Related papers: Chi-square Intervals for a Poisson Parameter - Bay…
In this paper, we have developed a new class of sampling schemes for estimating parameters of binomial and Poisson distributions. Without any information of the unknown parameters, our sampling schemes rigorously guarantee prescribed levels…
Cross-validation (CV) is one of the most widely used techniques in statistical learning for estimating the test error of a model, but its behavior is not yet fully understood. It has been shown that standard confidence intervals for test…
In this paper, we derive an explicit formula for constructing the confidence interval of binomial parameter with guaranteed coverage probability. The formula overcomes the limitation of normal approximation which is asymptotic in nature and…
In high energy physics, a widely used method to treat systematic uncertainties in confidence interval calculations is based on combining a frequentist construction of confidence belts with a Bayesian treatment of systematic uncertainties.…
One goal of contemporary particle physics is to determine the mixing angles and mass-squared differences that constitute the phenomenological constants that describe neutrino oscillations. Of great interest are not only the best fit values…
This paper considers the empirical likelihood (EL) construction of confidence intervals for a linear functional based on right censored lifetime data. Many of the results in literature show that log EL has a limiting scaled chi-square…
The paper proposes a formal estimation procedure for parameters of the fractional Poisson process (fPp). Such procedures are needed to make the fPp model usable in applied situations. The basic idea of fPp, motivated by experimental data…
Models of weak-scale supersymmetry offer viable dark matter (DM) candidates. Their parameter spaces are however rather large and complex, such that pinning down the actual parameter values from experimental data can depend strongly on the…
Measurements are generally collected as unilateral or bilateral data in clinical trials or observational studies. For example, in ophthalmology studies, the primary outcome is often obtained from one eye or both eyes of an individual. In…
Consider a linear regression model with independent and identically normally distributed random errors. Suppose that the parameter of interest is a specified linear combination of the regression parameters. We prove that the usual…
Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…
We consider the problem of interval estimation of the odds ratio. An asymptotic confidence interval is widely applied in medical research. Unfortunately that confidence interval has a poor coverage probability: it is significantly smaller…
Confidence intervals (CIs) are instrumental in statistical analysis, providing a range estimate of the parameters. In modern statistics, selective inference is common, where only certain parameters are highlighted. However, this selective…
The Bayesian data analysis framework has been proven to be a systematic and effective method of parameter inference and model selection for stochastic processes. In this work we introduce an information content model check which may serve…
We consider the classic problem of interval estimation of a proportion $p$ based on binomial sampling. The "exact" Clopper-Pearson confidence interval for $p$ is known to be unnecessarily conservative. We propose coverage-adjustments of the…
Probabilistic regression models typically use the Maximum Likelihood Estimation or Cross-Validation to fit parameters. These methods can give an advantage to the solutions that fit observations on average, but they do not pay attention to…
Confidence intervals are assessed according to two criteria, namely expected length and coverage probability. In an attempt to apply the decision-theoretic method to finding a good confidence interval, a loss function that is a linear…
I investigate the use of Pearson's chi-square statistic, the Maximum Likelihood Ratio statistic for Poisson distributions, and the chi-square-gamma statistic (Mighell 1999, ApJ, 518, 380) for the determination of the goodness-of-fit between…
Pearson's chi-squared test is widely used to test the goodness of fit between categorical data and a given discrete distribution function. When the number of sets of the categorical data, say $k$, is a fixed integer, Pearson's chi-squared…
Bayesian methods provide a natural means for uncertainty quantification, that is, credible sets can be easily obtained from the posterior distribution. But is this uncertainty quantification valid in the sense that the posterior credible…