Related papers: Hypotheses Testing: Poisson Versus Self-exciting
This work deals with a general problem of testing multiple hypotheses about the distribution of a discrete-time stochastic process. Both the Bayesian and the conditional settings are considered. The structure of optimal sequential tests is…
The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified. For…
In applied settings, tests of hypothesis where a nuisance parameter is only identifiable under the alternative often reduces into one of Testing One Hypothesis Multiple times (TOHM). Specifically, a fine discretization of the space of the…
Stationary stochastic processes with independent increments, of which the Poisson process is a prominent example, are widely used to describe real world events. With the basic assumption that a counting process is stationary and has…
In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…
Hypothesis testing is an essential statistical method in psychology and the cognitive sciences. The problems of traditional null hypothesis significance testing (NHST) have been discussed widely, and among the proposed solutions to the…
The problem of verifying whether a multi-component system has anomalies or not is addressed. Each component can be probed over time in a data-driven manner to obtain noisy observations that indicate whether the selected component is…
Constraint based causal structure learning for point processes require empirical tests of local independence. Existing tests require strong model assumptions, e.g. that the true data generating model is a Hawkes process with no latent…
Certain monotonicity properties of the Poisson approximation to the binomial distribution are established. As a natural application of these results, exact (rather than approximate) tests of hypotheses on an unknown value of the parameter…
Statistical hypothesis testing serves as statistical evidence for scientific innovation. However, if the reported results are intentionally biased, hypothesis testing no longer controls the rate of false discovery. In particular, we study…
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…
The analysis of count data is commonly done using Poisson models. Negative binomial models are a straightforward and readily motivated generalization for the case of overdispersed data, i.e., when the observed variance is greater than…
The test of homogeneity for normal mixtures has been conducted in diverse research areas, but constructing a theory of the test of homogeneity is challenging because the parameter set for the null hypothesis corresponds to singular points…
Suppose that at any stage of a statistical experiment a control variable $X$ that affects the distribution of the observed data $Y$ can be used. The distribution of $Y$ depends on some unknown parameter $\theta$, and we consider the…
A hypothesis testing scheme for entanglement has been formulated based on the Poisson distribution framework instead of the POVM framework. Three designs were proposed to test the entangled states in this framework. The designs were…
Two-sample hypothesis testing for random graphs arises naturally in neuroscience, social networks, and machine learning. In this paper, we consider a semiparametric problem of two-sample hypothesis testing for a class of latent position…
In this paper, our interest is in the problem of simultaneous hypothesis testing when the test statistics corresponding to the individual hypotheses are possibly correlated. Specifically, we consider the case when the test statistics…
Experiments often yield non-identically distributed data for statistical analysis. Tests of hypothesis under such set-ups are generally performed using the likelihood ratio test, which is non-robust with respect to outliers and model…
This paper studies optimal hypothesis testing for nonregular econometric models with parameter-dependent support. We consider both one-sided and two-sided hypothesis testing and develop asymptotically uniformly most powerful tests based on…
We describe the utility of point processes and failure rates and the most common point process for modeling failure rates, the Poisson point process. Next, we describe the uniformly most powerful test for comparing the rates of two Poisson…