Related papers: On Hypothesis Testing for Poisson Processes. Regul…
We consider the issue of reporting the result of search experiment in the most unbiased and efficient way, i.e. in a way which allows an easy interpretation and combination of results and which do not depend on whether the experimenters…
Modern statisticians are often presented with hundreds or thousands of hypothesis testing problems to evaluate at the same time, generated from new scientific technologies such as microarrays, medical and satellite imaging devices, or flow…
The problem of hypothesis testing is examined from both the historical and Bayesian points of view in the case that sampling is from an underlying joint probability distribution and the hypotheses tested for are those of independence and…
This paper proposes a model of interactions between two point processes, ruled by a reproduction function h, which is considered as the intensity of a Poisson process. In particular, we focus on the context of neurosciences to detect…
We propose to test the homogeneity of a Poisson process observed on a finite interval. In this framework, we first provide lower bounds for the uniform separation rates in $\mathbb{L}^2$ norm over classical Besov bodies and weak Besov…
Several authors have explained that the likelihood ratio measures the strength of the evidence represented by observations in statistical problems. This idea works fine when the goal is to evaluate the strength of the available evidence for…
We consider the standard Neyman-Pearson hypothesis test of a signal-plus-background hypothesis and background-only hypothesis in the presence of uncertainty on the background-only prediction. Surprisingly, this problem has not been…
Poisson processes and one-dimensional Poisson point processes satisfy three main properties: superposition, thinning, and conditioning. The proof of the first two relies on basic estimates involving the Poisson distribution that are also…
Particle physics experiments such as those run in the Large Hadron Collider result in huge quantities of data, which are boiled down to a few numbers from which it is hoped that a signal will be detected. We discuss a simple probability…
We consider the hypothesis testing problem of detecting a shift between the means of two multivariate normal distributions in the high-dimensional setting, allowing for the data dimension p to exceed the sample size n. Specifically, we…
Multiple hypothesis testing is widely used to evaluate scientific studies involving statistical tests. However, for many of these tests, p-values are not available and are thus often approximated using Monte Carlo tests such as permutation…
In this paper, we propose a simple and easy-to-implement Bayesian hypothesis test for the presence of an association, described by Kendall's \tau coefficient, between two variables measured on at least an ordinal scale. Owing to the absence…
Shape restrictions such as monotonicity on functions often arise naturally in statistical modeling. We consider a Bayesian approach to the problem of estimation of a monotone regression function and testing for monotonicity. We construct a…
Hypothesis test plays a key role in uncertain statistics based on uncertain measure. This paper extends the parametric hypothesis of a single uncertain population to multiple cases, thereby addressing a broader range of scenarios. First, an…
Hypothesis testing in the linear regression model is a fundamental statistical problem. We consider linear regression in the high-dimensional regime where the number of parameters exceeds the number of samples ($p> n$). In order to make…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…
Given a finite-valued sample $X_1,...,X_n$ we wish to test whether it was generated by a stationary ergodic process belonging to a family $H_0$, or it was generated by a stationary ergodic process outside $H_0$. We require the Type I error…
We consider the asymmetric formulation of quantum hypothesis testing, where two quantum hypotheses have different associated costs. In this problem, the aim is to minimize the probability of false negatives and the optimal performance is…
High complexity models are notorious in machine learning for overfitting, a phenomenon in which models well represent data but fail to generalize an underlying data generating process. A typical procedure for circumventing overfitting…
Motivated by the likelihood ratio test under the Gaussian assumption, we develop a maximum sum-of-squares test for conducting hypothesis testing on high dimensional mean vector. The proposed test which incorporates the dependence among the…