The Short-Cut Metropolis Method

Austerity in MCMC Land: Cutting the Metropolis-Hastings Budget

Can we make Bayesian posterior MCMC sampling more efficient when faced with very large datasets? We argue that computing the likelihood for N datapoints in the Metropolis-Hastings (MH) test to reach a single binary decision is computationally inefficient. We introduce an approximate MH rule based on a sequential hypothesis test that allows us to accept or reject samples with high confidence using only a fraction of the data required for the exact MH rule. While this method introduces an asymptotic bias, we show that this bias can be controlled and is more than offset by a decrease in variance …

Maximal couplings of the Metropolis-Hastings algorithm

Couplings play a central role in the analysis of Markov chain Monte Carlo algorithms and appear increasingly often in the algorithms themselves, e.g. in convergence diagnostics, parallelization, and variance reduction techniques. Existing couplings of the Metropolis-Hastings algorithm handle the proposal and acceptance steps separately and fall short of the upper bound on one-step meeting probabilities given by the coupling inequality. This paper introduces maximal couplings which achieve this bound while retaining the practical advantages of current methods. We consider the properties of thes…

用于 Metropolis-Hastings 算法的高效 Mirror 型核

Efficient Mirror-type Kernels for the Metropolis-Hastings Algorithm

本文提出融合 Mirror 移动与 MALA 的 MirrorMALA 核，并结合新型高维白化变换分析 GLMMs，在相近计算成本下实现显著更高采样效率。

随机游走 Metropolis 算法的可扩展耦合

Scalable couplings for the random walk Metropolis algorithm

本文研究高维 random walk Metropolis 算法的可扩展耦合，提出同步耦合的低秩修正并改进反射耦合，建立渐近最优性框架并通过数值实验验证。

Inference of Stochastic Disease Transmission Models Using Particle-MCMC and a Gradient Based Proposal

State-space models have been widely used to model the dynamics of communicable diseases in populations of interest by fitting to time-series data. Particle filters have enabled these models to incorporate stochasticity and so can better reflect the true nature of population behaviours. Relevant parameters such as the spread of the disease, $R_t$, and recovery rates can be inferred using Particle MCMC. The standard method uses a Metropolis-Hastings random-walk proposal which can struggle to reach the stationary distribution in a reasonable time when there are multiple parameters. In this paper …

MCMC using Hamiltonian dynamics

Hamiltonian dynamics can be used to produce distant proposals for the Metropolis algorithm, thereby avoiding the slow exploration of the state space that results from the diffusive behaviour of simple random-walk proposals. Though originating in physics, Hamiltonian dynamics can be applied to most problems with continuous state spaces by simply introducing fictitious "momentum" variables. A key to its usefulness is that Hamiltonian dynamics preserves volume, and its trajectories can thus be used to define complex mappings without the need to account for a hard-to-compute Jacobian factor - a pr…