Bayesian Inference in Nonparametric Dynamic State-Space Models

Anurag Ghosh, Soumalya Mukhopadhyay, Sandipan Roy, Sourabh Bhattacharya

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Abstract

We introduce state-space models where the functionals of the observational and the evolutionary equations are unknown, and treated as random functions evolving with time. Thus, our model is nonparametric and generalizes the traditional parametric state-space models. This random function approach also frees us from the restrictive assumption that the functional forms, although time-dependent, are of fixed forms. The traditional approach of assuming known, parametric functional forms is questionable, particularly in state-space models, since the validation of the assumptions require data on both the observed time series and the latent states; however, data on the latter are not available in state-space models. We specify Gaussian processes as priors of the random functions and exploit the "look-up table approach" of \ctn{Bhattacharya07} to efficiently handle the dynamic structure of the model. We consider both univariate and multivariate situations, using the Markov chain Monte Carlo (MCMC) approach for studying the posterior distributions of interest. In the case of challenging multivariate situations we demonstrate that the newly developed Transformation-based MCMC (TMCMC) of \ctn{Dutta11} provides interesting and efficient alternatives to the usual proposal distributions. We illustrate our methods with a challenging multivariate simulated data set, where the true observational and the evolutionary equations are highly non-linear, and treated as unknown. The results we obtain are quite encouraging. Moreover, using our Gaussian process approach we analysed a real data set, which has also been analysed by \ctn{Shumway82} and \ctn{Carlin92} using the linearity assumption. Our analyses show that towards the end of the time series, the linearity assumption of the previous authors breaks down.
Original languageEnglish
Pages (from-to)35 - 48
Number of pages14
JournalStatistical Methodology
Volume21
Early online date4 Mar 2014
DOIs
Publication statusPublished - 1 Nov 2014

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State-space Model
Bayesian inference
Random Function
Dynamic Model
Markov Chain Monte Carlo
Gaussian Process
Linearity
Time series
Unknown
Look-up Table
Parametric Model
Posterior distribution
Univariate
Breakdown
Generalise
Alternatives
Model
Demonstrate
Form

Keywords

  • stat.ME

Cite this

Bayesian Inference in Nonparametric Dynamic State-Space Models. / Ghosh, Anurag; Mukhopadhyay, Soumalya; Roy, Sandipan; Bhattacharya, Sourabh.

In: Statistical Methodology, Vol. 21, 01.11.2014, p. 35 - 48.

Research output: Contribution to journalArticle

Ghosh, Anurag ; Mukhopadhyay, Soumalya ; Roy, Sandipan ; Bhattacharya, Sourabh. / Bayesian Inference in Nonparametric Dynamic State-Space Models. In: Statistical Methodology. 2014 ; Vol. 21. pp. 35 - 48.
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