I have simulated data under three parameters of interest, say a, b, c. The prior I put on c was a Gamma, so it only takes positive values. The full conditionals of a and b are known distributions, but the full conditional of c is not a known distribution.
I performed 10,000 iterations of updating a and b with Gibbs and c with Metropolis using a normal proposal distribution. The function f that is proportional to the full conditional of c returns negative values if a negative c is inputed, so I automatically rejected if the candidate for c was negative.
Looking at a trace plot of c, it seems to converge, but to a much smaller value than the actual c. Am I doing something wrong?