Uncertainty Quantification • uqsa

library(uqsa)

Introduction to UQ

Uncertainty Quantification and global Sensitivity Analysis are both common tasks in systems biology. Uncertainty quantification aims to establish the amount of knowledge we have (or indeed lack) about the possible values of model parameters. The knowledge is expressed in the form of probability distributions over the parameters, even though the parameters are not random variables. In this case the probability is related to the randomness within the observed of data: the measurement noise. The noise has direct implications for the possible parameters: parameters with high probability density values can easily explain the data, while unlikely parameters require the random noise to have had uncharacteristically large values for the given measurements

This package aims to characterize the posterior probability distribution \(p(\theta|D)\), where \(\theta\) is a vector that directly maps to the model parameters and is used as a Markov chain variable, e.g.: \(\rho = \exp(\theta)\), where \(\rho\) are the real model parameters.

This target distribution quantifies the amount of knowledge we have about \(\theta\), and indirectly also about the internal parameters of the model. In the field of systems biology, the internal parameters \(\rho\) are typically quantities like reaction rate coefficients \(k_{\{f,b\}}\), dissociation constants (equilibrium constants) \(K_{D}\), Hill exponents \(m\), and other parameters that relate to gene expression, enzyme-substrate interaction, or other biochemical processes.