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    Neural data analysis: The Bayesics

    Difficulty level

    Bayesian neuron models and parameter estimation.

    Topics covered in this lesson
    • Statistics in computational neuroscience, deriving knowledge from limited and/or noisy data.
    • Statistical models can convey both knowledge and uncertainty, being explicit about what we do not know.
    • The loop of modelling-experiment-modelling.
    • Bayesian statistics.
    • Posterior and prior probabilities, likelihood. 
    • Generalized linear model (GLM) - relating stimuli to neural responses.
    • Poisson process, the mother of all spike train models.
    • Maximizing log-likelihood.
    • Time binning and how it affects the maximum likelihood.
    • Estimating posteriors.
    • Post-spike filters for mimicking different kinds of spiking.
    • GLMs model dependency of neural spike rate on time, stimulus, spike history.
    • Special case: linear non-linear Poisson neurons are GLMs without history.
    • Coupling terms for modelling dependence on other spiking neurons.
    • Latent variables. 
    • Outline of the expectation maximization algorithm. 
    • Bayesian inference - finding which parameters are consistent with data and prior knowledge
    • Likelihood-free inference a.k.a. Approximate Bayesian Computation (ABC) - "should be called intractable likelihood inference".
    • Training deep neural networks to approximate posterior distribution from data.
    • Applications: which parameters are well constrained by data?

    Calculus (integration and differentiation), basic linear algebra (matrices, determinants). Some basic transform theory, such as knowing what Fourier transforms do, what a convolution is.