ProbOnto is a knowledge base and ontology of probability distributions.

[1][2] ProbOnto 2.5 (released on January 16, 2017) contains over 150 uni- and multivariate distributions and alternative parameterizations, more than 220 relationships and re-parameterization formulas, supporting also the encoding of empirical and univariate mixture distributions.

ProbOnto was initially designed to facilitate the encoding of nonlinear-mixed effect models and their annotation in Pharmacometrics Markup Language (PharmML)[3][4] developed by DDMoRe,[5][6] an Innovative Medicines Initiative project.

However, ProbOnto, due to its generic structure can be applied in other platforms and modeling tools for encoding and annotation of diverse models applicable to discrete (e.g. count, categorical and time-to-event) and continuous data.

ProbOnto focuses on this aspect and features more than 15 distributions with alternative parameterizations.

This is due to the fact that it can be parameterized in terms of parameters on the natural and log scale, see figure.The available forms in ProbOnto 2.0 are ProbOnto knowledge base stores such re-parameterization formulas to allow for a correct translation of models between tools.

Consider the situation when one would like to run a model using two different optimal design tools, e.g. PFIM[15] and PopED.

All remaining re-parameterisation formulas can be found in the specification document on the project website.

[2] The knowledge base is built from a simple ontological model.

A distribution relates to a number of other individuals, which are instances of various categories in the ontology.

For example, these are parameters and related functions associated with a given probability distribution.

This strategy allows for the rich representation of attributes and relationships between domain objects.

The ontology can be seen as a conceptual schema in the domain of mathematics and has been implemented as a PowerLoom knowledge base.

[18] Output for ProbOnto are provided as supplementary materials and published on or linked from the probonto.org website.

The OWL version of ProbOnto is available via Ontology Lookup Service (OLS)[19] to facilitate simple searching and visualization of the content.

In addition the OLS API provides methods to programmatically access ProbOnto and to integrate it into applications.

[20] A PharmML interface is provided in form of a generic XML schema for the definition of the distributions and their parameters.

This example shows how the zero-inflated Poisson distribution is encoded by using its codename and declaring that of its parameters (‘rate’ and ‘probabilityOfZero’).