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

• Explain how to add qual explan variable, w/ more than two levels (case studies 3 et 4)

• Explain what an offset is, and how to code it (case study 4)

• More (ecological) interpretation, including random effects, allometry and BLUPS estimation; Show how to rebuild a[j] for partial pooling model

• Illustrate burn-in by running script w/ burning = 0 and nb.iter = 250

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

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

• Replace grain by seeds

• Replace crazy function using cosinus by prediction w/ rainfall/temperature (beware standardisation); Or do both

• Complete example on survival, w/ hypothesis testing, illustrate with Bayes factors? See 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

• Properly introduce GLMs; Illustrate how to find p from logit(p)

• 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

• Clean up section on convergence diagnostics, and make figures reproducible

• Switch to Nimble?

• Record again videos using M. Lajeunesse setup

• Finish up writing that book

• 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

• Debug GLMM practical

• 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

• Make code/outputs fit in slides

• raccourcir cours sur sélection modèle, voire l’intégrer dans un cours existant ; utiliser DIC plutôt que WAIC, plus simple ; mentionner WAIC

• 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)

• Update website