In this week's UCL Statistical Science seminar (31st March 14:00-15:00 ), Prof. Judith Rousseau (University of Oxford) will talk about:
The use of cut posterior for semi-parametric inference with application to nonparametric hidden Markov models
We consider the problem of estimation in Hidden Markov models with finite state space and nonparametric emission distributions. Efficient estimators for the transition matrix are exhibited, and a semiparametric Bernstein-von Mises result is deduced, extending previous work on mixture models to the HMM setting. Following from this, we propose a modular approach using the cut posterior to jointly estimate the transition matrix and the emission densities. We derive a general theorem on contraction rates for this approach, and we then show how this result may be applied to obtain a contraction rate result for the emission densities in our setting; a key intermediate step is an inversion inequality relating L1 distance between the marginal densities to L1 distance between the emissions. Finally, a contraction result for the smoothing probabilities is shown, which avoids the common approach of sample splitting. Simulations are provided which demonstrate both the theory and the ease of its implementation
This is joint work with Dan Moss.
More information / how to join:
https://www.ucl.ac.uk/statistics/seminar
Dr. F. Javier Rubio
Lecturer
Department of Statistical Science
University College London
https://sites.google.com/site/fjavierrubio67/
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