  The adaptive Metropolis (AM) algorithm of Haario, Saksman and Tamminen
[Bernoulli 7 (2001) 223-242] uses the estimated covariance of the target
distribution in the proposal distribution. This paper introduces a new robust
adaptive Metropolis algorithm estimating the shape of the target distribution
and simultaneously coercing the acceptance rate. The adaptation rule is
computationally simple adding no extra cost compared with the AM algorithm. The
adaptation strategy can be seen as a multidimensional extension of the
previously proposed method adapting the scale of the proposal distribution in
order to attain a given acceptance rate. The empirical results show promising
behaviour of the new algorithm in an example with Student target distribution
having no finite second moment, where the AM covariance estimate is unstable.
In the examples with finite second moments, the performance of the new approach
seems to be competitive with the AM algorithm combined with scale adaptation.
