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The technologies of quantum information and quantum control are rapidly improving, but full exploitation of their capabilities requires complete characterization and assessment of processes that occur within quantum devices. We present a…
Particle physics experiments rely on the (generalised) likelihood ratio test (LRT) for searches and measurements, which consist of composite hypothesis tests. However, this test is not guaranteed to be optimal, as the Neyman-Pearson lemma…
We consider the nonparametric estimation of the intensity function of a Poisson point process in a circular model from indirect observations $N_1,\ldots,N_n$. These observations emerge from hidden point process realizations with the target…
Multiple testing problems are a staple of modern statistical analysis. The fundamental objective of multiple testing procedures is to reject as many false null hypotheses as possible (that is, maximize some notion of power), subject to…
Quantization has become a predominant approach for model compression, enabling deployment of large models trained on GPUs onto smaller form-factor devices for inference. Quantization-aware training (QAT) optimizes model parameters with…
This thesis focuses on the experimental creation and detection of a variety of quantum correlations using nuclear magnetic resonance hardware. Quantum entanglement, being most common and counter-intuitive, is one of the main type considered…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
Joint measurements of non-commuting observables are characterized by unavoidable measurement uncertainties that can be described in terms of the error statistics for input states with well-defined values for the target observables. However,…
We analyze the effects of quantum correlations, such as entanglement and discord, on the efficiency of phase estimation by studying four quantum circuits that can be readily implemented using NMR techniques. These circuits define a standard…
Conducting a randomization test is a common method for testing causal null hypotheses in randomized experiments. The popularity of randomization tests is largely because their statistical validity only depends on the randomization design,…
Measurement error arises through a variety of mechanisms. A rich literature exists on the bias introduced by covariate measurement error and on methods of analysis to address this bias. By comparison, less attention has been given to errors…
While there is considerable work on change point analysis in univariate time series, more and more data being collected comes from high dimensional multivariate settings. This paper introduces the asymptotic concept of high dimensional…
We consider a multi-stage distributed detection scenario, where $n$ sensors and a fusion center (FC) are deployed to accomplish a binary hypothesis test. At each time stage, local sensors generate binary messages, assumed to be spatially…
Measuring the correlation (association) between two random variables is one of the important goals in statistical applications. In the literature, the covariance between two random variables is a widely used criterion in measuring the…
We investigate performance limits and design of communication in the presence of uniform output quantization with moderate to high resolution. Under independent and identically distributed (i.i.d.) complex Gaussian codebook and nearest…
In this paper, we consider Bayesian hypothesis testing for the balanced one-way random effects model. A special choice of the prior formulation for the ratio of variance components is shown to yield an explicit closed-form Bayes factor…
We investigate generalized measurements, based on positive-operator-valued measures, and von Neumann measurements for the unambiguous discrimination of two mixed quantum states that occur with given prior probabilities. In particular, we…
For testing conditional independence (CI) of a response Y and a predictor X given covariates Z, the recently introduced model-X (MX) framework has been the subject of active methodological research, especially in the context of MX knockoffs…
Neyman and Pearson's theory of testing hypotheses does not warrant minimal epistemic reliability: the feature of driving to true conclusions more often than to false ones. The theory does not protect from the possible negative effects of…
The no-signalling principle is a fundamental assumption in Bell-inequality and quantum-steering experiments. Nonetheless, experimental imperfections can lead to apparent violations beyond those expected from finite-sample statistics. Here,…