Analytic integration of profile likelihood vs marginal likelihood?











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I have questions about 1. Method of analytic integration 2. Statistics (marginal vs profile)



I have an expression



$p(N|a,s,b) = frac{exp[(-as+b)](as+b)^N}{N!} * frac{exp(-gs)(gs)^A}{Gamma(A+1)}*frac{exp(-hb)(hb)^B}{Gamma(AB+1)}$



which I need to analytically integrate into



$p(N|a)$



First, I understand s, and b are separable so it's easy to integrate AS LONG AS
$frac{(as+b)^N}{N!}$ can be somehow separated.....



Is there a way to separate the $frac{(as+b)^N}{N!}$ so I can separate the s and b variable and analytically integrate?



Second, What are two different ways to



a. compute profile likelihood $p(N|a)$ by maximizing probability above



and



b. compute marginal likelihood $p(N|a)$ by integrating above?



Thank you for your help for this newbie!






integration statistics binomial-theorem







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    up vote
    0
    down vote

    favorite












    I have questions about 1. Method of analytic integration 2. Statistics (marginal vs profile)



    I have an expression



    $p(N|a,s,b) = frac{exp[(-as+b)](as+b)^N}{N!} * frac{exp(-gs)(gs)^A}{Gamma(A+1)}*frac{exp(-hb)(hb)^B}{Gamma(AB+1)}$



    which I need to analytically integrate into



    $p(N|a)$



    First, I understand s, and b are separable so it's easy to integrate AS LONG AS
    $frac{(as+b)^N}{N!}$ can be somehow separated.....



    Is there a way to separate the $frac{(as+b)^N}{N!}$ so I can separate the s and b variable and analytically integrate?



    Second, What are two different ways to



    a. compute profile likelihood $p(N|a)$ by maximizing probability above



    and



    b. compute marginal likelihood $p(N|a)$ by integrating above?



    Thank you for your help for this newbie!






    integration statistics binomial-theorem







    share|cite|improve this question







    New contributor




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






















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      I have questions about 1. Method of analytic integration 2. Statistics (marginal vs profile)



      I have an expression



      $p(N|a,s,b) = frac{exp[(-as+b)](as+b)^N}{N!} * frac{exp(-gs)(gs)^A}{Gamma(A+1)}*frac{exp(-hb)(hb)^B}{Gamma(AB+1)}$



      which I need to analytically integrate into



      $p(N|a)$



      First, I understand s, and b are separable so it's easy to integrate AS LONG AS
      $frac{(as+b)^N}{N!}$ can be somehow separated.....



      Is there a way to separate the $frac{(as+b)^N}{N!}$ so I can separate the s and b variable and analytically integrate?



      Second, What are two different ways to



      a. compute profile likelihood $p(N|a)$ by maximizing probability above



      and



      b. compute marginal likelihood $p(N|a)$ by integrating above?



      Thank you for your help for this newbie!






      integration statistics binomial-theorem







      share|cite|improve this question







      New contributor




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











      I have questions about 1. Method of analytic integration 2. Statistics (marginal vs profile)



      I have an expression



      $p(N|a,s,b) = frac{exp[(-as+b)](as+b)^N}{N!} * frac{exp(-gs)(gs)^A}{Gamma(A+1)}*frac{exp(-hb)(hb)^B}{Gamma(AB+1)}$



      which I need to analytically integrate into



      $p(N|a)$



      First, I understand s, and b are separable so it's easy to integrate AS LONG AS
      $frac{(as+b)^N}{N!}$ can be somehow separated.....



      Is there a way to separate the $frac{(as+b)^N}{N!}$ so I can separate the s and b variable and analytically integrate?



      Second, What are two different ways to



      a. compute profile likelihood $p(N|a)$ by maximizing probability above



      and



      b. compute marginal likelihood $p(N|a)$ by integrating above?



      Thank you for your help for this newbie!






      integration statistics binomial-theorem




      integration statistics binomial-theorem






      share|cite|improve this question







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











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