Bayes' theorem

Fundamentals of Bayesian Data Analysis in R

Rasmus Bååth

Data Scientist

This is Bayes' theorem!

pars$probability <- pars$likelihood * pars$prior
pars$probability <- pars$probability / sum(pars$probability)
Fundamentals of Bayesian Data Analysis in R

This is Bayes' theorem!

pars$probability <- pars$likelihood * pars$prior
pars$probability <- pars$probability / sum(pars$probability)

Fundamentals of Bayesian Data Analysis in R

This is Bayes' theorem!

pars$probability <- pars$likelihood * pars$prior
pars$probability <- pars$probability / sum(pars$probability)

Fundamentals of Bayesian Data Analysis in R

This is Bayes' theorem!

pars$probability <- pars$likelihood * pars$prior
pars$probability <- pars$probability / sum(pars$probability)

Fundamentals of Bayesian Data Analysis in R

This is Bayes' theorem!

pars$probability <- pars$likelihood * pars$prior
pars$probability <- pars$probability / sum(pars$probability)

Fundamentals of Bayesian Data Analysis in R

This is Bayes' theorem!

Fundamentals of Bayesian Data Analysis in R

Grid approximation

  • Define a grid over all the parameter combinations you need to evaluate.
  • Approximate as it's often impossible try all parameter combinations.
  • (There are many more algorithms to fit Bayesian models, some more efficient than others...)
Fundamentals of Bayesian Data Analysis in R

A mathematical notation for models

Fundamentals of Bayesian Data Analysis in R

Up next: More parameters, more data!

Fundamentals of Bayesian Data Analysis in R

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