  The multi-point Metropolis algorithm is an advanced MCMC technique based on
drawing several correlated samples at each step and choosing one of them
according to some normalized weights. We propose a variation of this technique
where the weight functions are not specified, i.e., the analytic form can be
chosen arbitrarily. This has the advantage of greater flexibility in the design
of high-performance MCMC samplers. We prove that our method fulfills the
balance condition, and provide a numerical simulation. We also give new insight
into the functionality of different MCMC algorithms, and the connections
between them.
