Blind inversion needs distribution (BIND): general notion and case studies
Lei Li · Lecture notes-monograph series · 2003
A class of scientific measurement problems share a common feature which we refer to as "blind inversion."That is, we can regard a module of measurement instruments as a system with quantities to be measured as input and observations as output.In a blind inversion problem, both the effective system and the input are unknown to us.Due to either experimental design or the nature of scientific problem in question, very often the distributional knowledge of the input can be obtained.Given this piece of information, we apply a two-step scheme -abbreviated by BIND -to solve the blind inversion problem.First, we make use of the distributions of the input and output to estimate the system.Second, we reconstruct the value of each individual input using the system obtained in the first step.From this perspective, we have another look at two measurement problems that are part of Professor Speed's recent research in molecular biology.We also connect the idea with the long-standing predictive deconvolution method used in seismology and discuss assessment issues of BIND.