Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models

Dahlin, Johan; Schön, Thomas B.

doi:10.18637/jss.v088.c02

Cited by 18 publications

(24 citation statements)

References 63 publications

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“…In this section we will provide some background on particle filters, Markov chain Monte Carlo (MCMC) and related methods. For a more elaborate introduction, please refer to, e.g., Schön et al (2018); Dahlin and Schön (2016); Robert and Casella (2004). We will in particular discuss why models on the form (1) are problematic for most existing methods, and also introduce the notion of tempering.…”

Section: Background On Particle Filtering and Temperingmentioning

confidence: 99%

“…The settings of PMH can indeed be optimized by using more clever proposals than random walks (see, e.g., Dahlin and Schön (2016) for an overview) and methods for reducing the variance of z (such as adapted or bridging particle filter Del Moral and Murray (2015); Pitt and Shephard (1999); Del ). Such adaption would indeed push the performance further.…”

Section: A More Challenging Nonlinear Examplementioning

confidence: 99%

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Learning of state-space models with highly informative observations: A tempered sequential Monte Carlo solution

Svensson¹,

Schön²,

Lindsten³

2018

Mechanical Systems and Signal Processing

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2018. Learning of state-space models with highly informative observations: a tempered Sequential Monte Carlo solution. In Mechanical Systems and Signal Processing, Volume 104, pp. 915-928. @article{SvenssonSL:2018, author = {Svensson, Andreas and Sch\"on, Thomas B. and Lindsten, Fredrik}, title = {Learning of state-space models with highly informative observations: a tempered Sequential {Monte} {Carlo} solution}, journal = {Mechanical Systems and Signal Processing}, volume = {104}, year = {2018}, pages = {915--928}, } AbstractProbabilistic (or Bayesian) modeling and learning offers interesting possibilities for systematic representation of uncertainty using probability theory. However, probabilistic learning often leads to computationally challenging problems. Some problems of this type that were previously intractable can now be solved on standard personal computers thanks to recent advances in Monte Carlo methods. In particular, for learning of unknown parameters in nonlinear state-space models, methods based on the particle filter (a Monte Carlo method) have proven very useful. A notoriously challenging problem, however, still occurs when the observations in the state-space model are highly informative, i.e. when there is very little or no measurement noise present, relative to the amount of process noise. The particle filter will then struggle in estimating one of the basic components for probabilistic learning, namely the likelihood p(data|parameters). To this end we suggest an algorithm which initially assumes that there is substantial amount of artificial measurement noise present. The variance of this noise is sequentially decreased in an adaptive fashion such that we, in the end, recover the original problem or possibly a very close approximation of it. The main component in our algorithm is a sequential Monte Carlo (SMC) sampler, which gives our proposed method a clear resemblance to the SMC 2 method. Another natural link is also made to the ideas underlying the approximate Bayesian computation (ABC). We illustrate it with numerical examples, and in particular show promising results for a challenging Wiener-Hammerstein benchmark problem.

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Section: Background On Particle Filtering and Temperingmentioning

confidence: 99%

Section: A More Challenging Nonlinear Examplementioning

confidence: 99%

Learning of state-space models with highly informative observations: A tempered sequential Monte Carlo solution

Svensson¹,

Schön²,

Lindsten³

2018

Mechanical Systems and Signal Processing

Self Cite

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“…First, the chains’ trace plots are stationary around specific values, showing high quality and samples’ stability representing the posterior distribution [69] (Figs in S1 Fig, S2 Fig, S3 Fig, and S4 Fig). The second examines the auto-correlation as an essential indicator of the convergence [68]. We have minimal correlations between the samples and the previous ones (the correlation vanishes after the fourth lag).…”

Section: Resultsmentioning

confidence: 99%

“…The parallel estimation of the latent states and the parameters was a challenge. The combined evaluation will be like two loops: one outer loop for parameters’ estimation, and an inner loop for sequential Monte Carlo estimation of the latent states’ trajectory and the related likelihood functions based on the estimated parameters in the outer loop (see Algorithm 2) [68].…”

Section: Particle Independent Metropolis-hastingsmentioning

confidence: 99%

Quantifying non-communicable diseases’ burden in Egypt using State-Space model

El-Saadani

Saleh

Ibrahim

2021

Preprint

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The study aimed to model and quantify the health burden induced by four non-communicable diseases in Egypt, the first to be conducted in the context of a less developing county. The study used the State-Space model and adopted two Bayesian methods: Particle Filter and Particle Independent Metropolis-Hastings to model and estimate the NCDs’ health burden trajectories. We drew on time-series data of the International Health Metric Evaluation, CAPMAS’s Annual Bulletin of Health Services Statistics, the World Bank, and WHO data. Both Bayesian methods showed that the burden trajectories are on the rise. Most of the findings agreed with our assumptions and are in line with the literature. Previous year burden strongly predicts the burden of the current year. High prevalence of the risk factors, disease prevalence, and the disease’s severity level all increase illness burden. Years of life lost due to death has high loadings in most of the diseases. Contrary to the study assumption, results found a negative relationship between disease burden and health services utilization which can be attributed to the lack of full health insurance coverage and the pattern of health care seeking behavior in Egypt. Our study highlights that Particle Independent Metropolis-Hastings is sufficient in estimating the parameters of the study model, in the case of time-constant parameters. The study recommends using state Space models with Bayesian estimation approaches with time-series data in public health and epidemiology research.

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“…Joint static and dynamic parameter learning is achieved by embedding Metropolis-Hastings algorithm within Unscented Kalman Filtering framework. A general description of the framework is presented in 7 . The framework is fully Bayesian as the posterior probability of the static and dynamic parameters is obtained which is unique for the method, allowing for the measurement uncertainty quantification.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Joint Learning of Laser Relative Intensity and Frequency Noise from Single Experiment and Single Detected Quadrature

Brajato

Zibar

2018

2018 European Conference on Optical Communication (ECOC)

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Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models

Cited by 18 publications

References 63 publications

Learning of state-space models with highly informative observations: A tempered sequential Monte Carlo solution

Learning of state-space models with highly informative observations: A tempered sequential Monte Carlo solution

Quantifying non-communicable diseases’ burden in Egypt using State-Space model

Joint Learning of Laser Relative Intensity and Frequency Noise from Single Experiment and Single Detected Quadrature

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