Answering the question: Should I have a beach party?

Fundamentals of Bayesian Data Analysis in R

Rasmus Bååth

Data Scientist

The questions

What's likely the average water temperature on 20th of Julys?
What's the probability that the water temperature is going to be 18 or more on the next 20th?

The posterior distribution

pars

  mu sigma probability
17.5   1.9      0.0001
18.0   1.9      0.0003
18.5   1.9      0.0014
19.0   1.9      0.0043
19.5   1.9      0.0094
20.0   1.9      0.0142
20.5   1.9      0.0151
21.0   1.9      0.0112
21.5   1.9      0.0058
22.0   1.9      0.0021
...    ...       ...

sample_indices <- sample(1:nrow(pars), size = 10000, 
                         replace = TRUE, prob = pars$probability)

sample_indices <- sample(1:nrow(pars), size = 10000, 
                         replace = TRUE, prob = pars$probability)

head(sample_indices)

430  428 1010  383  343  385

pars_sample <- pars[sample_indices, c("mu", "sigma")]
head(pars_sample)

     mu sigma
1  20.0   2.8
2  19.0   2.8
3  17.5   6.7
4  19.0   2.5
5  21.5   2.2
6  20.0   2.5
7  20.0   2.8
8  20.5   1.6
9  19.0   2.5
10 17.0   4.0

The probability distribution over the mean temperature

hist(pars_sample$mu, 30)

The probability distribution over the mean temperature

quantile(pars_sample$mu, c(0.05, 0.95))

  5%  95% 
17.5 22.5

Is the temperature 18 or above on the 20th?

pred_temp <- rnorm(10000, mean = , sd = )

Is the temperature 18 or above on the 20th?

pred_temp <- rnorm(10000, mean = pars_sample$mu, sd = pars_sample$sigma)

Is the temperature 18 or above on the 20th?

pred_temp <- rnorm(10000, mean = pars_sample$mu, sd = pars_sample$sigma)
hist(pred_temp, 30)

Is the temperature 18 or above on the 20th?

pred_temp <- rnorm(10000, mean = pars_sample$mu, sd = pars_sample$sigma)
hist(pred_temp, 30)
sum(pred_temp >= 18) / length(pred_temp )

0.73

What about the IQ of zombies?

Fundamentals of Bayesian Data Analysis in R