R help - Sep 2011 - Poisson-Gamma computation (parameters and likelihood)

Good afternoon/morning readers. This is the first time I am trying to run
some Bayesian computation in R, and am experiencing a few problems.

I am working on a Poisson model for cancer rates which has a conjugate Gamma
prior.

1) The first question is precisely how I work out the parameters.

#Suppose I assign values to theta with *seq()*
*theta<-seq(0,1,len=500)*

#Then I try out the parameters that seem to fit with a certain prior idea on
theta (see next)
*a=182*
*b=3530*
*gaprior<-dgamma(theta,a,b)*
*
*
It should work by trial-and-error (according to "Bayesian Computation with
R") , but how can I check the parameters turned out well: should I just
look
at the plot, or evaluate it through the *1 - pgamma(x,a,b) *function, having
knowledge of the 5th percentile (data from US Cancer Statistics)?

2) Then, the next problem I have regards the likelihood distribution.

#Having the *react* table, I name the columns (with y=deaths, and
x=exposures)
*
react
    x  y
1   6 15
2   5 16
3   3 12
4   4  6
5  27 77
6   7 17
7   4 11
8   5 10
9  23 63
10 11 29

*
*yr <- react[,2]*
*xr <- react[,1]*



#I then compute the likelihood
*poislike=dpois(yr, theta*xr)*

#And this is what I come up with, which I really don't understand.
*poislike*
*[1] 0 0 0 0 0 0 0 0 0 0*

The values shouldn't be all null, otherwise my posterior cannot be computed
properly. Does anyone have any idea on where I could possibly have messed it
up?

Thank you very much for your attention.

Regards,

Sebastiano Putoto (University of Pavia, Italy)

	[[alternative HTML version deleted]]

Good afternoon/morning readers. This is the first time I am trying to run
some Bayesian computation in R, and am experiencing a few problems.

I am working on a Poisson model for cancer rates which has a conjugate Gamma
prior.

1) The first question is precisely how I work out the parameters.

#Suppose I assign values to theta with *seq()*
*theta<-seq(0,1,len=500)*

#Then I try out the parameters that seem to fit with a certain prior idea on
theta (see next)
*a=182*
*b=3530*
*gaprior<-dgamma(theta,a,b)*
*
*
It should work by trial-and-error (according to "Bayesian Computation with
R") , but how can I check the parameters turned out well: should I just
look
at the plot, or evaluate it through the *1 - pgamma(x,a,b) *function, having
knowledge of the 5th percentile (data from US Cancer Statistics)?

2) Then, the next problem I have regards the likelihood distribution.

#Having the *react* table, I name the columns (with y=deaths, and
x=exposures)
*
react
    x  y
1   6 15
2   5 16
3   3 12
4   4  6
5  27 77
6   7 17
7   4 11
8   5 10
9  23 63
10 11 29

*
*yr <- react[,2]*
*xr <- react[,1]*



#I then compute the likelihood
*poislike=dpois(yr, theta*xr)*

#And this is what I come up with, which I really don't understand.
*poislike*
*[1] 0 0 0 0 0 0 0 0 0 0*

The values shouldn't be all null, otherwise my posterior cannot be computed
properly. Does anyone have any idea on where I could possibly have messed it
up?

Thank you very much for your attention.

Regards,

Sebastiano Putoto (University of Pavia, Italy)

	[[alternative HTML version deleted]]

Good afternoon/morning readers. This is the first time I am trying to run
some Bayesian computation in R, and am experiencing a few problems.

I am working on a Poisson model for cancer rates which has a conjugate Gamma
prior.

1) The first question is precisely how I work out the parameters.

#Suppose I assign values to theta with seq()
theta<-seq(0,1,len=500)

#Then I try out the parameters that seem to fit with a certain prior idea on
theta (see next)
a=182
b=3530
gaprior<-dgamma(theta,a,b)

It should work by trial-and-error (according to "Bayesian Computation with
R") , but how can I check the parameters turned out well: should I just
look
at the plot, or evaluate it through the 1 - pgamma(x,a,b) function, having
knowledge of the 5th percentile (data from US Cancer Statistics)?

2) Then, the next problem I have regards the likelihood distribution.

#Having the react table, I name the columns (with y=deaths, and x=exposures)
react
    x  y
1   6 15
2   5 16
3   3 12
4   4  6
5  27 77
6   7 17
7   4 11
8   5 10
9  23 63
10 11 29

yr <- react[,2]
xr <- react[,1]



#I then compute the likelihood
poislike=dpois(yr, theta*xr)

#And this is what I come up with, which I really don't understand.
poislike
[1] 0 0 0 0 0 0 0 0 0 0

The values shouldn't be all null, otherwise my posterior cannot be computed
properly. Does anyone have any idea on where I could possibly have messed it
up?

Thank you very much for your attention.

Regards,

Sebastiano Putoto (University of Pavia, Italy)

	[[alternative HTML version deleted]]