In an MCMC model, what happens if the observed data contains negative and positive observations, but a strictly positive model (Gamma) is used?

Suppose that we observe data that range from negative to positive support. Now, suppose we use a likelihood specification that is a Gamma, or some other distribution with strict positive support. I can guess that whether this MCMC chain fails depends on the prior specification. In general, would the results of our MCMC chain be incorrect?

• If the observed aren't in the support of the likelihood, then the likelihood can't be computed and MCMC should fail. – Demetri Pananos Feb 28 at 20:46