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Accurate statistical inference in logistic regression models remains a critical challenge when the ratio between the number of parameters and sample size is not negligible. This is because approximations based on either classical asymptotic…
In Bayesian hypothesis testing and model selection, prior distributions must be chosen carefully. For example, setting arbitrarily large prior scales for location parameters, which is common practice in estimation problems, can lead to…
Analysing subgroups defined by biomarkers is of increasing importance in clinical research. In some situations the biomarker is subject to misclassification error, meaning the true subgroups are identified with imperfect sensitivity and…
Parameter estimation connects mathematical models to real-world data and decision making across many scientific and industrial applications. Standard approaches such as maximum likelihood estimation and Markov chain Monte Carlo estimate…
In the (special) smoothing spline problem one considers a variational problem with a quadratic data fidelity penalty and Laplacian regularisation. Higher order regularity can be obtained via replacing the Laplacian regulariser with a…
In Optimal Recovery, the task of learning a function from observational data is tackled deterministically by adopting a worst-case perspective tied to an explicit model assumption made on the functions to be learned. Working in the…
Given the prominence of targeted therapy and immunotherapy in cancer treatment, it becomes imperative to consider heterogeneity in patients' responses to treatments, which contributes greatly to the widely used proportional hazard…
Generalized linear model with $L_1$ and $L_2$ regularization is a widely used technique for solving classification, class probability estimation and regression problems. With the numbers of both features and examples growing rapidly in the…
Variational regularization is commonly used to solve linear inverse problems, and involves augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori information and is weighted by a regularization parameter.…
Machine learning models suffer from overfitting, which is caused by a lack of labeled data. To tackle this problem, we proposed a framework of regularization methods, called density-fixing, that can be used commonly for supervised and…
Extensions of linear models are very commonly used in the analysis of biological data. Whereas goodness of fit measures such as the coefficient of determination (R2) or the adjusted R2 are well established for linear models, it is not…
Reciprocity--the tendency of individuals to form mutual ties--is a fundamental structural feature of many directed networks. Despite its ubiquity, reciprocity remains insufficiently integrated into statistical network models, particularly…
We consider the linear model $\mathbf{y} = \mathbf{X} \mathbf{\beta}_\star + \mathbf{\epsilon}$ with $\mathbf{X}\in \mathbb{R}^{n\times p}$ in the overparameterized regime $p>n$. We estimate $\mathbf{\beta}_\star$ via generalized (weighted)…
Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…
Consider the use of $\ell_{1}/\ell_{\infty}$-regularized regression for joint estimation of a $\pdim \times \numreg$ matrix of regression coefficients. We analyze the high-dimensional scaling of $\ell_1/\ell_\infty$-regularized quadratic…
AIMS. The maximum-likelihood method is the standard approach to obtain model fits to observational data and the corresponding confidence regions. We investigate possible sources of bias in the log-likelihood function and its subsequent…
In high-dimensional regression, we attempt to estimate a parameter vector $\beta_0\in\mathbb{R}^p$ from $n\lesssim p$ observations $\{(y_i,x_i)\}_{i\leq n}$ where $x_i\in\mathbb{R}^p$ is a vector of predictors and $y_i$ is a response…
Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
Combining patient-level data from clinical trials can connect rare phenomena with clinical endpoints, but statistical techniques applied to a single trial may become problematical when trials are pooled. Estimating the hazard of a binary…