· r-2 rstats

R: Creating an object with functions to calculate conditional probability

I've been working through Alan Downey's Thinking Bayes and I thought it'd be an interesting exercise to translate some of the code from Python to R.

The first example is a simple one about conditional probablity and the author creates a class 'PMF' (Probability Mass Function) to solve the following problem:

Suppose there are two bowls of cookies. Bowl 1 contains 30 vanilla cookies and 10 chocolate cookies. Bowl 2 contains 20 of each. Now suppose you choose one of the bowls at random and, without looking, select a cookie at random. The cookie is vanilla. What is the probability that it came from Bowl 1?

In Python the code looks like this:


pmf = Pmf()
pmf.Set('Bowl 1', 0.5)
pmf.Set('Bowl 2', 0.5)

pmf.Mult('Bowl 1', 0.75)
pmf.Mult('Bowl 2', 0.5)

pmf.Normalize()

print pmf.Prob('Bowl 1')

The 'PMF' class is defined here.

We want to create something similar in R and the actual calculation is stragiht forward:


pBowl1 = 0.5
pBowl2 = 0.5

pVanillaGivenBowl1 = 0.75
pVanillaGivenBowl2 = 0.5

> (pBowl1 * pVanillaGivenBowl1) / ((pBowl1 * pVanillaGivenBowl1) + (PBowl2 * pVanillaGivenBowl2))
0.6

> (pBowl2 * pVanillaGivenBowl2) / ((pBowl1 * pVanillaGivenBowl1) + (pBowl2 * pVanillaGivenBowl2))
0.4

The problem is we have quite a bit of duplication and it doesn't read as cleanly as the Python version.

I'm not sure of the idiomatic way of handling this type of problem in R with mutable state in R but it seems like we can achieve this using functions.

I ended up writing the following function which returns a list of other functions to call.


create.pmf = function() {
  priors <<- c()
  likelihoods <<- c()
  list(
    prior = function(option, probability) {
      l = c(probability)  
      names(l) = c(option)
      priors <<- c(priors, l)
    },
    likelihood = function(option, probability) {
      l = c(probability)  
      names(l) = c(option)
      likelihoods <<- c(likelihoods, l)
    },
    posterior = function(option) {
      names = names(priors)
      normalised = 0.0
      for(name in names) {
        normalised = normalised + (priors[name] * likelihoods[name])
      }
      
      (priors[option] * likelihoods[option]) / normalised
    }    
  )
}

I couldn't work out how to get 'priors' and 'likelihoods' to be lexically scoped so I've currently got those defined as global variables. I'm using a list as a kind of dictionary following a suggestion on Stack Overflow.

The code doesn't handle the unhappy path very well but it seems to work for the example from the book:


pmf = create.pmf()

pmf$prior("Bowl 1", 0.5)
pmf$prior("Bowl 2", 0.5)

pmf$likelihood("Bowl 1", 0.75)
pmf$likelihood("Bowl 2", 0.5)

> pmf$posterior("Bowl 1")
Bowl 1 
   0.6 
> pmf$posterior("Bowl 2")
Bowl 2 
   0.4 

How would you solve this type of problem? Is there a cleaner/better way?

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