Lower bounds for the expected sample size in the classical and $d$-posterior statistical problems

In this report, the problem of construction of lower boundaries for the expected sample size of statistical inference procedures has been considered. The general methodology for construction of the lower bounds and the review of the main results for the classical statistical problems have been presented along with the analysis of the new and earlier results on adoption of the technique to the $d$-posterior approach. Namely, the hypothesis testing problem has been considered.