Exact and Approximate Bayesian Inference for Low Integer-Valued Time Series Models with Intractable Likelihoods
Exact and Approximate Bayesian Inference for Low Integer-Valued Time Series Models with Intractable Likelihoods
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DOI：
10.1214/15-ba950
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发表时间：
2016-06
影响因子：
4.4
通讯作者：
C. Drovandi;A. Pettitt;Roy A. McCutchan
中科院分区：
文献类型：
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作者：
C. Drovandi;A. Pettitt;Roy A. McCutchan
在本文中，我们提出了一种新的模拟方法，以获得精确或近似的贝叶斯推断模型的低价值的计数时间序列数据，具有计算要求的似然函数。该算法适用于粒子马尔可夫链蒙特卡罗（PMCMC）方法的框架内。粒子滤波器只需要模型模拟，在这方面，我们的方法与近似贝叶斯计算（ABC）。然而，在这种情况下使用PMCMC方法的一个优点是，模拟数据可以与一次一个观察到的数据相匹配，而不是试图同时匹配完整的数据集或低维不充分的汇总统计量，这是ABC中的常见做法。对于低值计数时间序列数据，我们发现，它往往是计算上可行的，以匹配模拟数据与观测数据。我们的粒子滤波器通过重复模拟来保持$N$个粒子，直到获得$N+1$个精确匹配。我们的算法创建了一个无偏估计的可能性，导致精确的后验推断时，包括在MCMC算法。在精确匹配在计算上是禁止的情况下，根据ABC引入公差。我们的方法的一个新颖的方面是，我们引入辅助变量到我们的粒子滤波器，使部分观察和/或非马尔可夫模型可以容纳。我们证明，贝叶斯模型选择问题可以很容易地在这个框架中处理。
In this paper we present a new simulation methodology in order to obtain exact or approximate Bayesian inference for models for low-valued count time series data that have computationally demanding likelihood functions. The algorithm fits within the framework of particle Markov chain Monte Carlo (PMCMC) methods. The particle filter requires only model simulations and, in this regard, our approach has connections with approximate Bayesian computation (ABC). However, an advantage of using the PMCMC approach in this setting is that simulated data can be matched with data observed one-at-a-time, rather than attempting to match on the full dataset simultaneously or on a low-dimensional non-sufficient summary statistic, which is common practice in ABC. For low-valued count time series data we find that it is often computationally feasible to match simulated data with observed data exactly. Our particle filter maintains $N$ particles by repeating the simulation until $N+1$ exact matches are obtained. Our algorithm creates an unbiased estimate of the likelihood, resulting in exact posterior inferences when included in an MCMC algorithm. In cases where exact matching is computationally prohibitive, a tolerance is introduced as per ABC. A novel aspect of our approach is that we introduce auxiliary variables into our particle filter so that partially observed and/or non-Markovian models can be accommodated. We demonstrate that Bayesian model choice problems can be easily handled in this framework.