  We present a new multiple-try Metropolis-Hastings algorithm designed to be
especially beneficial when a tailored proposal distribution is available. The
algorithm is based on a given acyclic graph $G$, where one of the nodes in $G$,
$k$ say, contains the current state of the Markov chain and the remaining nodes
contain proposed states generated by applying the tailored proposal
distribution. The Metropolis-Hastings algorithm alternates between two types of
updates. The first update type is using the tailored proposal distribution to
generate new states in all nodes in $G$ except in node $k$. The second update
type is generating a new value for $k$, thereby changing the value of the
current state. We evaluate the effectiveness of the proposed scheme in an
example with previously defined target and proposal distributions.
