The problem of computing posterior functionals in general high-dimensional statistical models with possibly non-log-concave likelihood functions is considered. Based on the proof strategy of [49], but using only local likelihood conditions and without relying on M-estimation theory, nonasymptotic statistical and computational guarantees are provided for a gradient based MCMC algorithm. Given a suitable initialiser, these guarantees scale polynomially in key algorithmic quantities. The abstract results are applied to several concrete statistical models, including density estimation, nonparametric regression with generalised linear models and a canonical statistical non-linear inverse problem from PDEs.

翻译：本文研究了在可能具有非对数凹似然函数的一般高维统计模型中计算后验泛函的问题。基于[49]的证明策略，但仅使用局部似然条件且不依赖M估计理论，我们为基于梯度的MCMC算法提供了非渐近的统计与计算保证。在给定合适初始化条件下，这些保证在关键算法量上具有多项式标度。我们将抽象结果应用于若干具体统计模型，包括密度估计、广义线性模型下的非参数回归，以及来自偏微分方程的一个典型统计非线性反问题。