Stochastic Approximation and Newton's Estimate of a Mixing Distribution

判别式贝叶斯滤波为最小化对数凸函数的随机牛顿法提供动量

Discriminative Bayesian filtering lends momentum to the stochastic Newton method for minimizing log-convex functions

该研究将最小化对数凸函数平均值的随机牛顿优化问题转化为判别式观测的潜状态空间序列贝叶斯推断问题，提出结合梯度与海森矩阵历史的贝叶斯滤波优化算法，推导了类重球动量的旧观测衰减条件，并辅以示例阐释。

无限维贝叶斯反问题计算框架：第二部分。随机牛顿MCMC方法及其在冰盖流动反问题中的应用

A computational framework for infinite-dimensional Bayesian inverse problems: Part II. Stochastic Newton MCMC with application to ice sheet flow inverse problems

本文提出一种解决无限维反问题的计算框架，采用随机牛顿MCMC方法，通过低秩近似Hessian来加速采样，应用于冰盖流动反问题，展示了方法在收敛速度和计算成本上的优势。

A stochastic Stein Variational Newton method

Stein variational gradient descent (SVGD) is a general-purpose optimization-based sampling algorithm that has recently exploded in popularity, but is limited by two issues: it is known to produce biased samples, and it can be slow to converge on complicated distributions. A recently proposed stochastic variant of SVGD (sSVGD) addresses the first issue, producing unbiased samples by incorporating a special noise into the SVGD dynamics such that asymptotic convergence is guaranteed. Meanwhile, Stein variational Newton (SVN), a Newton-like extension of SVGD, dramatically accelerates the convergen…

Quasi-Newton particle Metropolis-Hastings

Particle Metropolis-Hastings enables Bayesian parameter inference in general nonlinear state space models (SSMs). However, in many implementations a random walk proposal is used and this can result in poor mixing if not tuned correctly using tedious pilot runs. Therefore, we consider a new proposal inspired by quasi-Newton algorithms that may achieve similar (or better) mixing with less tuning. An advantage compared to other Hessian based proposals, is that it only requires estimates of the gradient of the log-posterior. A possible application is parameter inference in the challenging class of…

Nonparametric estimation of a mixing distribution for a family of linear stochastic dynamical systems

In this paper we develop a nonparametric maximum likelihood estimate of the mixing distribution of the parameters of a linear stochastic dynamical system. This includes, for example, pharmacokinetic population models with process and measurement noise that are linear in the state vector, input vector and the process and measurement noise vectors. Most research in mixing distributions only considers measurement noise. The advantages of the models with process noise are that, in addition to the measurements errors, the uncertainties in the model itself are taken into the account. For example, fo…

基于二项式混合分布样本的混合分布精确置信区间

Exact confidence intervals for the mixing distribution from binomial mixture distribution samples

本文提出一种基于二项式混合分布样本构建混合分布累积分布函数和分位数逐点精确置信区间的方法，通过反演复合零假设的精确检验实现，并利用分层贝叶斯方法与有限 Polya Trees 建模提供稳定的去卷积估计。