Bayes posteriograms












1












$begingroup$


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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    1












    $begingroup$


    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!










    share|improve this question







    New contributor




    user3116297 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.







    $endgroup$















      1












      1








      1





      $begingroup$


      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!










      share|improve this question







      New contributor




      user3116297 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.







      $endgroup$




      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!







      python bayesian scipy probabilistic-programming






      share|improve this question







      New contributor




      user3116297 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      share|improve this question







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      Check out our Code of Conduct.









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      share|improve this question






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      asked 2 days ago









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