Efficient Parameter Estimation for Stochastic Simulations

Overview

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 observations given the model and parameters, is unavailable. This has led to a substantial volume of research in so-called simulation-based inference, in which repeated stochastic simulations are used as a substitute for the likelihood.

The computational requirements of these approaches are the major challenge for practical statistical analysis of data using stochastic simulations. There are many opportunities to reduce this computational burden using approximations and appropriate corrections to reduce the number of simulations while maintaining accuracy of parameter estimates. See, for examples, our recent work (Warne et al., 2022a https://doi.org/10.1016/j.jcp.2022.111543, and Warne et al., 2022b https://doi.org/10.1080/10618600.2021.2000419). Improving these methods has the potential to greatly advance scientific discoveries.

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

Research activities

This project could involve:

• developing stochastic models for common biological processes
• implementation of stochastic simulation schemes
• implementation of simulation-based methods for parameter estimation
• comparison of computational performance and statistically accuracy for different choices of method and model choices
• application of stochastic models to interpret real data from biology, ecology, or epidemiology.

Outcomes

The outcomes of the project include:

• algorithms and software for statistical analysis of data using stochastic simulations
• evaluation of computational properties of simulation-based parameter estimation for realistic statistical analysis tasks
• recommendations for algorithm configuration for various applications.

Skills and experience

The following skills will be necessary:

• basic understanding of probability or stochastic modelling
• programming abilities (preferred languages are MATLAB, R, Python, or Julia)
• understanding of statistical inference or data science is desirable
• experience working with real data is desirable.

Scholarships

You may be eligible to apply for a research scholarship.

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Keywords

• uncertainty quantification
• likelihood approximations
• bias corrections
• variance reduction
• stochastic models
• simulation-based inference
• likelihood-free methods

Contact

Contact the supervisor for more information.