Statistics in Neuroscience: inference for stochastic processes and for point processes
Sprache des Vortragstitels:
In many signal-processing applications, it is of primary interest to decode/reconstruct the unobserved signal based on some partially observed information. Some examples are all type of recognition (e.g. automatic speech, face, gesture, handwriting), chemistry, genetics and neuroscience (ion channels modelling). From a statistical point of view, this corresponds to perform statistical inference of the underlying model parameters from fully/partially observed stochastic processes (e.g. discrete observations of one or more other coordinates) and (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). We will briefly discuss a couple of examples (with application on lung cancer data and visual data) where the underlying likelihood function can be derived, leading to maximum likelihood estimation. Quite often though, the underlying likelihood is unknown or intractable. Among likelihood-free statistical methods, we will focus on Approximate Bayesian Computation. After presenting the method, we will illustrate it on two examples arising from neuroscience, with data corresponding to partially observed stochastic processes.