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
asked Nov 19 at 16:04
trenta coollime
11
add a comment |
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
asked Nov 19 at 16:04
trenta coollime
11
add a comment |
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
asked Nov 19 at 16:04
trenta coollime
11
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
asked Nov 19 at 16:04
trenta coollime
11
asked Nov 19 at 16:04
trenta coollime
11
asked Nov 19 at 16:04
trenta coollime
11
asked Nov 19 at 16:04
trenta coollime
11
asked Nov 19 at 16:04
trenta coollime
11
11
add a comment |
add a comment |
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