Using Influence Diagrams to Solve a Calibration Problem

A measuring instrument measures a unit and records an observation y. The non-measurable variable of interest, the “true” measurement, x, of the unit is to be inferred from y, the measurable variable. If P(y|x) is the likelihood of y given x and x has prior p(x), then by Bayes’ Theorem $$ {\rm{p}}({\rm{x}}|{\rm{y}}) \propto {\rm{p}}({\rm{y}}|{\rm{x}}){\rm{p(x)}}{\rm{.}} $$