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In this paper we develop a new general Bayesian methodology thatsimultaneously estimates parameters of interest and the marginal likelihood ofthe model. The proposed methodology builds on Simulated Tempering, which is apowerful algorithm that enables sampling from multi-modal distributions.However, Simulated Tempering comes with the practical limitation of needing tospecify a prior for the temperature along a chosen discretization schedule thatwill allow calculation of normalizing constants at each temperature. Ourproposed model defines the prior for the temperature so as to remove the needfor calculating normalizing constants at each temperature and thereby enables acontinuous temperature schedule, while preserving the sampling efficiency ofthe Simulated Tempering algorithm. The resulting algorithm simultaneouslyestimates parameters while estimating marginal likelihoods throughthermodynamic integration. We illustrate the applicability of the new algorithmto different examples involving mixture models of Gaussian distributions andordinary differential equation models.

Parallel Tempering via Simulated Tempering Without Normalizing Constants