Adaptive Independent Metropolis-Hastings by Fast Estimation of Mixtures   of Normals
  We construct an adaptive independent Metropolis-Hastings sampler that uses a mixture of normals as a proposal distribution. To take full advantage of the potential of adaptive sampling our algorithm updates the mixture of normals frequently, starting early in the chain. The algorithm is built for speed and reliability and its sampling performance is evaluated with real and simulated examples. Our article outlines conditions for adaptive sampling to hold and gives a readily accessible proof that under these conditions the sampling scheme generates iterates that converge to the target distribution. 
P. Giordani and R. Kohn