  The multiple Try Metropolis (MTM) algorithm is an advanced MCMC technique
based on drawing and testing several candidates at each iteration of the
algorithm. One of them is selected according to certain weights and then it is
tested according to a suitable acceptance probability. Clearly, since the
computational cost increases as the employed number of tries grows, one expects
that the performance of an MTM scheme improves as the number of tries
increases, as well. However, there are scenarios where the increase of number
of tries does not produce a corresponding enhancement of the performance. In
this work, we describe these scenarios and then we introduce possible solutions
for solving these issues.
