Neural data analysis: The Bayesics

# Neural data analysis: The Bayesics

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?

External Links

Prerequisites

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

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