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Cours 29 Bayesian stats cours

  1. design the model (data story)
  2. condition on the data (update the model)
  3. evaluate the model (critique)

ex : 9 times dta : W (water) or L (land)

p = proba de W proba de L = 1-p

prior : information before the data (p in [0;1]) posterior : update info of each value of p conditional on data

chaque postérior est le prior du prochain posterior plus on a de données plus il est aisé d’avoir un résulat précis

Define generative relations between the variables

W, L, W p * (1-p) *p = p2(1-p)1 : relative number to see W

Vraissemblance :

29.1 Grid approximation (to define posterior) :

posterior proba = standardizez product of proba of the data and prior proba standardisé : add up all the products and divide by this sum

grid approximation uses finite grid of parameter values instead of continuous space too expensive with more yhan a few parameters

Sampling from the posterior

Intervals : how much mass

Percentile intervals (PI): equal area in each tail Hightest posterior density intervals (HPDI) : narrowest interval containing mass

Mean nearly always more sensible than the mode

Model :