University of Birmingham > Talks@bham > Data Science and Computational Statistics Seminar > Variational Bayesian inference for point processes - a latent variable approach

Variational Bayesian inference for point processes - a latent variable approach

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We consider Bayesian inference for estimating the intensity function of inhomogeneous Poisson processes, where the intensity function is modelled by a Gaussian process (GP) prior via a sigmoidal link function. Augmenting the model by a latent marked Poisson process and Polya-Gamma random variables we obtain a representation of the likelihood which is conditionally conjugate to the GP prior. To allow for tractable inference, we use a variational approach where the exact posterior distribution over unknown functions and latent variables is approximated by a simpler factorising distribution which minimises the Kullback-Leibler divergence to the exact posterior. We will present extensions of the latent variable approach to Bayesian nonparametric density estimation, to kinetic Ising models for the analysis of the binary spiking activity from ensembles of neurons and to Hawke’s processes for the modelling of earthquake occurrences.

This talk is part of the Data Science and Computational Statistics Seminar series.

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