Dyadic Product Formula Representations of Confidence Measures and Decision Rules for Dyadic Data Set Samples
Linda A. Ness · 2016
A methodology for representing and computing confidence distributions for parametric representations of sets of samples of data is presented. The method assumes that the universe of the data samples is a dyadic set whose dyadic structure is an ordered binary tree of subsets of the universe with a measure defined on the dyadic sets. In this case the samples can be represented as the set of product coefficient parameters for the dyadic product formula representing the measure. If a dyadic structure is defined on the universe of product coefficient parameters, which is a high-dimensional cube, and a measure is defined on the dyadic sets of the cube, a confidence measure on the set of parameters is determined whose product formula can be determined by computing its parameters. When the original samples of data are labeled, decision rules based on their confidence distributions can be defined. The methodology is demonstrated on an a 12 dimensional network time series with 6 sources.