Charles Taylor

Karim Kadry, Abhishek Karmakar, Andreas Schuh et al.

Coronary computed tomography angiography (CCTA) provides 3D information on obstructive coronary artery disease, but cannot fully visualize high-resolution features within the vessel wall. Intravascular imaging, in contrast, can spatially resolve atherosclerotic in cross sectional slices, but is limited in capturing 3D relationships between each slice. Co-registering CCTA and intravascular images enables a variety of clinical research applications but is time consuming and user-dependent. This is due to intravascular images suffering from non-rigid distortions arising from irregularities in the imaging catheter path. To address these issues, we present a morphology-based framework for the rigid and non-rigid matching of intravascular images to CCTA images. To do this, we find the optimal virtual catheter path that samples the coronary artery in CCTA image space to recapitulate the coronary artery morphology observed in the intravascular image. We validate our framework on a multi-center cohort of 40 patients using bifurcation landmarks as ground truth for longitudinal and rotational registration. Our registration approach significantly outperforms other approaches for bifurcation alignment. By providing a differentiable framework for multi-modal vascular co-registration, our framework reduces the manual effort required to conduct large-scale multi-modal clinical studies and enables the development of machine learning-based co-registration approaches.

Yaojun Zhang, Lanpeng Ji, Georgios Aivaliotis et al.

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 paper, 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.

Boshra Alarfaj, Charles Taylor, Leonid Bogachev

The Erdős-Rényi random graph is the simplest model for node degree distribution, and it is one of the most widely studied. In this model, pairs of $n$ vertices are selected and connected uniformly at random with probability $p$, consequently, the degrees for a given vertex follow the binomial distribution. If the number of vertices is large, the binomial can be approximated by Normal using the Central Limit Theorem, which is often allowed when $\min (np, n(1-p)) > 5$. This is true for every node independently. However, due to the fact that the degrees of nodes in a graph are not independent, we aim in this paper to test whether the degrees of per node collectively in the Erdős-Rényi graph have a multivariate normal distribution MVN. A chi square goodness of fit test for the hypothesis that binomial is a distribution for the whole set of nodes is rejected because of the dependence between degrees. Before testing MVN we show that the covariance and correlation between the degrees of any pair of nodes in the graph are $p(1-p)$ and $1/(n-1)$, respectively. We test MVN considering two assumptions: independent and dependent degrees, and we obtain our results based on the percentages of rejected statistics of chi square, the $p$-values of Anderson Darling test, and a CDF comparison. We always achieve a good fit of multivariate normal distribution with large values of $n$ and $p$, and very poor fit when $n$ or $p$ are very small. The approximation seems valid when $np \geq 10$. We also compare the maximum likelihood estimate of $p$ in MVN distribution where we assume independence and dependence. The estimators are assessed using bias, variance and mean square error.