School of Mathematical Sciences

Continuation Bayesian inference

Date(s)
Wednesday 11th December 2024 (14:00-15:00)
Contact
Event Convenor Contact: Luis.Espath@nottingham.ac.uk

Description
Speaker's Name: Ben Mansour Dia
Speaker's Affiliation: College of Petroleum Engineering & Geosciences, KFUPM, KSA
Speaker's Research Theme(s): Statistics and Probability,Applied Mathematics
Abstract:
We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. We interpret the posterior probability distribution as the final state of a path of transition distributions. A computationally stable scaling domain for the likelihood is explored for approximation of the expected deviance, where we restrict the evaluations of the forward predictive model at the prior stage. To obtain a solution formulation for the expected deviance, we derive a partial differential equation governing the moment-generating function of the log-likelihood. The effectiveness of the proposed method is demonstrated using four numerical examples. These focus on analyzing the computational bias generated by the method, assessing its use in Bayesian inference with non-Gaussian noise, evaluating its ability to invert a multimodal parameter of interest, and quantifying its performance in terms of computational cost. Finally, we discuss the use of the continuation framework in experimental design.

Venue: MS Teams
Online Conference Link: https://teams.microsoft.com/l/meetup-join/19%3ab47138845b244539bd7eb85b7fe2c72d%40thread.tacv2/1733134113436?context=%7b%22Tid%22%3a%2267bda7ee-fd80-41ef-ac91-358418290a1e%22%2c%22Oid%22%3a%22eb81f9d3-cc74-4322-b462-c8f8f467bfcf%22%7d

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

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