Inference for bounded parameters

The estimation of signal frequency count in the presence of background noise has had much discussion in the recent physics literature, and Mandelkern [1] brings the central issues to the statistical community, leading in turn to extensive discussion by statisticians. The primary focus however in [1] and the accompanying discussion is on the construction of a confidence interval. We argue that the likelihood function and $p$-value function provide a comprehensive presentation of the information available from the model and the data. This is illustrated for Gaussian and Poisson models with lower bounds for the mean parameter

Perspectives of Malaysian academics on the preparation of fourth industrial revolution for Construction Technology Program

The purpose of this study is to examine the perspective of Construction Technology academics from Malaysia vocational colleges on implementing the aspects of the industrial revolution 4.0 (IR 4.0). It was achieved by determining the degree of leadership support for vocational colleges, implementation of IR 4.0 components by academics, readiness for both generic and IR 4.0-related technical skills. This study was conducted using a survey method (cross-sectional study) where data collection and research findings were done only once during this study was conducted by applying the questionnaire method. The sample was chosen from among 408 academics from 42 vocational schools in Malaysia using Fisher's Formula. By choosing to work with a 95% confidence level, a standard deviation of 0.5, and a confidence interval (margin of error) of ± 5%, this study requires 198 samples for a better data findings and analysis. From 198 instruments distributed, only 45 instruments managed to be collected and analyzed due to limitation during global pandemic. The findings of this study were analyzed using Statistical Packages for Social Sciences (SPSS) software, version 20 by taking the mean value of each variable studied. The results of the study showed that the average mean score for each of the overall objectives of the study was at a high level which is between the mean ranges of 3.98 - 4.38. This shows that the level of implementation and readiness from the perspectives of vocational college academics in Malaysia in the field of Construction Technology is at a high level

A Unified Approach to the Classical Statistical Analysis of Small Signals

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.Comment: 40 pages, 15 figures. Changes 15-Dec-99 to agree more closely with published version. A few small changes, plus the two substantive changes we made in proof back in 1998: 1) The definition of "sensitivity" in Sec. V(C). It was inconsistent with our actual definition in Sec. VI. 2) "Note added in proof" at end of the Conclusio

Another Look at Confidence Intervals: Proposal for a More Relevant and Transparent Approach

The behaviors of various confidence/credible interval constructions are explored, particularly in the region of low statistics where methods diverge most. We highlight a number of challenges, such as the treatment of nuisance parameters, and common misconceptions associated with such constructions. An informal survey of the literature suggests that confidence intervals are not always defined in relevant ways and are too often misinterpreted and/or misapplied. This can lead to seemingly paradoxical behaviours and flawed comparisons regarding the relevance of experimental results. We therefore conclude that there is a need for a more pragmatic strategy which recognizes that, while it is critical to objectively convey the information content of the data, there is also a strong desire to derive bounds on models and a natural instinct to interpret things this way. Accordingly, we attempt to put aside philosophical biases in favor of a practical view to propose a more transparent and self-consistent approach that better addresses these issues.Comment: 23 pages, 11 figure

Statistical Models with Uncertain Error Parameters

In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable with a given standard deviation (the corresponding "systematic error"). Although the assigned systematic errors are usually treated as constants, in general they are themselves uncertain. A type of model is presented where the uncertainty in the assigned systematic errors is taken into account. Estimates of the systematic variances are modeled as gamma distributed random variables. The resulting confidence intervals show interesting and useful properties. For example, when averaging measurements to estimate their mean, the size of the confidence interval increases for decreasing goodness-of-fit, and averages have reduced sensitivity to outliers. The basic properties of the model are presented and several examples relevant for Particle Physics are explored.Comment: 26 pages, 27 figure