# Leeds Stats PGR Seminar 2022-23 Term 2

This is *Term 2 2022-23*, so all the dates below correspond to the year 2023

*Copyright disclaimer: The titles and abstracts of the talks are the property of the speakers and their colaborators.*

## February 10th

### Regression Analysis for Directional Data

*Norah Almasoud*

In this project, the aim is to build a regression model to predict the effect of linear explanatory variables on a circular response variable. Circular regressions are classified into two groups based on the data type. One group with a circular response variable and the other group with a linear response variable. There are two classes in each group. When the response variable is linear we have linear-linear regression and circular-linear regression. On the other hand, we have linear-circular regression and circular-circular regression when the response variable is circular. Here we concentrate on regression models with circular response variable, more specifically linear-circular regression. Regression models of this type are common in a variety of applications such as medicine, biology, geology, and meteorology. For example, the dependence of an animalâ€™s movement direction on the distance travelled and the dependence of wind direction on wind speed Fisher and Lee [1992].

## February 24th

### Inverse Problem under the Bayesian view—based on the medical image application

*Muyang Zhang*

I am going to talk about something serious which is not relative to my project’s statistical results, as in, bias, variance and MSE (Mean Square Error) are not the most exciting. My first two years of work are—to understand the meaning of the inverse problem, Bayesian methods with homogenous/inhomogeneous parameters. Therefore, it consists of the definition of each term and reasons why we are looking into them. Since it is close to the final stage of being a PhD candidate, it is the time to reveal “the mystery cover” and provide a certain explanation.

## March 10th

### Bayesian CART models for insurance claims frequency

*Yaojun Zhang*

Accuracy and interpretability of a (non-life) insurance pricing model are essential qualities to ensure fair and transparent premiums for policy-holders, that reflect their risk. In recent years, the classification and regression trees (CARTs) and their ensembles have gained popularity in the actuarial literature, since they offer good prediction performance and are relatively easily interpretable. In this talk, we introduce Bayesian CART models for insurance pricing, with a particular focus on claims frequency modelling. Additionally to the common Poisson and negative binomial (NB) distributions used for claims frequency, we implement Bayesian CART for the zero-inflated Poisson (ZIP) distribution to address the difficulty arising from the imbalanced insurance claims data. To this end, we introduce a general MCMC algorithm using data augmentation methods for posterior tree exploration. We also introduce the deviance information criterion (DIC) for the tree model selection. The proposed models are able to identify trees which can better classify the policy-holders into risk groups. Some simulations and real insurance data will be discussed to illustrate the applicability of these models.

## March 24th

### Data analysis for the kidney transplant patient’s data and the smart city’s data by parametric and nonparametric functional data clustering method

*Mizhen Xie*

As modern sensors are being applied in many aspects of daily life, more and more high-frequency data arises. This type of data, usually considered functional data, needs to be appropriately analysed. This presentation focuses on clustering real-world data using parametric and nonparametric clustering methods.