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扩散模型贝叶斯推断的流形马尔可夫链蒙特卡洛方法AI 解读

Abstract Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction, and accompanying methodology—borrowing ideas from statistical physics and computational chemistry—for inferring the posterior distribution of latent diffusion paths and model parameters, given observations of the process. Joint…

延迟接受随机游走 Metropolis 算法的效率AI 解读

Delayed-acceptance Metropolis–Hastings and delayed-acceptance pseudo-marginal Metropolis–Hastings algorithms can be applied when it is computationally expensive to calculate the true posterior or an unbiased stochastic approximation thereof, but a computationally cheap deterministic approximation is available. An initial accept–reject stage uses the cheap approximation for computing the Metropolis–Hastings ratio; proposals which are accepted at this stage are subjected to a…

利用无偏估计量平均值的伪边际 Metropolis–Hastings 抽样AI 解读

Summary We consider a pseudo-marginal Metropolis–Hastings kernel ${\mathbb{P}}_m$ that is constructed using an average of $m$ exchangeable random variables, and an analogous kernel ${\mathbb{P}}_s$ that averages $s<m$ of these same random variables. Using an embedding technique to facilitate comparisons, we provide a lower bound for the asymptotic variance of any ergodic average associated with ${\mathbb{P}}_m$ in terms of the asymptotic variance of the corresponding ergodic…

论非负无偏估计量AI 解读

We study the existence of algorithms generating almost surely nonnegative unbiased estimators. We show that given a nonconstant real-valued function $f$ and a sequence of unbiased estimators of $\lambda\in\mathbb{R}$, there is no algorithm yielding almost surely nonnegative unbiased estimators of $f(\lambda)\in\mathbb{R}^{+}$. The study is motivated by pseudo-marginal Monte Carlo algorithms that rely on such nonnegative unbiased estimators. These methods allow “exact…

伪边际随机游走Metropolis算法的效率AI 解读

We examine the behaviour of the pseudo-marginal random walk Metropolis algorithm, where evaluations of the target density for the accept/reject probability are estimated rather than computed precisely. Under relatively general conditions on the target distribution, we obtain limiting formulae for the acceptance rate and for the expected squared jump distance, as the dimension of the target approaches infinity, under the assumption that the noise in the estimate of the…