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My main objective is to predict the posterior probability of an individual belonging to one of the classes, using Bayes theorem. The information I have is:

  1. value of the data point
  2. mean and stdev of the 2 potential populations, that this data point could belong to (=the potential classes
  3. normal distributions drawn on those 2 classes

I'm using numpy to create a probability distribution over a given mean and stdev. Let's say that this distribution represents the average weight of a population. I have drawn distributions of the weights of 2 populations, such that the means differ considerably.

  • G1 = scipy.stats.norm(50, 1)
  • G2 = scipy.stats.norm(100,2)

I have a data point, suppose A = weight of one single individual. If I get probability of 'a' on one of the curves, using:

  • weightofA = 45 kg
  • probA_G1 = G1.pdf(weightofA)

what would this probability be? The likelihood or the posterior? If it's the likelihood, how will I get the prior? I only have 1 data point. How will I calculate the marginal, of the gaussians?

Thanks so much!

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