On some properties of Markov chain Monte Carlo simulation methods based on the particle filter

By Michael K. Pitt, Ralph S. Silva, Paolo Giordani, Robert Kohn. 2012

297 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f1647f05e3c090d033a29e80e9a8dc6b773969bd

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Citations in the corpus

Self-Exciting Jumps, Learning, and Asset Pricing Implications (2015, methodology): “Pitt et al. (2012) provide practical guidelines on how to choose optimal number of state particles (M).”
Particle gibbs with ancestor sampling (2014, background): “PMCMC has in a relatively short period of time found many applications in areas such as hydrology (Vrugt et al., 2013), finance (Pitt et al., 2012), systems biology (Golightly and Wilkinson, 2011), and epidemiology (Rasmussen et al., 2011), to mention a few.”
Particle Value Functions (2017, background): “The result is an unbiased estimator )) of the desired probability (Del Moral, 2004; Pitt et al., 2012).”
Variational Sequential Monte Carlo (2017, methodology): “The normalization constant estimate of the SMC sampler, (cid:98) p ( y 1: T ) , is unbiased [Del Moral, 2004, Pitt et al., 2012, Naesseth et al., 2014].”
Bayesian State-Space Modelling on High-Performance Hardware Using LibBi (2013, background): “For PMMH and SMC2, a critical measure of performance is the variance of the estimate of the marginal likelihood delivered by SMC (see e.g., Pitt et al. 2012; Doucet et al. 2013; Murray et al. 2013).”
Nonlinear System Identification: A User-Oriented Road Map (2019, methodology): “What is perhaps most relevant for the present discussion is that the SMC method is capable of producing unbiased estimators of the likelihood [43], [44].”
Bayesian Model Comparison for Time-Varying Parameter VARs with Stochastic Volatility (2018, unknown): “The model of Primiceri (2005)—with both time-varying parameters and stochastic volatility—is overwhelmingly favored by the data compared to a conventional VAR according to both criteria.”
Bayesian forecasting in economics and finance: A modern review (2022, methodology): “We refer the reader to Raftery et al. (2010) for the initial proposal of DMA, Koop and Korobilis (2012) for the application of the method to forecasting inflation, and Nonejad (2021) for a recent review of the methodology, with a focus on applications in economics and finance.”
Filtering Variational Objectives (2017, background): “Because p̂N (x1:T ) is an unbiased estimator of p(x1:T ), proven in the Appendix and in [23, 24, 25, 26], it defines an MCO, which we call FIVO: Definition 2.”
On the efficiency of pseudo-marginal random walk Metropolis algorithms (2013, background): “[24] consider the (unrealistic) case where the Metropolis–Hastings algorithm is an independence sampler which proposes from the desired target distribution for x, and obtain an optimal variance of 0.”
The correlated pseudomarginal method (2015, unknown): “Assuming that the likelihood estimator is evaluated using importance sampling or particle filters for state-space models with N particles, it has also been shown under various assumptions in [45], [18] and [48] that N should be selected such that the variance of the loglikelihood ratio estimator sho”
Interacting Particle Markov Chain Monte Carlo (2016, background): “There exist theoretical and experimental results (Pitt et al., 2012; Bérard et al., 2014; Doucet et al., 2015) that show that the distributions of the normalisation constants are wellapproximated by their log-Normal limiting distributions.”
Importance Sampling Squared for Bayesian Inference in Latent Variable Models (2013, methodology): “As demonstrated in Pitt et al. (2012), the representation in terms of z is useful because it allows us to use the available properties of z to study the properties of the estimators.”