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Scalable Bayesian Inference using Multilevel Monte Carlo

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, Vacation research experience scheme
Faculty
Faculty of Science
School
School of Mathematical Sciences
Research centre(s)
Centre for Data Science

Making the most of many models

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, Vacation research experience scheme
Faculty
Faculty of Science
School
School of Mathematical Sciences
Research centre(s)
Centre for Data Science

Advances in hypothesis testing

You would have learnt about several hypothesis tests already in your degree, such as t-tests and F-tests (think ANOVA). These tests are designed for the situation where you have a single hypothesis you want to check and you know how many observations you’re going to collect before you collect your data.Unfortunately, these assumptions can be problematic in real applications. For example, consider the situation where it’s time-consuming and expensive to collect data. Can you stop early if you’re getting very …

Study level
Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Faculty of Science
School
School of Mathematical Sciences
Research centre(s)
Centre for Data Science

Topics in computational Bayesian statistics

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, Vacation research experience scheme
Faculty
Faculty of Science
School
School of Mathematical Sciences
Research centre(s)
Centre for Data Science

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