Detection of hormesis by empirical data as an ill-posed problem

To detect the hormesis by empirical data, use is made of the function of the ratio of the mortality risk in a group found to be under stress to the mortality risk in a control group not subjected to stress and also of the function of the likelihood ratio for these groups. These functions can be thought of as "dose-effect" ratios. Formally, the estimates of these functions result from the solution of linear operator equations with inaccurately prescribed right sides and, possibly, inaccurately prescribed operators. The procedure of solving these problems, which are ill-posed ones, by means of the regularization method is set out. The cases of homogeneous and heterogeneous populations are considered.