Particle Metropolis-adjusted Langevin algorithms

Markov chain Monte Carlo algorithms are a popular and well-studied methodology that can be used to draw samples from posterior distributions. Over the past few years these algorithms have been extended to tackle problems where the model likelihood is intractable (Beaumont, 2003). Andrieu and Roberts (2009) showed that within the Metropolis-Hastings algorithm, if the likelihood is replaced with an unbiased estimate, then the sampler still targets the correct stationary distribution. Andrieu et al. (2010) extended this work further to create a class of 1 Markov chain algorithms that use sequential Monte Carlo methods, also known as particle filters. Current implementations of pseudo-marginal and particle Markov chain Monte Carlo use random-walk proposals to update the parameters (e.g., Golightly and Wilkinson, 2011; Knape and de Valpine, 2012) and shall be referred to herein as particle random-walk Metropolis algorithms. Random walk-based algorithms propose a new value from some symmetric density centred on the current value.