for One Pseudo - Sample is Enough in Approximate Bayesian Computation MCMC

where eg,H is the spectral measure associated with g and H , i.e., the finite positive measure on [−1, 1] such that 〈g,H g〉μ = ∫ 1 −1 x eg,H(dx) for all i ∈ N. For nonnegative definite transition 15 kernels H the spectral measure, and the integrals, are over the narrower range [0, 1]. Denote by H2,α the transition kernel of the pseudo-marginal algorithm with proposal kernel q, target marginal distribution μ, and estimator T2,x,α of the unnormalized target. We note that H2,α = αI + (1− α)H2, (2)