Description

There are many physical systems that scientists aim to understand, including the creation of the universe, the effects of climate change, the effects of an epidemic through a population (now very topical!), or, as is the case for this project, the hormonal crosstalk in the roots of a plant (Arabidopsis).  Understanding of hormonal crosstalk in Arabidopsis is important since it is informative for understanding the crosstalk in agricultural plants such as wheat and other crops - crucial to permit genetic modification to make the plants grow healthier in our adversely-changing climate.  A crucial aspect of understanding such systems is construction of a computer model, which in this case seek to describe the major biological processes governing the hormonal interactions within the plant.  Such models typically represent the system as execution of computer code, for example, numerically solving sets of differential equations.  These equations are usually determined by sets of rate parameters, for example, representing chemical rates of reaction. 

This project aims to investigate simulation of plant models for the purpose of making inferences about their rate parameters, and hence corresponding properties in the plants and possible genetic mutations, by comparing model output and data.  In so doing, we shall discover that many of these models are slow and take time to evaluate.  We will therefore utilise Gaussian process regression, or emulation, to statistically approximate computer model output at any finite collection of input points by a multivariate normal distribution.  Such statistical approximation is made more interesting when there are particular hyperplanes, or boundaries, in the input space where the model can be solved analytically.  In particular, we look to investigate how these hyperplanes can be used to efficiently improve our approximation.

The possible directions for this project are diverse, including extension to calibration-type methods (such as history matching, Approximate Bayesian Computation).  Substantial coding (for example, in R) will be necessary to practically carry out and investigate the biological plant models and Gaussian process regression.

Prerequisites

• Statistical Concepts II
• Statistical Methods III

Resources

• A nice introduction to both computer models and Gaussian process regression can be found in Chapters 1 and 5 respectively of the book Surrogates by Robert Gramacy.

• For an alternative take on such approximations, and in particular a possible approach to eliciting rate parameters, see Vernon et al. (2018): Bayesian uncertainty analysis for complex systems biology models: emulation, global parameter searches and evaluation of gene functions, BMC Systems Biology.

• Investigation of emulation in the context of  biological plant model with known hyperplanes can be seen in Vernon et al. (2019): Known Boundary Emulation of Complex Computer Models, SIAM/AS Journal on Uncertainty Quantification.