function Rx=Posterior(nmax, t, pN, A, komb)
% Rx=Posterior(nmax, t, pN, A, komb)
% 
%   Rx(n+1, x+1) posterior probability of x=0:nmax-n remaining items given
%   that t time units have been spent and n=0:nmax prey items taken. 
% 
%   nmax is maximum number of prey in a patch, and pN is the frequency
%   distribution for prey densities.
% 
%   A is the searching efficiency of the forager.
% 
%   komb is 'x over n' and should be created using XoverN before running 
%   this function.
% 
%   The function should work for any prey distribution, but this is not
%   formally proven.
%
% - Equation 1 from 
% 
%   Olsson, O & Holmgren NMA. 1998. The survival-rate-maximizing policy for
%       Bayesian foragers: wait for good news. Behav.Ecol. 9: 345-353.
% 
% See also XoverN

% OO 2008-08-08

Rx=zeros(nmax+1);
for n=0:nmax
    x=0:nmax-n;
    N=x+n;
    Non=komb(N+1, n+1)'; 
    Rx(n+1, x+1)=pN(N+1).*Non.*exp(-A.*t.*x);   %eq 1 in O&H 1998
end
sRx=sum(Rx, 2);
Rx=Rx./repmat(sRx, 1, nmax+1);