For a Markov transition kernel P and a probability distribution
μ on nonnegative integers, a time-sampled Markov chain evolves according
to the transition kernel Pμ = Σkμ(k)Pk. 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
