Likelihood

Now we are ready to write the likelihood function. As usual, I define a new class that extends thinkbayes.Suite:

class Price(thinkbayes.Suite):

    def __init__(self, pmf, player):
        thinkbayes.Suite.__init__(self, pmf)
        self.player = player

pmf represents the prior distribution and player is a Player object as described in the previous section. Here’s Likelihood:

    def Likelihood(self, data, hypo):
        price = hypo
        guess = data

        error = price - guess
        like = self.player.ErrorDensity(error)

        return like

hypo is the hypothetical price of the showcase. data is the contestant’s best guess at the price. error is the difference, and like is the likelihood of the data, given the hypothesis.

ErrorDensity is defined in Player:

# class Player:

    def ErrorDensity(self, error):
        return self.pdf_error.Density(error)

ErrorDensity works by evaluating pdf_error at the given value of error. The result is a probability density, so it is not really a probability. But remember that Likelihood doesn’t need to compute a probability; it only has to compute something proportional to a probability. As long as the constant of proportionality is the same for all likelihoods, it gets canceled out when we normalize the posterior distribution.

And therefore, a probability density is a perfectly good likelihood.

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