(A bit of modelling and) Statistical inference for non-renewal point processes via Approximate Bayesian Computation. An application to neuroscience.
Sprache des Vortragstitels:
In many signal-processing applications, it is of primary interest to decode or reconstruct the unobserved signal based on some partially observed information. Statistically, this corresponds to perform statistical inference of the underlying model parameters from partially observed stochastic processes and/or non-renewal point processes (where each event is the epoch when a coordinate reaches/crosses a certain value, yielding the so-called first-passage-time problem). Moreover, due to the increasing complexity of the processes, the underlying likelihoods are often unknown or intractable. The problem belongs to the class of intractable-likelihood inference problems, requiring the investigation of new ad-hoc mathematical, numerical and statistical techniques to handle it. Here I focus on likelihood-free methods, and in particular on Approximate Bayesian Computation (ABC) method, and I illustrate it in the framework of stochastic modelling of single neuron dynamics.
More specifically, I consider a bivariate stochastic process where available observations are the hitting times of one coordinate to the other, and discuss it in the framework of stochastic modelling of single neuron dynamics. The considered multi-timescale adaptive threshold model can be derived from the detailed Hodgkin-Huxley model, can accurately predict spike times and incorporate the effects of slow K+ currents, usually mediating adaptation. When performing statistical inference of the underlying model parameters, four difficulties arise: none of the two model components is directly observed; the considered process is not of hidden Markov model type; the underlying likelihood is unknown/intractable; consecutive hitting times are neither independent nor identically distributed. I tackle these statistical issues considering a simple acceptance-rejection ABC algorithm. After presenting the ABC method and discussing its criticality and challenges, I illustrate how to use it on the considered model.