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 [56], but using only local likelihood conditions and without relying on M-estimation theory, non-asymptotic statistical and computational guarantees are provided for gradient based MCMC algorithms. 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 cononical statistical non-linear inverse problem from PDEs.

翻译：根据[56]的验证战略,但仅使用当地可能性条件,不依赖M-估计理论,为基于梯度的MCMC算法提供非抽查统计和计算保证。鉴于这种保证是适当的,这些保证在关键算法数量中是多元的,抽象结果适用于若干具体的统计模型,包括密度估计、与一般线性模型的非对称回归以及PDEs的非线性问题。