Consider Ambiguity in Probabilistic Descriptions Using Density
Ratio Classes
Description
Consider ambiguity in probabilistic descriptions by replacing a parametric probabilistic description of uncertainty by a non-parametric set of probability distributions in the form of a Density Ratio Class. This is of particular interest in Bayesian inference.
The Density Ratio Class is particularly suited for this purpose as it is invariant under Bayesian inference, marginalization, and propagation through a deterministic model. Here, invariant means that the result of the operation applied to a Density Ratio Class is again a Density Ratio Class. In particular the invariance under Bayesian inference thus enables iterative learning within the same framework of Density Ratio Classes.
The use of imprecise probabilities in general, and Density Ratio Classes in particular, lead to intervals of characteristics of probability distributions, such as cumulative distribution functions, quantiles, and means.
The package is based on a sample of the distribution proportional to the upper bound of the class. Typically this will be a sample from the posterior in Bayesian inference. Based on such a sample, the package provides functions to calculate lower and upper class boundaries and lower and upper bounds of cumulative distribution functions, and quantiles.
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Sriwastava, A. and Reichert, P. "Robust Bayesian Estimation of Value Function Parameters using Imprecise Priors." Submitted. .