Introduction to 'Particle Metropolis-Hastings using gradient and Hessian information' by J. Dahlin, F. Lindsten, T. Schoen

Christophe Andrieu

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Introduction to 'Particle Metropolis-Hastings using gradient and Hessian information' by J. Dahlin, F. Lindsten, T. Schoen

机译：J. Dahlin，F。Lindsten和T. Schoen撰写的“使用梯度和Hessian信息的大都市-黑斯廷斯”简介

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The authors investigate the use of metropolis adjusted Langevin algorithms (MALA) in the context of particle MCMC algorithms. The ability to use this type of updates can lead to more efficient MCMC algorithms. The challenge in this context is that MALA and more sophisticated versions require the evaluation of the gradient of the log-likelihood and/or its Hessian, which are not available analytically. A way around this consists of estimating these quantities numerically. This can be achieved efficiently by exploiting the particle filter output used to compute the estimator of the likelihood function required to implement particle MCMCs. This idea was proposed originally in Doucet et al. (2011) and similar ideas have been subsequently investigated in Nemeth and Fearnhead (2014) and Dahlin et al. (2013) and Dahlin et al. (2014).

机译：作者研究了在粒子MCMC算法的背景下大都会调整的Langevin算法（MALA）的使用。使用这种类型的更新的能力可以导致更有效的MCMC算法。在这种情况下的挑战是，MALA和更复杂的版本要求对数似然和/或其Hessian的梯度进行评估，而这在分析上是不可用的。解决这个问题的方法是通过数字估算这些数量。这可以通过利用用于计算实现粒子MCMC所需的似然函数的估计量的粒子滤波器输出来有效地实现。这个想法最初是在Doucet等人中提出的。（2011年）和类似的想法随后在Nemeth和Fearnhead（2014年）和Dahlin等人中进行了研究。（2013）和Dahlin等。（2014）。

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《Statistics and computing》 |2015年第1期|79-79|共1页
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Christophe Andrieu;
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Department of Mathematics, University of Bristol, Bristol BS8 1TW, UK;

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Introduction to 'Particle Metropolis-Hastings using gradient and Hessian information' by J. Dahlin, F. Lindsten, T. Schoen

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