Study level

  • PhD
  • Master of Philosophy
  • Honours
  • Vacation research experience scheme

Faculty/School

Topic status

We're looking for students to study this topic.

Research centre

Supervisors

Professor Matthew Simpson
Position
Professor
Division / Faculty
Faculty of Science
Dr David Warne
Position
Lecturer in Statistical Inference for Complex Models
Division / Faculty
Faculty of Science

External supervisors

  • Dr Alexander Browning (University of Oxford)

Overview

Stochastic models are used in biology to account for inherent randomness in many cellular processes, for example gene regulatory networks. Noise is often thought to obscure information, however, there is an increasing understanding that some randomness contains vitally important information about underlying biological processes.

When applying these models to interpret and learn from data, unknown parameters in the model need to be estimated. However, not all data will contribute to a given estimation task regardless of the data quantity and quality. That is, for some parameters of interest, the data may hold no information. Understanding these limits can inform better experiments and improve our modelling approaches.

To estimate parameters using data, statistical inference methods are applied. However, if the data has no information about a parameter, then inference results can be wildly inaccurate. The question of what can be learned about model parameters from data is called the identifiability problem. The identifiability properties of a model can have profound implications for the limitations of statistical inferences related to a given model. Furthermore, an understanding of identifiability can inform the suitability of a model for a given scientific question before data collection.

The majority of research effort to-date analyses identifiability for deterministic models without any noise. Such systems ignore the noise that is ubiquitous to many biological processes.  There are many opportunities for the development of new methods for identifiability that are relevant to stochastic models.

This topic could be developed into various projects appropriate for VRES, Honours, MPhil and PhD level project.

Research activities

This project could involve:

  • Develop stochastic models for common biological processes.
  • Implementation of stochastic simulation schemes.
  • Implementation of methods for assessing identifiability with synthetic data.
  • Comparison of identifiability results for stochastic models with deterministic counterparts.
  • Use of methods of assessing theoretical limits of identifiability, and interpretation results.
  • Exploiting existing methods using deterministic systems derived from stochastic models.

Outcomes

The outcomes of the project include:

  • Algorithms and software to assess parameter identifiability for stochastic models.
  • Insight into relationships and differences between the identifiability properties of deterministic systems and their stochastic counterparts.
  • Assessment of implications of unidentifiable parameters for inference tasks.
  • Recommendations for adjustment of models or experiments considering identifiability implications.

Skills and experience

The following skills will be necessary:

  • Basic understanding of probability and stochastic modelling.
  • Programming abilities (preferred languages are MATLAB, R, Python, or Julia).

The following skills are not essential, but will be useful:

  • Understanding of statistical inference (classical or Bayesian).
  • Knowledge of differential equations.
  • Experience working with data.

Scholarships

You may be eligible to apply for a research scholarship.

Explore our research scholarships

Keywords

Contact

Contact the supervisor for more information.