Christian P. Robert, Wu Changye
In this chapter, we review some of the most standard MCMC tools used in Bayesian computation, along with vignettes on standard misunderstandings of these approaches taken from Q \&~A's on the forum Cross-validated answered by the first author.
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The study of animal behavioural states inferred through hidden Markov models and similar state switching models has seen a significant increase in popularity in recent years. The ability to account for varying levels of behavioural scale has become possible through hierarchical hidden Markov models, but additional levels lead to higher complexity and increased correlation between model components. Maximum likelihood approaches to inference using the EM algorithm and direct optimisation of likelihoods are more frequently used, with Bayesian approaches being less favoured due to computational de…
In this study, two-state Markov switching multinomial logit models are proposed for statistical modeling of accident injury severities. These models assume Markov switching in time between two unobserved states of roadway safety. The states are distinct, in the sense that in different states accident severity outcomes are generated by separate multinomial logit processes. To demonstrate the applicability of the approach presented herein, two-state Markov switching multinomial logit models are estimated for severity outcomes of accidents occurring on Indiana roads over a four-year time interval…
GPU-Parallelization of Markov Chain Pool Decoding with Unbiased MCMC
本文针对马尔可夫链池解码（MCPD）在GPU上的并行化问题，提出得分加权更新方案并结合无偏MCMC框架，实验显示其在高噪声下的克隆恢复效果优于均匀解码器。
In this paper, two-state Markov switching models are proposed to study accident frequencies. These models assume that there are two unobserved states of roadway safety, and that roadway entities (roadway segments) can switch between these states over time. The states are distinct, in the sense that in the different states accident frequencies are generated by separate counting processes (by separate Poisson or negative binomial processes). To demonstrate the applicability of the approach presented herein, two-state Markov switching negative binomial models are estimated using five-year acciden…
Parameterizations for Gradient-based Markov Chain Monte Carlo on the Stiefel Manifold: A Comparative Study
本研究在等效条件下比较了Stiefel流形上基于梯度的马尔可夫链蒙特卡洛的四种正交矩阵参数化方法，发现极坐标展开参数化在高维和复杂问题中效率最高，但所有方法在极高维任务中仍存在局限性。
The Traceplot Thickens: Developing All-Purpose Convergence Diagnostics for any Markov Chain Monte Carlo Algorithm
本文提出将原始样本空间映射到实数轴后再评估收敛诊断的通用方法，解决了维度变化或大量离散参数场景下经典MCMC收敛诊断失效的问题，并在Dirichlet过程混合模型和贝叶斯核机器回归模型上验证了有效性。
We propose moment-based variational inference as a flexible framework for approximate smoothing of latent Markov jump processes. The main ingredient of our approach is to partition the set of all transitions of the latent process into classes. This allows to express the Kullback-Leibler divergence between the approximate and the exact posterior process in terms of a set of moment functions that arise naturally from the chosen partition. To illustrate possible choices of the partition, we consider special classes of jump processes that frequently occur in applications. We then extend the result…
Zigzag path connects two Monte Carlo samplers: Hamiltonian counterpart to a piecewise deterministic Markov process
本文建立了zigzag采样器与基于Laplace动量的Hamiltonian Monte Carlo变体之间的理论联系，证明在频繁动量刷新下前者强收敛于后者，并表明保留完整动量的Hamiltonian zigzag能更好探索高相关参数分布。
Probabilistic models are conceptually powerful tools for finding structure in data, but their practical effectiveness is often limited by our ability to perform inference in them. Exact inference is frequently intractable, so approximate inference is often performed using Markov chain Monte Carlo (MCMC). To achieve the best possible results from MCMC, we want to efficiently simulate many steps of a rapidly mixing Markov chain which leaves the target distribution invariant. Of particular interest in this regard is how to take advantage of multi-core computing to speed up MCMC-based inference, b…
A key challenge for modern Bayesian statistics is how to perform scalable inference of posterior distributions. To address this challenge, variational Bayes (VB) methods have emerged as a popular alternative to the classical Markov chain Monte Carlo (MCMC) methods. VB methods tend to be faster while achieving comparable predictive performance. However, there are few theoretical results around VB. In this paper, we establish frequentist consistency and asymptotic normality of VB methods. Specifically, we connect VB methods to point estimates based on variational approximations, called frequenti…
Almost sure convergence rates of adaptive increasingly rare Markov chain Monte Carlo
本文研究了自适应递增稀疏MCMC算法的几乎必然收敛速度，通过收缩假设推导了收敛速率上界，并展示了在不同设置下的应用。
Structural equation models are commonly used to capture the relationship between sets of observed and unobservable variables. Traditionally these models are fitted using frequentist approaches but recently researchers and practitioners have developed increasing interest in Bayesian inference. In Bayesian settings, inference for these models is typically performed via Markov chain Monte Carlo methods, which may be computationally intensive for models with a large number of manifest variables or complex structures. Variational approximations can be a fast alternative; however, they have not been…
Estimation of High-Dimensional Markov-Switching VAR Models with an Approximate EM Algorithm
针对高维时间序列机制转换估计难题，提出适用于马尔可夫切换VAR模型的近似EM算法，证明其高维一致性，经模拟和癫痫脑电数据验证有效。
MCMC using $\textit{bouncy}$ Hamiltonian dynamics: A unifying framework for Hamiltonian Monte Carlo and piecewise deterministic Markov process samplers
本文提出基于弹性哈密顿动力学的无拒绝Metropolis提案框架，将哈密顿蒙特卡洛与分段确定性马尔可夫过程采样统一，提升贝叶斯推断的扩展性与创新性。
Detecting individual-level infections using sparse group-testing through graph-coupled hidden Markov models
本文扩展图耦合隐马尔可夫模型，以个体感染状态为隐状态、分组检测结果为观测，证明每日初期分组筛查可较准确推断个体感染状态。
Variational Bayesian analysis of survival data using a log-logistic accelerated failure time model
本研究针对对数逻辑加速失效时间模型，提出嵌入分段近似技术的平均场变分贝叶斯推断算法，在保证估计精度的同时降低了计算成本。
We consider the problem of estimating the maximum posterior probability (MAP) state sequence for a finite state and finite emission alphabet hidden Markov model (HMM) in the Bayesian setup, where both emission and transition matrices have Dirichlet priors. We study a training set consisting of thousands of protein alignment pairs. The training data is used to set the prior hyperparameters for Bayesian MAP segmentation. Since the Viterbi algorithm is not applicable any more, there is no simple procedure to find the MAP path, and several iterative algorithms are considered and compared. The main…
In this paper, we explore the class of the Hidden Semi-Markov Model (HSMM), a flexible extension of the popular Hidden Markov Model (HMM) that allows the underlying stochastic process to be a semi-Markov chain. HSMMs are typically used less frequently than their basic HMM counterpart due to the increased computational challenges when evaluating the likelihood function. Moreover, while both models are sequential in nature, parameter estimation is mainly conducted via batch estimation methods. Thus, a major motivation of this paper is to provide methods to estimate HSMMs (1) in a computationally…
Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current state or on the time elapsed from the starting of the process. The former models are called semi-Markov while the latter are known as inhomogeneous Markov models. Inference for both the models presents computational difficulties when the process is only observed at discrete time points with no additional information about the state transitions. Indeed, in b…
Bayesian inference for the Markov-modulated Poisson process with an outcome process
本文提出一种带死亡状态的马尔可夫调制泊松过程贝叶斯推断方法，通过吉布斯采样同时建模潜在健康状态、观测时机和终止事件，并在加拿大医疗数据上验证其有效性。
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