  For a Markov transition kernel $P$ and a probability distribution $ \mu$ on
nonnegative integers, a time-sampled Markov chain evolves according to the
transition kernel $P_{\mu} = \sum_k \mu(k)P^k.$ In this note we obtain CLT
conditions for time-sampled Markov chains and derive a spectral formula for the
asymptotic variance. Using these results we compare efficiency of Barker's and
Metropolis algorithms in terms of asymptotic variance.
