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Monte-Carlo techniques are standard numerical tools for exploringnon-Gaussian and multivariate likelihoods. Many variants of the originalMetropolis-Hastings algorithm have been proposed to increase the samplingefficiency. Motivated by Ensemble Monte Carlo we allow the number of Markovchains to vary by exchanging particles with a reservoir, controlled by aparameter analogous to a chemical potential $\mu$, which effectivelyestablishes a random process that samples microstates from a macrocanonicalinstead of a canonical ensemble. In this paper, we develop the theory ofmacrocanonical sampling for statistical inference on the basis of Bayesianmacrocanonical partition functions, thereby bringing to light the relationsbetween information-theoretical quantities and thermodynamic properties.Furthermore, we propose an algorithm for macrocanonical sampling,$\texttt{Avalanche Sampling}$, and apply it to various toy problems as well asthe likelihood on the cosmological parameters $\Omega_m$ and $w$ on the basisof data from the supernova distance redshift relation.

Partition function approach to non-Gaussian likelihoods: macrocanonical partitions and replicating Markov-chains