I've noticed some weird facts about integral2. These are probably due to my limitations in understanding how it works. I have some difficulties in integrating out variables when I have particular functions. For instance, look at the following Code:
function Output = prova(p,Y)
x = p(1);
y = p(2);
w = p(3);
z = p(4);
F1 = @(Data,eta_1,eta_2,x,y,w,z) F2(eta_1,eta_2,Data) .* normpdf(eta_1,x,y) .* normpdf(eta_2,w,z);
Output = integral2(@(eta_1,eta_2)F1(Y,eta_1,eta_2,0,1,10,2),-5,5,-5,5);
end
function O = F2(pp1,pp2,D)
O = pp1 + pp2 + sum(D);
end
In this case the are no problems in evaluating the integral. But if I change the code in this way I obtain some errors, although the output of F2 is exactly the same:
function Output = prova(p,Y)
x = p(1);
y = p(2);
w = p(3);
z = p(4);
F1 = @(Data,eta_1,eta_2,x,y,w,z) F2(eta_1,eta_2,Data) .* normpdf(eta_1,x,y) .* normpdf(eta_2,w,z);
Output = integral2(@(eta_1,eta_2)F1(Y,eta_1,eta_2,0,1,10,2),-5,5,-5,5);
end
function O = F2(pp1,pp2,D)
o = sum([pp1 pp2]);
O = o + sum(D);
end
The problems increase if F2 for example have some matrix multiplication in which "eta_1" and "eta_2", which I want to integrate out, are involved. This problems makes practically impossible to solve computations in which, for instance, we have to integrate out a variable X which is inside a Likelihood Function (whose calculation could require some internal Loop, or Sum, or Prod involving our variable X). What is the solution?
