Multilevel particle filters: normalizing constant estimation
| Autor: | Kengo Kamatani, Ajay Jasra, Prince Peprah Osei, Yan Zhou |
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| Rok vydání: | 2016 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Discrete mathematics Mathematical optimization Discretization Mean squared error Normalizing constant Order (ring theory) 010103 numerical & computational mathematics Statistics - Computation 01 natural sciences Marginal likelihood Theoretical Computer Science 010104 statistics & probability symbols.namesake Computational Theory and Mathematics Euler's formula symbols Almost surely 0101 mathematics Statistics Probability and Uncertainty Particle filter Computation (stat.CO) Mathematics |
| Zdroj: | Statistics and Computing. 28:47-60 |
| ISSN: | 1573-1375 0960-3174 |
| DOI: | 10.1007/s11222-016-9715-5 |
| Popis: | In this article we introduce two new estimates of the normalizing constant (or marginal likelihood) for partially observed diffusion (POD) processes, with discrete observations. One estimate is biased but non-negative and the other is unbiased but not almost surely non-negative. Our method uses the multilevel particle filter of Jasra et al (2015). We show that, under assumptions, for Euler discretized PODs and a given $\varepsilon>0$. in order to obtain a mean square error (MSE) of $\mathcal{O}(\varepsilon^2)$ one requires a work of $\mathcal{O}(\varepsilon^{-2.5})$ for our new estimates versus a standard particle filter that requires a work of $\mathcal{O}(\varepsilon^{-3})$. Our theoretical results are supported by numerical simulations. arXiv admin note: substantial text overlap with arXiv:1510.04977 |
| Databáze: | OpenAIRE |
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