  The Metropolis algorithm is one of the Markov chain Monte Carlo (MCMC)
methods that realize sampling from the target probability distribution. In this
paper, we are concerned with the sampling from the distribution in
non-identifiable cases that involve models with Fisher information matrices
that may fail to be invertible. The theoretical adjustment of the step size,
which is the variance of the candidate distribution, is difficult for
non-identifiable cases. In this study, to establish such a principle, the
average acceptance rate, which is used as a guideline to optimize the step size
in the MCMC method, was analytically derived in non-identifiable cases. The
optimization principle for the step size was developed from the viewpoint of
the average acceptance rate. In addition, we performed numerical experiments on
some specific target distributions to verify the effectiveness of our
theoretical results.
