HMM exercises
83 The probability of standing still

About DataSAI for Neuroscience Summer School 2025
Polars and split-apply-combine
Data display
Data file formats
Probability: The foundation for generative modeling
Sampling out of probability distributions
- 14 Random number generation
- 15 Random number generation using Numpy
Simulating generative distributions
Markov chain Monte Carlo
Bayesian modeling and inference
Statistical inference with Markov chain Monte Carlo
Principled inference pipelines
Model assessment
- 35 Model comparison
- 36 Model comparison in practice
Summarizing posterior distributions with maxima
Hierarchical models
Principal component analysis and related models
Hidden Markov models
- 52 Hidden Markov models
Generalized linear models
- 53 Generalized linear models: An introduction
- 54 GLMs applied to neurons and aggression
Polars and split-apply-combine exercises
Data visualization exercises
- 59 Plotting with Palmer penguins
- 60 Exploratory data analysis of a zebrafish sleep study
File formats exercises
- 61 Opening a 7z file
Probability exercises
Sampling and simulation exercises
Introductory MCMC exercises
- 68 Sampling out of a bivariate Normal distribution
- 69 Funnel of hell
Bayesian modeling exercises
Inference with MCMC exercises
Optimization exercises
- 77 Optimization and spiking
- 78 Heavy-tailed distributions and outliers
Hierarchical exercises
- 79 Hierarchical models are hiding in plain sight
- 80 Modeling pole descent
PCA exercises
- 81 Downsampling and PCA with spiking and EMG/ ephys data
- 82 PCA on time series
HMM exercises
- 83 The probability of standing still
- 84 Simulating HMMs
GLM exercises
- 85 A GLM connecting neuronal activity and movement
- 86 GLM for EMG data
Appendices
- Notation
  - A Notation
- Computing

HMM exercises
83 The probability of standing still

83 The probability of standing still

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For a hidden Markov model, what is the probability of staying in state \(i\) for exactly \(T\) time steps?

84 Simulating HMMs

DataSAI 2025