Likelihood-free methods for the inference of non-renewal point processes arising from neuroscience
Sprache des Vortragstitels:
European Conference of Mathematical and Theoretical Biology 2018
Sprache des Tagungstitel:
In many signal-processing applications, it is of primary interest to decode or reconstruct the unobserved signal based on some partially observed information. Some examples are all type of recognition (e.g. automatic speech, face, gesture, handwriting), genetics, genomics and neuroscience (ion channels modelling). From a mathematical point of view, this corresponds to estimate model parameters of an unknown coordinate based on discrete observations of one or more other coordinates.
Here we consider a bivariate stochastic process where available observations are 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 is not simply an ad-hoc model, but 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. We tackle these statistical issues by considering Approximate Bayesian Computation, a likelihood-free method requiring the development of suitable distance criteria to apply, e.g., in an algorithm similar to acceptance-rejection. After presenting the method and proposing several possible distances, I illustrate how to use it on the considered model.
Sprache der Kurzfassung:
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