Scalable Bayesian Inference using Multilevel Monte Carlo

Overview

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 computational cost, bias and variance of the statistical inferences. The resulting estimators can be orders of magnitude more efficient than alternatives.

This research could easily develop into an Honours or MPhil project if desired.

Research activities

Research activities include:

• implementing Bayesian methods for a challenging stochastic model
• implementing MLMC estimators for Bayesian inference
• evaluating the performance of MLMC estimators numerically
• comparing numerical results to theoretical convergence properties.

Outcomes

The outcomes of the project include:

• MLMC algorithm and software
• comparison of difference MLMC techniques
• rules-of-thumb for configuration and tuning of MLMC methods.

Skills and experience

You must have:

• programming abilities (preferred languages are MATLAB, R, Python, or Julia)
• an understanding of stochastic modelling or probability theory is desirable
• an understanding of statistical inference (classical or Bayesian) is also desirable.

Scholarships

You may be eligible to apply for a research scholarship.

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Keywords

• stochastic modelling
• stochastic simulation
• computational statistics
• Monte Carlo modelling
• statistical inference

Contact

Contact the supervisor for more information.