Model assessment
About the course
Course logistics
Schedule overview
Course policies
1
What are we doing?
Probability: The foundation for generative modeling
2
Probability as the logic of science
3
Probability distributions
4
Entropy and the Kullback-Leibler divergence
Sampling out of probability distributions
5
Random number generation
6
Random number generation using Numpy
Simulating generative distributions
7
Simulating the Luria-Delbrück distribution
8
The noisy leaky integrate-and-fire model
9
Modeling nonhomogeneous Poisson spiking
Markov chain Monte Carlo
10
The basics of Markov chain Monte Carlo
11
“Hello, world” —Stan
12
Nonhomogeneous Poisson process arrival times with Stan
Bayesian modeling and inference
13
Basics of Bayesian modeling
14
Conjugacy
15
Choosing priors
16
Advice on using distributions
17
What about machine learning and artificial intelligence?
18
Bayes's theorem as a model for learning
19
Model building with prior predictive checks
Statistical inference with Markov chain Monte Carlo
20
Parameter estimation with Markov chain Monte Carlo
21
Display of MCMC samples
22
Reporting summaries of the posterior
23
Posterior predictive checks
Mixture models
24
Mixture models and label switching with MCMC
Model assessment
25
Model comparison
26
Model comparison in practice
Principled inference pipelines
27
MCMC diagnostics via a case study: Artificial funnel of hell
28
Principled analysis pipelines
29
Simulation based calibration and related checks in practice
Summarizing posterior distributions with maxima
30
Bayesian approach to parameter estimation by optimization
31
Parameter estimation by optimization case study: Gamma likelihood
32
Minorize-maximize algorithms
33
The expectation-maximization (EM) algorithm
34
EM applied to a Gaussian mixture model
35
An example application of the EM algorithm to a Gaussian mixture model
36
K-means clustering
Variate-covariate models
37
Model building
38
Variate-covariate models with MCMC
Hierarchical models
39
Modeling repeated experiments
40
Choosing a hierarchical prior
41
Generalization of hierarchical models
42
Implementation of a hierarchical model
43
General implementation of hierarchical models
Principal component analysis and related models
44
Principal component analysis: A heuristic approach
45
Factor analysis
46
Special cases of factor analysis
Hidden Markov models
47
Hidden Markov models
Generalized linear models
48
Generalized linear models: An introduction
49
GLMs applied to neurons and aggression
Gaussian processes
50
Introduction to Gaussian processes
51
Gaussian process hyperparameters by optimization
52
MCMC with GPs with Normal likelihoods
53
Calculating derivatives from data with GPs
54
Gaussian processes with non-Normal likelihoods
Homework
HW 1.1: First attempts at Bayesian generative modeling
Appendices
A
Notation
B
Configuring your computer to use Python for scientific computing
Model assessment
Herein, we go beyond the graphical in model assessment.
24
Mixture models and label switching with MCMC
25
Model comparison