This repository holds the source materials used at https://oliviergimenez.github.io/bayesian-stats-with-R/
Text and figures are licensed under Creative Commons Attribution CC BY 4.0. Any computer code (R, HTML, CSS, etc.) in slides and worksheets, including in slide and worksheet sources, is also licensed under MIT.
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Add a section on posterior predictive checks (https://m-clark.github.io/bayesian-basics/diagnostics.html#predictive-accuracy-model-comparison and https://stats.stackexchange.com/questions/115157/what-are-posterior-predictive-checks-and-what-makes-them-useful), to comply with the 3 steps of a Bayesian analysis as defined by Gelman (set up a probabilistic model, inference and model checking; iterate to improve model).
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More details on confidence, credible and HPD intervals.
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Add a section on LOO, and discuss complementarity with WAIC.
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Properly introduce GLMs.
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Switch to Nimble.
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Finish up writing that book.
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Add equivalent analysis in brms so that non-coder can still use bayes stats.
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Clean up section on convergence diagnostics. Make figure reproducible.
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Add a plot with several lines from posterior distribution of regression parameters to a plot of mean response function of a covariate; then get the credible interval on the prediction.
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Prior predictive check for logistic storks and lmm plants sample_mu <- rnorm( 1e4 , 178 , 20 ) sample_sigma <- runif( 1e4 , 0 , 50 ) prior_h <- rnorm( 1e4 , sample_mu , sample_sigma ) dens( prior_h )
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Add another Metropolis example, with adaptation, with the beta-binomial example, and discuss several levels of acceptance. Metropolis RW sur binomial avec adaptatif et burnin https://bayesball.github.io/BOOK/simulation-by-markov-chain-monte-carlo.html. Maybe do a flexdashboard.
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Use ggplot throughout (MCMC diagnostics library(bayesplot), https://www.tjmahr.com/plotting-partial-pooling-in-mixed-effects-models/). Add short introduction to the
Tidyverse. -
Add animation joyplots Rasmus Baath http://www.sumsar.net/blog/2018/12/visualizing-the-beta-binomial/ ou https://relaxed-beaver-4b4dc8.netlify.app/exercises_part1.html
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Typos:
- Beta distribution: use
$a, b$ or$\alpha, \beta$ throughout - End of the first stops at incorporating info in prior capture-recapture example
- Beta distribution: use
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Add something on equivalence w/ MLE: say binomial lik
$Bin(n,k)$ and beta prior$Beta(a,b)$ then posterior is beta$Beta(a+k, b+n-k)$ ; posterior mean is$(a+k)/(a+b+n)$ which can be written$(1-w)(a/a+b) + w k/n$ . Posterior mean is weighted average of prior mean and MLE. When sample size is big,$n$ tends to infinity and posterior mean tends to MLE, whatever the prior. Same reasoning with variance shows that Bayes gives reasonable results, even w/ small sample size.