Related papers: A note on Delta ln L = -1/2 Errors
Comparisons are carried out of the confidence intervals constructed with Neyman's frequentist method and with the \Delta L=1/2 likelihood method, using the example of low-statistics life time estimates.
We present improved numerical approximations to the exact Poissonian confidence limits for small numbers n of observed events following the approach of Gehrels (1986). Analytic descriptions of all parameters used in the approximations are…
Following Selberg it is known that uniformly for V << (logloglog T)^{1/2 - \epsilon} the measure of those t \in [T;2T] for which log |\zeta(1/2 + it)| > V*((1/2)loglog T)^{1/2} is approximately T times the probability that a standard…
Test log-likelihood is commonly used to compare different models of the same data or different approximate inference algorithms for fitting the same probabilistic model. We present simple examples demonstrating how comparisons based on test…
One of the major goals of cosmological observations is to test theories of structure formation. The most straightforward way to carry out such tests is to compute the likelihood function L, the probability of getting the data given the…
The following proposition is justified from several different points of view. If you use P = 0.05 to suggest that you have made a discovery, you will be wrong at least 30 percent of the time. If, as is often the case, experiments are…
INTRODUCTION: Wald's, the likelihood ratio (LR) and Rao's score tests and their corresponding confidence intervals (CIs), are the three most common estimators of parameters of Generalized Linear Models. On finite samples, these estimators…
A model of Poissonian observation having a jump (change-point) in the intensity function is considered. Two cases are studied. The first one corresponds to the situation when the jump size converges to a non-zero limit, while in the second…
By employing recent data on non-mesonic decay of s-shell Lambda-hypernuclei we study, within the phenomenological model of Block and Dalitz, the validity of the Delta I=1/2 rule in the Lambda N--> NN process. Due to the low experimental…
We consider a system of dependent Poisson variables, where each variable is the sum of an independent variate and a common variate. It is the common variate that creates the dependence. Within this system, a test of independence may be…
This study aims to evaluate the performance of power in the likelihood ratio test for changepoint detection by bootstrap sampling, and proposes a hypothesis test based on bootstrapped confidence interval lengths. Assuming i.i.d normally…
We compute bias, variance, and approximate confidence intervals for the efficiency of a random selection process under various special conditions that occur in practical data analysis. We consider the following cases: a) the number of…
It is shown that the mass dependence of the $\Lambda$-lifetime in heavy hypernuclei is sensitive to the ratio of neutron-induced to proton-induced non-mesonic decay rates R_n/R_p. A comparison of the experimental mass dependence of the…
Introduction: estimation of confidence intervals (CIs) of binomial proportions has been reviewed more than once but the directional interpretation, distinguishing the overestimation from the underestimation, was neglected while the sample…
The double hypothesis test (DHT) is a test that allows controlling Type I (producer) and Type II (consumer) errors. It is possible to say whether the batch has a defect rate, p, between 1.5 and 2%, or between 2 and 5%, or between 5 and 10%,…
Rigorous statistical evaluations of large language models (LLMs), including valid error bars and significance testing, are essential for meaningful and reliable performance assessment. Currently, when such statistical measures are reported,…
Positive and negative likelihood ratios are parameters which are used to assess and compare the effectiveness of binary diagnostic tests. Both parameters only depend on the sensitivity and specificity of the diagnostic test and are…
This paper concerns the construction of confidence intervals in standard seroprevalence surveys. In particular, we discuss methods for constructing confidence intervals for the proportion of individuals in a population infected with a…
Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by…
The purpose of the present paper is to assess the efficacy of confidence intervals for Rosenthal's fail-safe number. Although Rosenthal's estimator is highly used by researchers, its statistical properties are largely unexplored. First of…