## Proc MCMC Error: doesn't produce a positive log likelihood in SAS University Edition

Hi,

I am applying MCMC in SAS University edition, I got the error that the log likelihood is not positive.

This is a part of the code.

``````p= A**(x+B)**C + D*exp(-1*E*(log(x)-log(F))**2) + G*(H**x)/(1+G*(H**x));
model y ~ binomial(n,p);``````

A to H are parameters which have prior distribution of uniform.

Thanks.

2 REPLIES 2

## Re: Proc MCMC Error: doesn't produce a positive log likelihood in SAS University Edition

What is the range and typical values of x?  Obviously x must be greater than 0, but also x > B so that the expression (x-B)**C is defined.  Is B always bounded above by some B0 and x > B0? Otherwise  you're going to have problems.

It also looks like it is possible to choose parameters such that p is greater than 1, which will cause problems in the binomial(n,p) computation.

What are you trying to accomplish?

## Re: Proc MCMC Error: doesn't produce a positive log likelihood in SAS University Edition

x is age grouped in five years, it ranges from 0 to 110 (eg. 0,5,10,...110). B ranges from 0 to 1. The exponent is (x+B) not (x-B) so it is always defined.

It rarely happens in the models that p is greater than 1 but anyway I put a condition that if it is greater than 1 then substitute with 0.999.

I am trying to approximate a posterior distribution of the parameters (A to H) through slice sampling or Metropolis Hastings method. but the problem here is that the deaths is binomial and the prior distributions are not for the probability of success of the binomial, they are for the parameters that are in Heligman Pollard model (the p equation).