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Duality methods in Bayesian inference for hidden Markov models


   Department of Mathematics `G. Peano'

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  Prof Matteo Ruggiero  No more applications being accepted  Competition Funded PhD Project (Students Worldwide)

About the Project

Abstract

The project deals with Bayesian inference on the trajectory of a diffusion process or on the parameters that characterize its drift and volatility, under the assumption of a hidden Markov model framework with noisy data collection. The target of inference is the trajectory of the diffusion, called signal, which in this framework is assumed to be unobserved and to modulate the so called emission distribution, namely the conditional distribution of the data given the current value of the process. Duality typically allows to write the conditional distributions of the signal given the data in simpler forms than those obtained through the transition density of the signal, especially when the latter is only available as a series expansion. In particular, when the dual process lives on a discrete space, these distributions become finite or countable mixtures of kernels that belong to the same family of the emission distribution. These can be shown to characterise the filtering and, under additional assumptions, the smoothing distribution and the likelihood. These quantities then can in turn be used to set up MCMC strategies that target the estimation of the parameters of the diffusion.

The current project aims at expanding on the results obtained in [1,2,3] and related papers, investigating new scenarios which may include different signals or different type of dualities, approximations of exact results and other acceleration techniques, both from the theoretical point of view and concerning the implementations for inference.

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General Info

This project will be carried out in the Department of Economics Social Sciences and Management.

This PhD project is part of a call for 5 fully funded PhD scholarships in the framework of the PhD in Modeling and Data Science https://dottorato-mds.campusnet.unito.it/do/home.pl at the University of Turin (Italy). The call will open on 28 April 2022 (date TBC). The scholarship is for three years, starting in October 2022. We are looking for expressions of interests for the PhD Program, and we welcome full applications once the call is live. 

The PhD program is interdisciplinary, and it involves branches of mathematics, informatics, economics, statistics, and physics.

 All interested candidates should submit their application online via the link https://www.phd.unito.it/do/home.pl/View?doc=Submitting_your_application.html. Deadline for applying is 30 May 2022 (date TBC). Notice that the application requires two reference letters, which should be submitted via the same link by the referees before the application deadline. The referees will be able to submit their letters only after the candidate has input all the required information and closed their (part of the) application. If the letters are not submitted by the deadline the application will not be valid.

 For more information, do not hesitate to contact the supervisor(s). More information, including the official call and all relevant (confirmed) deadlines, can also be found here https://dottorato-mds.campusnet.unito.it/do/home.pl/View?doc=/content/Admission.html.

The call for applications is available at the page https://www.dottorato.unito.it/do/home.pl/View?doc=Bando_XXXVIII_ciclo.html

Admission details and the list of projects can be found here https://www.dottorato.unito.it/do/documenti.pl/ShowFile?_id=g3ot;field=file;key=JbqgKqg0lroYaYMa8BXEFYBVz1z8MXSdAKr7fGFtPR2;t=3298


Funding Notes

A call for 5 fully funded PhD scholarships in the framework of the PhD in Modeling and Data Science https://dottorato-mds.campusnet.unito.it/do/home.pl at the University of Turin (Italy) will open on 28 April 2022 (date TBC). The scholarship is for three years, starting in October 2022. Deadline for applying is 30 May 2022 (date TBC).

References

[1] Papaspiliopoulos, O. and Ruggiero, M. (2014). Optimal filtering and the dual process. Bernoulli 20, 1999-2019.
[2] Papaspiliopoulos, O., Ruggiero, M., and Spanò, D. (2016). Conjugacy properties of time-evolving Dirichlet and gamma random measures. Electronic Journal of Statistics 10, 3452-3489.
[3] Kon Kam King, G., Papaspiliopoulos, O. and Ruggiero, M. (2021). Exact inference for a class of hidden Markov models on general state spaces. Electronic Journal of Statistics 15, 2832-2875.
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