Bayesian statistics for ecology

This repository holds the source materials used at https://oliviergimenez.github.io/bayesian-stats-with-R/

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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.

To-do list

• 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).

• More details on confidence, credible and HPD intervals.

• Add a section on LOO, and discuss complementarity with WAIC.

• Properly introduce GLMs.

• Switch to Nimble.

• Finish up writing that book.

• Add equivalent analysis in brms so that non-coders can still use bayes stats.

• Clean up section on convergence diagnostics. Make figure reproducible.

• 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.

• 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 )

• 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.

• 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

• Typos:

  • Beta distribution: use $a, b$ or $\alpha, \beta$ throughout
  • End of the first stops at incorporating info in prior capture-recapture example

• 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.

• More (ecological) interpretation

• Add a script to plot stuff in white stork example

• Add a script to TP 9 to show how we can build models of increasing complexity

• Besides (or instead of) wAIC use DIC which is given by JAGS (unpopular opinion)

• Explain how to add qual explan variable (more than two levels)

• Explain offset

• Update website

• Record again videos using M. Lajeunesse setup

• Include all four case studies that I used for Master exam

• Aller jusqu’au bout de l’exemple survie, en faisant test d’hypothèse

• Pourquoi ne pas illustrer dans le contexte du point précédent, le calcul des Bayes factors? Voir https://rstudio-pubs-static.s3.amazonaws.com/358672_09291d0b37ce43f08cf001cfd25c16c2.html, https://stackoverflow.com/questions/60278806/bayes-factor-in-r-with-jaggs, https://www.martinmodrak.cz/2021/03/28/three-ways-to-compute-a-bayes-factor/, http://yourdomain.com/statistics,/modeling/2017/07/07/BF_computation.html ou encore https://michael-franke.github.io/statistics,/modeling/2017/07/07/BF_computation.html

• Pas vraiment des prior predictive checks

• Passer tout en nimble - ca résout pb calcul WAIC

• Montrer le burn-in en faisant tourner le script avec burning = 0 et nb.iter = 250

• Réconcilier interprétation des estimations pour les modèles plants no pooling / complete pooling et partial pooling ; check calcul du DIC qui donne modèle nul (sans cov) comme meilleur modèle

• Montrer comment on reconstruit les a[j] pour partial pooling model

• Régler pb de mise en page

• Basculer des éléments de mes chapitres de bouquin dans ce cours

• Add random-intercept random-slope example? See Alford et al Global amphibian population declines as suggested by B. Bolker?