Prior distributions fro stochastic matrices
Lead Research Organisation:
University of Leeds
Department Name: Statistics
Abstract
The objectives of the research are to improve the predictions of land use from satellite imagery. In particular, in order to
estimate risks of plant disease spreading and risks to future food security, we would like to be able to estimate the amount and
location of crops and susceptible plant species based upon coarse satellite imagery.
For a methodological development point-of-view, we would like to build statistical models that link the satellite imagery with
known processes (e.g., disease spreading or crop rotation planning). To facilitate this, we will develop methods for handling
right-stochastic matrices within Bayesian analyses. Right-stochastic matrices are used in the modelling of Markov processes
(transition matrices) and of misclassification proportions (confusion matrices). We are researching methods for 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.
estimate risks of plant disease spreading and risks to future food security, we would like to be able to estimate the amount and
location of crops and susceptible plant species based upon coarse satellite imagery.
For a methodological development point-of-view, we would like to build statistical models that link the satellite imagery with
known processes (e.g., disease spreading or crop rotation planning). To facilitate this, we will develop methods for handling
right-stochastic matrices within Bayesian analyses. Right-stochastic matrices are used in the modelling of Markov processes
(transition matrices) and of misclassification proportions (confusion matrices). We are researching methods for 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.
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509681/1 | 01/10/2016 | 30/09/2021 | |||
| 1956125 | Studentship | EP/N509681/1 | 01/10/2017 | 30/09/2021 | Anastasia Frantsuzova |
| Description | We have explored the ways of quantifying uncertainty about data represented by proportions. This is used as an inferential tool in Bayesian Statistics, where historical data is sparse for such analysis. Through the process of questioning experts in a particular field in a rigorous manner (expert elicitation), this uncertainty can be represented in terms of probability distributions. 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. In applied environmental work with Fera, we have used some of the above statistical techniques explore 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. |
| Exploitation Route | Extending the Fera project once more data becomes available, to explore the extent to which our conclusions are transferable to other geographical locations. The expert elicitation overview could be directly used by applied scientists in numerous fields, to guide them through the process and conduct it as rigorously as possible, with the help of a trained statistician. |
| Sectors | Environment,Other |