We can calculate!

Fundamentals of Bayesian Data Analysis in R

Rasmus Bååth

Data Scientist

Simulation vs calculation

  • Simulation using 'r'-functions, for example, rbinom and rpois
  • Simulating P(n_visitors = 13 | prob_success = 10%)
n_visitors <- rbinom(n = 100000, size = 100, prob = 0.1)
sum(n_visitors == 13) / length(n_visitors)

0.074
  • Calculation using the 'd'-functions, for example, dbinom and dpois
  • Calculating P(n_visitors = 13 | prob_success = 10%)
dbinom(13, size = 100, prob = 0.1)

0.074
Fundamentals of Bayesian Data Analysis in R
  • Calculating P(n_visitors = 13 or n_visitors = 14 | prob_success = 10%)
dbinom(13, size = 100, prob = 0.1) + dbinom(14, size = 100, prob = 0.1)

0.126
  • Calculating P(n_visitors | prop_success = 10%)
n_visitors = seq(0, 100, by = 1)
probability <- dbinom(n_visitors, size = 100, prob = 0.1)

n_visitors

0 1 2 3 4 5 6 7 ...

probability

0.000 0.000 0.002 0.006 0.016 0.034 0.060 0.089 ...
Fundamentals of Bayesian Data Analysis in R

Plotting a calculated distribution

plot(n_visitors, probability, type = "h")

Fundamentals of Bayesian Data Analysis in R

Continuous distributions

  • The Uniform distribution
x <- runif(n = 100000, min = 0.0, max = 0.2)
hist(x)

Fundamentals of Bayesian Data Analysis in R

Continuous distributions

  • The Uniform distribution
    • The d-version of runif is dunif:
dunif(x = 0.12, min = 0.0, max = 0.2)

5
  • Probability density: Kind of a relative probability
x = seq(0, 0.2, by=0.01)
dunif(x, min = 0.0, max = 0.2)

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
Fundamentals of Bayesian Data Analysis in R

Try this out!

Fundamentals of Bayesian Data Analysis in R

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