eprintid: 1474758 rev_number: 21 eprint_status: archive userid: 608 dir: disk0/01/47/47/58 datestamp: 2017-03-29 14:57:56 lastmod: 2020-02-12 21:26:39 status_changed: 2017-03-29 14:57:56 type: article metadata_visibility: show creators_name: Ghosh, A creators_name: Mukhopadhyay, S creators_name: Roy, S creators_name: Bhattacharya, S title: Bayesian inference in nonparametric dynamic state-space models ispublished: pub divisions: UCL divisions: A01 divisions: B04 divisions: C06 keywords: Evolutionary equation; Gaussian process; Look-up table; Markov Chain Monte Carlo; Observational equation; State-space model. note: Copyright © 2014 Elsevier B.V. This manuscript version is made available under the CC-BY-NC-ND 4.0 license (http://creativecommons.org/licenses/by-nc-nd/4.0/) abstract: We introduce state-space models where the functionals of the observational and 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 Bhattacharya (2007) 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. We illustrate our methods with simulated data sets, in both univariate and multivariate situations. Moreover, using our Gaussian process approach we analyze a real data set, which has also been analyzed by Shumway & Stoffer (1982) and Carlin, Polson & Stoffer (1992) using the linearity assumption. Interestingly, our analyses indicate that towards the end of the time series, the linearity assumption is perhaps questionable. date: 2014-11 official_url: http://dx.doi.org/10.1016/j.stamet.2014.02.004 oa_status: green full_text_type: other language: eng primo: open primo_central: open_green article_type_text: Journal Article verified: verified_manual elements_id: 792185 doi: 10.1016/j.stamet.2014.02.004 lyricists_name: Roy, Sandipan lyricists_id: SROYX33 actors_name: Roy, Sandipan actors_id: SROYX33 actors_role: owner full_text_status: public publication: Statistical Methodology volume: 21 pagerange: 35-48 issn: 1572-3127 citation: Ghosh, A; Mukhopadhyay, S; Roy, S; Bhattacharya, S; (2014) Bayesian inference in nonparametric dynamic state-space models. Statistical Methodology , 21 pp. 35-48. 10.1016/j.stamet.2014.02.004 <https://doi.org/10.1016/j.stamet.2014.02.004>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/1474758/1/1108.3262v5.pdf