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Replicability is central to scientific progress, and the partial conjunction (PC) hypothesis testing framework provides an objective tool to quantify it across disciplines. Existing PC methods assume independent studies. Yet many modern…
Conformal prediction methods are statistical tools designed to quantify uncertainty and generate predictive sets with guaranteed coverage probabilities. This work introduces an innovative refinement to these methods for classification…
$P$-values that are derived from continuously distributed test statistics are typically uniformly distributed on $(0,1)$ under least favorable parameter configurations (LFCs) in the null hypothesis. Conservativeness of a $p$-value $P$…
Combining p-values from independent statistical tests is a popular approach to meta-analysis, particularly when the data underlying the tests are either no longer available or are difficult to combine. A diverse range of p-value combination…
High dimensional case control studies are ubiquitous in the biological sciences, particularly genomics. To maximise power while constraining cost and to minimise type-1 error rates, researchers typically seek to replicate findings in a…
Evaluation of novel treatment effect estimators frequently relies on simulation studies lacking formal statistical comparisons and using arbitrary numbers of replications ($J$). This hinders reproducibility and efficiency. We propose the…
We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…
Using a Coulomb gas technique, we compute analytically the probability $\mathcal{P}_\beta^{(C)}(N_+,N)$ that a large $N\times N$ Cauchy random matrix has $N_+$ positive eigenvalues, where $N_+$ is called the index of the ensemble. We show…
When working with large biological data sets, exploratory analysis is an important first step for understanding the latent structure and for generating hypotheses to be tested in subsequent analyses. However, when the number of variables is…
Composite likelihood provides approximate inference when the full likelihood is intractable and sub-likelihood functions of marginal events can be evaluated relatively easily. It has been successfully applied for many complex models.…
In prior work we have introduced an asymptotic threshold of sufficient randomness for causal inference from observational data. In this paper we extend that prior work in three main ways. First, we show how to empirically estimate a lower…
This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP construct the predictive set based on random samples from…
The increasing interest in subpopulation analysis has led to the development of various new trial designs and analysis methods in the fields of personalized medicine and targeted therapies. In this paper, subpopulations are defined in terms…
Conditional independence (CI) testing arises naturally in many scientific problems and applications domains. The goal of this problem is to investigate the conditional independence between a response variable $Y$ and another variable $X$,…
A randomized controlled trial (RCT) is widely regarded as the gold standard for assessing the causal effect of a treatment or intervention, assuming perfect implementation. In practice, however, randomization can be compromised for various…
We propose a new empirical Bayes method for covariate-assisted multiple testing with false discovery rate (FDR) control, where we model the local false discovery rate for each hypothesis as a function of both its covariates and p-value. Our…
While randomised controlled trials (RCTs) are the gold standard for estimating causal treatment effects, their limited sample sizes and restrictive criteria make it difficult to extrapolate to a broader population. Observational data, while…
In this paper, we present a novel approach for conformal prediction (CP), in which we aim to identify a set of promising prediction candidates -- in place of a single prediction. This set is guaranteed to contain a correct answer with high…
This paper develops and analyzes a generic method for reconstructing solutions to the abstract Cauchy problem in a general Hilbert space, from noisy measured data. The method is based on the relationship between a partial differential…
In a computer system, multiple indispensable components-such as the CPU, memory, and others-work together with other essential components to produce an overall effect, which can only be measured on an independently running system. Since the…