that improve uniformly on the MRE density under Kullback…

Quasi-Bayesian analysis of nonparametric instrumental variables models

This paper aims at developing a quasi-Bayesian analysis of the nonparametric instrumental variables model, with a focus on the asymptotic properties of quasi-posterior distributions. In this paper, instead of assuming a distributional assumption on the data generating process, we consider a quasi-likelihood induced from the conditional moment restriction, and put priors on the function-valued parameter. We call the resulting posterior quasi-posterior, which corresponds to ``Gibbs posterior'' in the literature. Here we focus on priors constructed on slowly growing finite-dimensional sieves. We …

hdtg: An R package for high-dimensional truncated normal simulation

Simulating from the multivariate truncated normal distribution (MTN) is required in various statistical applications yet remains challenging in high dimensions. Currently available algorithms and their implementations often fail when the number of parameters exceeds a few hundred. To provide a general computational tool to efficiently sample from high-dimensional MTNs, we introduce the hdtg package that implements two state-of-the-art simulation algorithms: harmonic Hamiltonian Monte Carlo (harmonic-HMC) and zigzag Hamiltonian Monte Carlo (Zigzag-HMC). Both algorithms exploit analytical soluti…

A frequentist framework of inductive reasoning

Reacting against the limitation of statistics to decision procedures, R. A. Fisher proposed for inductive reasoning the use of the fiducial distribution, a parameter-space distribution of epistemological probability transferred directly from limiting relative frequencies rather than computed according to the Bayes update rule. The proposal is developed as follows using the confidence measure of a scalar parameter of interest. (With the restriction to one-dimensional parameter space, a confidence measure is essentially a fiducial probability distribution free of complications involving ancillar…