Prior distributions fro stochastic matrices

这项研究的目的是改进从卫星图像对土地利用的预测。特别是，为了估计植物疾病传播的风险和对未来粮食安全的风险，我们希望能够根据粗略的卫星图像估计作物和易感植物物种的数量和位置。从方法学发展的角度来看，我们希望建立统计模型，将卫星图像与已知过程（例如，疾病传播或作物轮作计划）。为了促进这一点，我们将开发的方法来处理贝叶斯分析中的右随机矩阵。右随机矩阵用于马尔可夫过程（转移矩阵）和误分类比例（混淆矩阵）的建模。我们正在研究构建合理的概率分布的方法，这些概率分布可以用来封装关于这种结构化矩阵的信念，并比较这些分布的属性及其在暴露于数据时的效果。

The objectives of the research are to improve the predictions of land use from satellite imagery. In particular, in order toestimate risks of plant disease spreading and risks to future food security, we would like to be able to estimate the amount andlocation 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 withknown processes (e.g., disease spreading or crop rotation planning). To facilitate this, we will develop methods for handlingright-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 constructingsensible probability distributions that can be used to encapsulate beliefs about such structured matrices and compare theproperties of the distributions and their effects when exposed to data.