We give a classical confidence belt construction which unifies the treatment of upper confidence limits for null results and two-sided confidence intervals for non-null results. The unified treatment solves a problem (apparently not previously recognized) that the choice of upper limit or two-sided intervals leads to intervals which are not confidence intervals if the choice is based on the data. We apply the construction to two related problems which have recently been a battle-ground between classical and Bayesian statistics: Poisson processes with background, and Gaussian errors with a bounded physical region. In contrast with the usual classical construction for upper limits, our construction avoids unphysical confidence intervals. In contrast with some popular Bayesian intervals, our intervals eliminate conservatism (frequentist coverage greater than the stated confidence) in the Gaussian case and reduce it to a level dictated by discreteness in the Poisson case. We generalize the method in order to apply it to analysis of experiments searching for neutrino oscillations. We show that this technique both gives correct coverage and is powerful, while other classical techniques that have been used by neutrino oscillation search experiments fail one or both of these criteria.

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Unified approach to the classical statistical analysis of small signals

Recent developments promise to increase greatly the popularity of maximum likelihood (ml) as a technique for estimating variance components. Patterson and Thompson (1971) proposed a restricted maximum likelihood (reml) approach which takes into account the loss in degrees of freedom resulting from estimating fixed effects. Miller (1973) developed a satisfactory asymptotic theory for ml estimators of variance components. There are many iterative algorithms that can be considered for computing the ml or reml estimates. The computations on each iteration of these algorithms are those associated with computing estimates of fixed and random effects for given values of the variance components.

Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems

A procedure is derived for extracting the observed information matrix when the EM algorithm is used to find maximum likelihood estimates in incomplete data problems. The technique requires computation of a complete-data gradient vector or second derivative matrix, but not those associated with the incomplete data likelihood. In addition, a method useful in speeding up the convergence of the EM algorithm is developed. Two examples are presented.

Finding the Observed Information Matrix When Using the EM Algorithm

BackgroundNon–small-cell lung cancer (NSCLC) harboring the anaplastic lymphoma kinase gene (ALK) rearrangement is sensitive to the ALK inhibitor crizotinib, but resistance invariably develops. Ceritinib (LDK378) is a new ALK inhibitor that has shown greater antitumor potency than crizotinib in preclinical studies. MethodsIn this phase 1 study, we administered oral ceritinib in doses of 50 to 750 mg once daily to patients with advanced cancers harboring genetic alterations in ALK. In an expansion phase of the study, patients received the maximum tolerated dose. Patients were assessed to determine the safety, pharmacokinetic properties, and antitumor activity of ceritinib. Tumor biopsies were performed before ceritinib treatment to identify resistance mutations in ALK in a group of patients with NSCLC who had had disease progression during treatment with crizotinib. ResultsA total of 59 patients were enrolled in the dose-escalation phase. The maximum tolerated dose of ceritinib was 750 mg once daily; dose-l...

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Ceritinib in ALK-Rearranged Non–Small-Cell Lung Cancer

(1987). Applied Probability and Queues. Journal of the Operational Research Society: Vol. 38, No. 11, pp. 1095-1096.

https://link.springer.com/content/pdf/10.1057%2Fjors.1987.184.pdf

Applied Probability and Queues

Goodness-of-fit is used for the evaluation a model. They are commonly used to compare among competing models. The material is mostly classic. For more on the subject the reader is referred to the R...

Shelemyahu Zacks

Papers

Goodness-of-fit of statistical distributions