Prior distributions for stochastic matrices

Right-stochastic matrices are used in the modelling of discrete-time Markov processes, with a property that the matrix elements are non-negative and each row sums to one. If we consider the problem of estimating these probabilities from a Bayesian standpoint, we are interested in constructing sensible probability distributions that can be used to encapsulate expert beliefs about such structures before any data is observed. Through the process of expert elicitation, this un- certainty can be represented in terms of probability distributions. In this thesis, we explore multivariate distributions on the simplex support from the view of expert elicitation. We explore properties and constraints of these distributions, and ways to elicit expert judgement about their parameters. This is interesting both mathematically and from a practical standpoint, particularly where there are many such variables to explore, which can prove cognitively challenging and tiring for the experts. Similarly, data representing proportions of a whole can be unified into the com- positional framework (Aitchison, 1986) with similar non-negativity and unit-sum properties. This thesis also explores the study of compositional data analysis, its problems and modern ways of approaching them. Application of these methods is found in exploring how high resolution imagery obtained over rural areas could be used in order to identify the distribution of tree species found in those areas where monitoring is prohibited

SARS-CoV-2 RNA levels in Scotland’s wastewater

Nationwide, wastewater-based monitoring was newly established in Scotland to track the levels of SARS-CoV-2 viral RNA shed into the sewage network, during the COVID-19 pandemic. We present a curated, reference dataset produced by this national programme, from May 2020 to February 2022. Viral levels were analysed by RT-qPCR assays of the N1 gene, on RNA extracted from wastewater sampled at 162 locations. Locations were sampled up to four times per week, typically once or twice per week, and in response to local needs. We report sampling site locations with geographical coordinates, the total population in the catchment for each site, and the information necessary for data normalisation, such as the incoming wastewater flow values and ammonia concentration, when these were available. The methodology for viral quantification and data analysis is briefly described, with links to detailed protocols online. These wastewater data are contributing to estimates of disease prevalence and the viral reproduction number (R) in Scotland and in the UK