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We address the problem of estimating the difference between two probability densities. A naive approach is a two-step procedure of first estimating two densities separately and then computing their difference. However, such a two-step…
Roughness parameters that characterize contacting surfaces with regard to friction and wear are commonly stated without uncertainties, or with an uncertainty only taking into account a very limited amount of aspects such as repeatability of…
We present a novel method for image anomaly detection, where algorithms that use samples drawn from some distribution of "normal" data, aim to detect out-of-distribution (abnormal) samples. Our approach includes a combination of encoder and…
We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems…
In this paper, we use partially rank-ordered set (PROS) sampling design with multiple concomitants in a breast cancer study and propose a method to estimate the proportion of patients with malignant (cancerous) breast tumours in a given…
We present the asymptotic distribution for two-sided tests based on the profile likelihood ratio with lower and upper boundaries on the parameter of interest. This situation is relevant for branching ratios and the elements of unitary…
Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. We consider sequential algorithms that…
A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to…
One of the fundamental elements of both traditional and certain deep learning medical image registration algorithms is measuring the similarity/dissimilarity between two images. In this work, we propose an analytical solution for measuring…
Two-phase sampling is commonly adopted for reducing cost and improving estimation efficiency. In many two-phase studies, the outcome and some cheap covariates are observed for a large sample in Phase I, and expensive covariates are obtained…
High-resolution microscopy images of tissue specimens provide detailed information about the morphology of normal and diseased tissue. Image analysis of tissue morphology can help cancer researchers develop a better understanding of cancer…
We examine the problem of construction of confidence intervals within the basic single-parameter, single-iteration variation of the method of quasi-optimal weights. Two kinds of distortions of such intervals due to insufficiently large…
We propose small-variance asymptotic approximations for the inference of tumor heterogeneity (TH) using next-generation sequencing data. Understanding TH is an important and open research problem in biology. The lack of appropriate…
A novel numerical technique has been proposed to solve a two-phase tumour growth model in one spatial dimension without needing to account for the boundary dynamics explicitly. The equivalence to the standard definition of a weak solution…
Shape-valued data are of interest in applied sciences, particularly in medical imaging. In this paper, inspired by a specific medical imaging example, we introduce a hypothesis testing method via the smooth Euler characteristic transform to…
This paper considers the two-dataset problem, where data are collected from two potentially different populations sharing common aspects. This problem arises when data are collected by two different types of researchers or from two…
In this paper we compare two regression curves by measuring their difference by the area between the two curves, represented by their $L^1$-distance. We develop asymptotic confidence intervals for this measure and statistical tests to…
Statistical shape modeling is an essential tool for the quantitative analysis of anatomical populations. Point distribution models (PDMs) represent the anatomical surface via a dense set of correspondences, an intuitive and easy-to-use…
Anomaly detection is not an easy problem since distribution of anomalous samples is unknown a priori. We explore a novel method that gives a trade-off possibility between one-class and two-class approaches, and leads to a better performance…
Mendelian randomization is the use of genetic variants to assess the existence of a causal relationship between a risk factor and an outcome of interest. Here, we focus on two-sample summary-data Mendelian randomization analyses with many…