# Distributions and Ranges Hinxton Proposal

NB: This page is in development. For a recent status of the package, see the statistical model workshop, the proposal that was derived from it, and the sbml-distrib discussion list.

## Proposal title

**Distributions** (abbreviation *distrib*)

## Proposal authors

## Proposal tracking number

Number 3324561 in the SBML issue tracking system.

## Version information

### Version number and date of public release

Version X released on DD Month YYYY.

### URL for this version of the proposal

### URL for the previous version of this proposal

## Introduction and motivation

## Background

### Problems with current SBML approaches

### Past work on this problem or similar topics

## Proposed syntax and semantics

## Package dependencies

## Use-cases and examples

### Stochastic events and initialisations

Original motivation for development of distrib package. Even in the context of deterministic simulations, it is sometimes useful to describe the sampling of a random number during simulation. Darren gave an example of a cell dividing once it had grown to a given volume. It would be more realistic to initialise species concentrations in the resultant daughter cell with random numbers to reflect stocastic segragation of proteins, than to have a wholly deterministic segragation.

### Bayesian MCMC Parameter Inference for Dynamic Simulation Models

These classes of parameter inference tools (e.g. OpenBUGS, GNUMCSim, CaliBayes,Monolix) need to be able to represent particle-type distribution objects (e.g. posterior distributions, possibly prior distributions) and use standard statistical distribution functions (e.g. prior distributions) to describe uncertainty in model parameter values. For prior distributions this is uncertainty before comparison of model and data, and for posterior distributions uncertainty in model parameters given data.

### Bayesian MCMC Parameter Inference for Hierarchical Statistical Models

OpenBUGS, GNUMCSim and Monolix need to be able to describe uncertainty at a level higher than a single forward simulation. For example, consider a pharmacokinetic model of a patient, applied to understanding the distribution of characteristics (represented by PK model parameters) in a population of patients (represented by hierarchical model statistical distributions).

### PK Model

A simple pharmacokinetic model example (above) was encoded in SBML with proposed distrib extensions. This model is suitable for describing a population of patients, each summarised by 3 parameters, each parameter drawn from a statistical distribution (relevant for distrib package). The model could also be used to demonstrate full, hierarchical, statistical analysis (outside of distrib package).

We updated the xml above during the afternoon. The latest version can be found, together with some discussion, on collabedit here however I think this version may have included invalid UncertML.