Parameter Estimation for Hidden Markov Models with Intractable Likelihoods

THOMAS A. DEAN; SUMEETPAL S. SINGH; AJAY JASRA; GARETH W. PETERS

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Parameter Estimation for Hidden Markov Models with Intractable Likelihoods

机译：具有难以解决的隐马尔可夫模型的参数估计

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摘要

Approximate Bayesian computation (ABC) is a popular technique for analysing data for complex models where the likelihood function is intractable. It involves using simulation from the model to approximate the likelihood, with this approximate likelihood then being used to construct an approximate posterior. In this paper, we consider methods that estimate the parameters by maximizing the approximate likelihood used in ABC. We give a theoretical analysis of the asymptotic properties of the resulting estimator. In particular, we derive results analogous to those of consistency and asymptotic normality for standard maximum likelihood estimation. We also discuss how sequential Monte Carlo methods provide a natural method for implementing our likelihood-based ABC procedures.

机译：近似贝叶斯计算（ABC）是一种流行的技术，用于分析似然函数难于处理的复杂模型的数据。它涉及使用来自模型的模拟来近似可能性，然后将该近似可能性用于构造近似后验。在本文中，我们考虑通过最大化ABC中使用的近似似然来估计参数的方法。我们对所得估计量的渐近性质进行理论分析。特别是，我们得出类似于标准最大似然估计的一致性和渐近正态性的结果。我们还将讨论顺序蒙特卡洛方法如何为实施基于似然的ABC程序提供自然方法。

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来源
《Scandinavian journal of statistics》 |2014年第4期|970-987|共18页
作者
THOMAS A. DEAN; SUMEETPAL S. SINGH; AJAY JASRA; GARETH W. PETERS;
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作者单位

Department of Engineering, University of Cambridge;

Department of Engineering, University of Cambridge, Cambridge, CB2 1PZ, UK;

Department of Statistics and Applied Probability, National University of Singapore;

Department of Statistical Science, University College London;

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正文语种 eng
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关键词
approximate Bayesian computation; hidden Markov model; parameter estimation; sequential Monte Carlo;

机译：近似贝叶斯计算;隐马尔可夫模型参数估计;顺序蒙特卡洛;

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专利

1. Parameter Estimation in Hidden Markov Models With Intractable Likelihoods Using Sequential Monte Carlo [J] . Yildirim Sinan, Singh Sumeetpal S., Dean Thomas, Journal of computational and graphical statistics: A joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America . 2015,第3期

机译：隐马尔可夫模型的似然性隐马尔可夫模型的参数估计
2. Gradient Free Parameter Estimation for Hidden Markov Models with Intractable Likelihoods [J] . Elena Ehrlich, Ajay Jasra, Nikolas Kantas Methodology and Computing in Applied Probability . 2015,第2期

机译：具有难以解决的隐马尔可夫模型的梯度自由参数估计
3. Gradient Free Parameter Estimation for Hidden Markov Models with Intractable Likelihoods [J] . Ehrlich Elena, Jasra Ajay, Kantas Nikolas Methodology and computing in applied probability . 2015,第2期

机译：具有难以解决的隐马尔可夫模型的梯度自由参数估计
4. Weighted Maximum Likelihood for Parameters Learning Based on Noisy Labels in Discrete Hidden Markov Models [C] . Pablo Juesas Cano, Emmanuel Ramasso European conference on symbolic and quantitative approaches to reasoning with uncertainty . 2015

机译：离散隐马尔可夫模型中基于噪声标签的参数学习加权最大似然
5. Automatic feature learning and parameter estimation for Hidden Markov models using MCE and Gibbs sampling. [D] . Zhang, Xuping. 2009

机译：使用MCE和Gibbs采样对隐马尔可夫模型进行自动特征学习和参数估计。
6. A novel algorithm for parameter estimation of Hidden Markov Model inspired by Ant Colony Optimization [O] . Akram Emdadi, Fatemeh Ahmadi Moughari, Fatemeh Yassaee Meybodi, 2019

机译：蚁群优化启发的隐马尔可夫模型参数估计新算法
7. Parameter Estimation for Hidden Markov Models with Intractable Likelihoods [O] . Thomas A. Dean, Sumeetpal S. Singh, Ajay Jasra, 2014

机译：具有棘手似然性的隐马尔可夫模型的参数估计

Parameter Estimation for Hidden Markov Models with Intractable Likelihoods

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