Right-stochastic matrices are used in the modelling of Markov processes (transition matrices) and of misclassification proportions (confusion matrices). The key property of these square matrices is that all the elements are non-negative and each row sums to one. If we consider the problem of estimating these probabilities from a Bayesian standpoint, we should model our prior beliefs about the matrices before we observe any data. We are interested in constructing sensible probability distributions that can be used to encapsulate beliefs about such structured matrices and compare the properties of the distributions and their effects when exposed to data. This research strand draws heavily on the modelling approaches adopted for compositional data, and we are also interested in extending our findings to accommodate doubly-stochastic matrices (both rows and columns sum to one).
Applications of these methods will be found in land classification, stochastic modelling of biological systems and Markov-chain modelling of financial markets. I aim to complete my thesis by March 2021.
- MSc Statistics, University of St Andrews
- BSc Mathematics with Statistics, City, University of London