  Markov chain Monte Carlo (MCMC) methods allow to sample a distribution known
up to a multiplicative constant. Classical MCMC samplers are known to have very
poor mixing properties when sampling multimodal distributions. The Equi-Energy
sampler is an interacting MCMC sampler proposed by Kou, Zhou and Wong in 2006
to sample difficult multimodal distributions. This algorithm runs several
chains at different temperatures in parallel, and allow lower-tempered chains
to jump to a state from a higher-tempered chain having an energy 'close' to
that of the current state. A major drawback of this algorithm is that it
depends on many design parameters and thus, requires a significant effort to
tune these parameters. In this paper, we introduce an Adaptive Equi-Energy
(AEE) sampler which automates the choice of the selection mecanism when jumping
onto a state of the higher-temperature chain. We prove the ergodicity and a
strong law of large numbers for AEE, and for the original Equi-Energy sampler
as well. Finally, we apply our algorithm to motif sampling in DNA sequences.
