Student topics

Stochastic simulation-based models are routinely used in many areas of science to describe inherent randomness in many real-world systems. Applications include the study of particle physics, imaging if black holes, biochemical processes, the migration of animals, and the spread of infectious diseases. To apply these models to interpret data requires statistical methods to estimate model parameters.Unfortunately, standard statistical techniques are not capable of analysing data using these models. This is largely due to the model likelihood, the probability of the …

Study level

PhD, Master of Philosophy, Honours

Faculty

Faculty of Science

School

School of Mathematical Sciences

Research centre(s)

Centre for Data Science

Cancer is an extremely heterogeneous disease, particularly at the cellular level. Cells within a single cancerous tumour undergo vastly different rates of proliferation based on their location and specific genetic mutations. Capturing this stochasticity in cell behaviour and its effect on tumour growth is challenging with a deterministic system, e.g. ordinary differential equations, however, is possible with an agent-based model (ABM). In an ABM, cells are modelled as individual agents that have a probability of proliferation and movement in each …

Study level

Master of Philosophy, Honours

Faculty

Faculty of Science

School

School of Mathematical Sciences

Research centre(s)

Centre for Data Science

Bayesian inference is a popular statistical framework for estimating the parameters of statistical models based on data. However, Bayesian methods are well known to be computationally intensive. This fact inhibits the scalability of Bayesian analysis for real-world applications involving complex stochastic models. Such models are common in the fields of biology and ecology.Multilevel Monte Carlo (MLMC) methods are a promising class of techniques for dealing with the scalability challenge. These approaches use hierarchies of approximations to optimise the trade-off between …

Study level

Master of Philosophy, Honours

Faculty

Faculty of Science

School

School of Mathematical Sciences

Research centre(s)

Centre for Data Science

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. …

Study level

PhD, Master of Philosophy, Honours

Faculty

Faculty of Science

School

School of Mathematical Sciences

Research centre(s)

Centre for Data Science

Bayesian statistics provide a framework for a statistical inference for quantifying the uncertainty of unknowns based on information pre and post data collection.This information is captured in the posterior distribution, which is a probability distribution over the space of unknowns given the observed data.The ability to make inferences based on the posterior essentially amounts to efficiently simulating from the posterior distribution, which can generally not be done perfectly in practice.This task of sampling may be challenging for various reasons:The posterior …

Study level

PhD, Master of Philosophy, Honours

Faculty

Faculty of Science

School

School of Mathematical Sciences

Research centre(s)

Centre for Data Science

In the age of Big Data, machine learning methods, and modern statistics the adage "all models are wrong but some are useful" has never been so true. This project will investigate data science approaches where more than one model makes sense for the data. Is it better to choose a single model or is there something to be gained from multiple models?This project will look at variable selection methods, penalised regression, Bayesian model averaging and conformal prediction. The research has …

Study level

Honours

Faculty

Faculty of Science

School

School of Mathematical Sciences

Research centre(s)

Centre for Data Science

Random walk models are often used to represent the motion of biological cells. These models are convenient because they allow us to capture randomness and variability. However, these approaches can be computationally demanding for large populations.One way to overcome the computational limitation of using random walk models is to take a continuum limit description, which can efficiently provide insight into the underlying transport phenomena.While many continuum limit descriptions for homogeneous random walk models are available, continuum limit descriptions for heterogeneous …

Study level

PhD, Master of Philosophy, Honours

Faculty

Faculty of Science

School

School of Mathematical Sciences

Research centre(s)

Centre for Data Science

Stochastic simulation-based models are very attractive to study population-biology, disease transmission, development and disease. These models naturally incorporate randomness in a way that is consistent with experimental measurements that describe natural phenomena.Standard statistical techniques are not directly compatible with data produced by simulation-based stochastic models since the model likelihood function is unavailable. Progress can be made, however, by introducing an auxiliary likelihood function can be formulated, and this auxiliary likelihood function can be used for identifiability analysis, parameter estimation and …

Study level

PhD, Master of Philosophy

Faculty

Faculty of Science

School

School of Mathematical Sciences

Research centre(s)

Centre for Data Science

Mathematical models of particle transport are fundamental to many applied disciplines including physics, biology, ecology and medicine. Particle transport is typically modelled using either a stochastic model, where probability rules govern the motion of individual particles, or a continuum model, where partial differential equations govern the concentration of particles in space and time. This project aims to use analytical and numerical techniques from applied and computational mathematics to address one or both of the following questions:what is the average time …

Study level

Master of Philosophy, Honours

Faculty

Faculty of Science

School

School of Mathematical Sciences

To conserve species in disturbed natural environments, we need to use mathematical models to predict the consequences of different interventions. Unfortunately, these models are based on partial information of complex systems, and the systems themselves are subject to substantial observational and process noise.We often use ordinary differential equations to describe ecosystems, like the classic logistic growth model:dn/dt = r n (1 - n / k)However, these models are deterministic, and they assume we know the values of the key parameters …

Study level

Master of Philosophy, Honours

Faculty

Faculty of Science

School

School of Mathematical Sciences

Research centre(s)

Centre for Data Science
Centre for the Environment