A software tool to to aggregate several probability distributions into a single integrated one.

Rubik's cube © IIASA

About the tool

Studies of complex systems are non-separable from the analysis of partial and imprecise information received from alternative sources.

A system analyst deals with a set of ensemble outcomes which needs to be integrated into one estimate in order to install the ensemble into the modelling chain or provide support for the informed decision making.

This software tool provides means to aggregate several probability distributions into a single integrated one.

Suppose that, several independent methods are used to observe a deterministic element and each method represents the latter as a probability distribution. Thus, we deal with a family of probability distributions providing alternative descriptions to the same object. The problem is how to combine information from the prior estimates.

How it works

This package implements the posterior integration method (Kryazhimskiy, 2013), which is based on the assumption that model outcomes are mutually compatible (I.E. We should observe identical outcomes after the use of model ensemble).

For comparison, an implementation of simple averaging of the input distributions is added.


Kryazhimskiy, A. (2016). A Posteriori Integration of Probabilities. Elementary Theory. Theory of Probability & Its Applications 60 (1), 62-87. 10.1137/S0040585X97T987466.

Rovenskaya, E. , Shchiptsova, A., & Kovalevsky, D. (2016). Reconciling Information From Climate-Economic Model Ensembles. Geoinformatics Research Papers 4, BS4002. 10.2205/2016BS01Sochi.

Shchiptsova, A., Kovalevsky, D., & Rovenskaya, E. (2015). Reconciling Information from Alternative Climate-economic Models: A Posterior Integration Approach. In: Systems Analysis 2015 - A Conference in Celebration of Howard Raiffa, 11 -13 November, 2015, Laxenburg, Austria.

Kryazhimskiy, A.V. (2013). Posterior Integration of Independent Stochastic Estimates. IIASA Interim Report. IIASA, Laxenburg, Austria: IR-13-006


This work received support from the EU FP7 project COMPLEX (grant no. 308601)