OxCSML seminar this week: Mathieu Gerber
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Hai Dang Dau
Mar 4, 2024, 11:11:11 AM3/4/24
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Dear all,
This week we welcome Mathieu Gerber from University of Bristol to give a talk in our OxCSML seminar. Details can be found below.
Looking forward to seeing you there,
Rebecca, Saif, and Hai-Dang
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Speaker: Mathieu Gerber (University of Bristol)
Time and date: 2-3pm, Friday 8 March
Place: Large Lecture Theatre (LG.01), Department of Statistics
Zoom: https://zoom.us/j/98174740718?pwd=VzB4YTdqTXpJM1p4a2k0dmFXQm9nQT09
Title: Online parameter and state estimation in state space models
Abstract: The idea to perform online state and parameter estimation in state-space models (SSMs) by treating the model parameter as an additional state variable, and then by applying a standard filtering technique on the extended model, almost dates back to the origin of the Kalman filter algorithm. However, the implementation of this idea in a theoretically justified way has remained an open problem, mainly for the following reason: On the one hand, we ideally want to treat the model parameter as a hidden Markov chain with no dynamic, so that the corresponding filtering distribution coincides with the Bayesian posterior distribution of the model. But on the other hand, particle filter algorithms require the state variables to have a proper dynamic to be deployed. Following an idea proposed by some authors, we show in this work that we can bypass this problem by adding an artificial dynamic on the parameter of the model. The filtering distribution of the resulting SSM can be easily estimated using a standard particle filter algorithm, and we prove that the marginal filtering distribution for the model parameter concentrates on the target parameter value. We also derive convergence guarantees for the predictions computed with the extended SSM and, as a by-product of these results, we introduce an improved version of the iterated filtering algorithm for computing the maximum likelihood estimator in SSMs.
Joint work with Christophe Andrieu, Yuan Chen and Randal Douc.
Time and date: 2-3pm, Friday 8 March
Place: Large Lecture Theatre (LG.01), Department of Statistics
Zoom: https://zoom.us/j/98174740718?pwd=VzB4YTdqTXpJM1p4a2k0dmFXQm9nQT09
Title: Online parameter and state estimation in state space models
Abstract: The idea to perform online state and parameter estimation in state-space models (SSMs) by treating the model parameter as an additional state variable, and then by applying a standard filtering technique on the extended model, almost dates back to the origin of the Kalman filter algorithm. However, the implementation of this idea in a theoretically justified way has remained an open problem, mainly for the following reason: On the one hand, we ideally want to treat the model parameter as a hidden Markov chain with no dynamic, so that the corresponding filtering distribution coincides with the Bayesian posterior distribution of the model. But on the other hand, particle filter algorithms require the state variables to have a proper dynamic to be deployed. Following an idea proposed by some authors, we show in this work that we can bypass this problem by adding an artificial dynamic on the parameter of the model. The filtering distribution of the resulting SSM can be easily estimated using a standard particle filter algorithm, and we prove that the marginal filtering distribution for the model parameter concentrates on the target parameter value. We also derive convergence guarantees for the predictions computed with the extended SSM and, as a by-product of these results, we introduce an improved version of the iterated filtering algorithm for computing the maximum likelihood estimator in SSMs.
Joint work with Christophe Andrieu, Yuan Chen and Randal Douc.
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