Bayesian Inference for State Space Models using Block and Correlated Pseudo Marginal Methods

Choppala, Praveen B.; Gunawan, David; Chen, J.; Tran, Minh‐Ngoc; Kohn, Robert

doi:10.48550/arxiv.1612.07072

Cited by 4 publications

(5 citation statements)

References 17 publications

(32 reference statements)

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“…Deligiannidis et al (2018) use the Hilbert sorting method of Skilling (2004) to order multidimensional state particles. Our article uses a simpler and faster method proposed by Choppala et al (2016) and given in Section S3 of the Supplement. Algorithm S1 in Section S1 of the Supplement outlines the correlated disturbance particle filter algorithm used by the MPM algorithm described in Section 3.3.…”

Section: The Disturbance Particle Filtermentioning

confidence: 99%

“…Step (2a) sorts the state or disturbance particles from smallest to largest using the simple Euclidean sorting procedure of Choppala et al (2016) to obtain the sorted disturbance particles, sorted state particles and weights. Algorithm S2 resamples the particles using multinomial resampling to obtain the ancestor index a 1:N t−1 in the original order of particles in steps (2b) and (2c).…”

Section: S1 the Disturbance Particle Filter Algorithmmentioning

confidence: 99%

“…• (2a) Sort the state particles z i t−1 or disturbance particles i t−1 using the Euclidean sorting method of Choppala et al (2016) and obtain the sorted index ζ i for i = 1, ..., N , and the sorted state particles, disturbance particles, and weights…”

Section: Algorithm S1mentioning

confidence: 99%

See 2 more Smart Citations

An efficient pseudo marginal method for state space models

Gunawan¹,

Chatterjee²,

Kohn³

2021

Preprint

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Pseudo Marginal Metropolis-Hastings (PMMH) is a general approach to carry out Bayesian inference when the likelihood is intractable but can be estimated unbiasedly. Our article develops an efficient PMMH method for estimating the parameters of complex and high-dimensional state space models and has the following features. First, it runs multiple particle filters in parallel and uses their averaged unbiased likelihood estimate. Second, it combines block and correlated PMMH sampling. The first two features enable our sampler to scale up better to longer time series and higher dimensional state vectors than previous approaches. Third, the article develops an efficient auxiliary disturbance particle filter, which is necessary when the bootstrap filter is inefficient, but the state transition density cannot be expressed in closed form. Fourth, it uses delayed acceptance to make the make the sampler more efficient. The performance of the sampler is investigated empirically by applying it to Dynamic Stochastic General Equilibrium models with relatively high state dimensions and with intractable state transition densities. Although our focus is on applying the method to state space models, the approach will be useful in a wide range of applications such as large panel data models and stochastic differential equation models with mixed effects.

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Section: The Disturbance Particle Filtermentioning

confidence: 99%

Section: S1 the Disturbance Particle Filter Algorithmmentioning

confidence: 99%

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An efficient pseudo marginal method for state space models

Gunawan¹,

Chatterjee²,

Kohn³

2021

Preprint

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“…While the likelihood of the UCSV model is intractable, exact posterior inference can be evaluated here using particle, MCMC or other methods (Chan, 2013, Kantas et al, 2015, Choppala et al, 2016, Katzfuss et al, 2019, and we do so to judge the accuracy of our VA. For comparison we also calibrate the structured Gaussian VA…”

Section: Estimationmentioning

confidence: 99%

Fast and Accurate Variational Inference for Models with Many Latent Variables

Loaiza-Maya¹,

Smith²,

Nott³

et al. 2020

Preprint

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Models with a large number of latent variables are often used to fully utilize the information in big or complex data. However, they can be difficult to estimate using standard approaches, and variational inference methods are a popular alternative. Key to the success of these is the selection of an approximation to the target density that is accurate, tractable and fast to calibrate using optimization methods. Mean field or structured Gaussian approximations are common, but these can be inaccurate and slow to calibrate when there are many latent variables. Instead, we propose a family of tractable variational approximations that are more accurate and faster to calibrate for this case. The approximation is a parsimonious copula model for the parameter posterior, combined with the exact conditional posterior of the latent variables. We derive a simplified expression for the re-parameterization gradient of the variational lower bound, which is the main ingredient of efficient optimization algorithms used to implement variational estimation. We illustrate using two substantive econometric examples. The first is a nonlinear state space model for U.S. inflation. The second is a random coefficients tobit model applied to a rich marketing dataset with one million sales observations from a panel of 10,000 individuals. In both cases, we show that our approximating family is faster to calibrate than either mean field or structured Gaussian approximations, and that the gains in posterior estimation accuracy are considerable.

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“…This is particularly useful when T is large as it decreases the computational cost of PMH. See Dahlin et al (2015a), Choppala et al (2016) and Deligiannidis et al (2018) for more information and source code.…”

Section: Outlook: Generalizationsmentioning

confidence: 99%

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

Dahlin¹,

Schön²

2019

J. Stat. Soft.

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This tutorial provides a gentle introduction to the particle Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear state-space models together with a software implementation in the statistical programming language R. We employ a step-by-step approach to develop an implementation of the PMH algorithm (and the particle filter within) together with the reader. This final implementation is also available as the package pmhtutorial from the Comprehensive R Archive Network (CRAN) repository. Throughout the tutorial, we provide some intuition as to how the algorithm operates and discuss some solutions to problems that might occur in practice. To illustrate the use of PMH, we consider parameter inference in a linear Gaussian state-space model with synthetic data and a nonlinear stochastic volatility model with real-world data.

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Bayesian Inference for State Space Models using Block and Correlated Pseudo Marginal Methods

Cited by 4 publications

References 17 publications

An efficient pseudo marginal method for state space models

An efficient pseudo marginal method for state space models

Fast and Accurate Variational Inference for Models with Many Latent Variables

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

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