Time of Arrival from Bohmian Flow

We develop a new conception for the quantum mechanical arrival time distribution from the perspective of Bohmian mechanics. A detection probability for detectors sensitive to quite arbitrary spacetime domains is formulated. Basic positivity and monotonicity properties are established. We show that our detection probability improves and generalises earlier proposals by Leavens and McKinnon. The difference between the two notions is illustrated through application to a free wave packet.Comment: 18 pages, 8 figures, to appear in Journ. Phys. A; representation of ref. 5 improved (thanks to Rick Leavens

On the quantum probability flux through surfaces

We remark that the often ignored quantum probability current is fundamental for a genuine understanding of scattering phenomena and, in particular, for the statistics of the time and position of the first exit of a quantum particle from a given region, which may be simply expressed in terms of the current. This simple formula for these statistics does not appear as such in the literature. It is proposed that the formula, which is very different from the usual quantum mechanical measurement formulas, be verified experimentally. A full understanding of the quantum current and the associated formula is provided by Bohmian mechanics.Comment: 15 pages, 3 figures, revised and more detailed version, to be published in Journal of Statistical Physics, August 9

On-line monitoring using Multi-Process Kalman Filtering

On-line monitoring of time series becomes more and more important in different areas of application like medicine, biometry and finance. In medicine, on-line monitoring of patients after transplantation of renals (Smith83) is an easy and prominent example. In finance, fast end reliable recognition of changes in level and trend of intra-daily stock market prices is of obvious interest for ordering and purchasing. In this project, we currently consider monitoring of surgical data like heart-rate, blood pressure and oxygenation. From a statistical point of view, on-line monitoring can be considered as on-line detection of changepoints in time series. That means, changepoints have to be detected in real time as new observations come in, usually in short time intervals. Retrospective detection of changepoints, after the whole batch of observations has been recorded, is nice but useless in monitoring patients during an operation. There are various statistical approaches conceivable for on-line detection of changepoints in time series. Dynamic or state space models seem particularly well suited because ``filtering'' has historically been developed exactly for on-line estimation of the ``state'' of some system. Our approach is based on a recent extension of the so-called multi-process Kalman filter for changepoint detection (Schnatter94). It turned out, however, that some important issues for adequate and reliable application have to be considered, in particular the (appropriate) handling of outliers and, as a central point, adaptive on-line estimation of control- or hyper-parameters. In this paper, we describe a filter model that has this features and can be implemented in such a way that it is useful for real time applications with high frequency time series data. Recently, simulation based methods for estimation of non-Gaussian dynamic models have been proposed that may also be adapted and generalized for the purpose of changepoint detection. Most of them solve the smoothing problem, but very recently some proposals have been made that could be useful also for filtering and, thus, for on-line monitoring (Kitagawa96a,Kitagawa96b,Shephard96). If these approaches are a useful alternative to our development needs a careful comparison in future and is beyond the scope of this paper

CMA – a comprehensive Bioconductor package for supervised classification with high dimensional data

For the last eight years, microarray-based class prediction has been a major topic in statistics, bioinformatics and biomedicine research. Traditional methods often yield unsatisfactory results or may even be inapplicable in the p > n setting where the number of predictors by far exceeds the number of observations, hence the term “ill-posed-problem”. Careful model selection and evaluation satisfying accepted good-practice standards is a very complex task for inexperienced users with limited statistical background or for statisticians without experience in this area. The multiplicity of available methods for class prediction based on high-dimensional data is an additional practical challenge for inexperienced researchers. In this article, we introduce a new Bioconductor package called CMA (standing for “Classification for MicroArrays”) for automatically performing variable selection, parameter tuning, classifier construction, and unbiased evaluation of the constructed classifiers using a large number of usual methods. Without much time and effort, users are provided with an overview of the unbiased accuracy of most top-performing classifiers. Furthermore, the standardized evaluation framework underlying CMA can also be beneficial in statistical research for comparison purposes, for instance if a new classifier has to be compared to existing approaches. CMA is a user-friendly comprehensive package for classifier construction and evaluation implementing most usual approaches. It is freely available from the Bioconductor website at http://bioconductor.org/packages/2.3/bioc/html/CMA.html

Reducing the Probability of False Positive Research Findings by Pre-Publication Validation - Experience with a Large Multiple Sclerosis Database

*Objective*
We have assessed the utility of a pre-publication validation policy in reducing the probability of publishing false positive research findings. 
*Study design and setting*
The large database of the Sylvia Lawry Centre for Multiple Sclerosis Research was split in two parts: one for hypothesis generation and a validation part for confirmation of selected results. We present case studies from 5 finalized projects that have used the validation policy and results from a simulation study.
*Results*
In one project, the "relapse and disability" project as described in section II (example 3), findings could not be confirmed in the validation part of the database. The simulation study showed that the percentage of false positive findings can exceed 20% depending on variable selection. 
*Conclusion*
We conclude that the validation policy has prevented the publication of at least one research finding that could not be validated in an independent data set (and probably would have been a "true" false-positive finding) over the past three years, and has led to improved data analysis, statistical programming, and selection of hypotheses. The advantages outweigh the lost statistical power inherent in the process

Times of arrival: Bohm beats Kijowski

We prove that the Bohmian arrival time of the 1D Schroedinger evolution violates the quadratic form structure on which Kijowski's axiomatic treatment of arrival times is based. Within Kijowski's framework, for a free right moving wave packet, the various notions of arrival time (at a fixed point x on the real line) all yield the same average arrival time. We derive an inequality relating the average Bohmian arrival time to the one of Kijowksi. We prove that the average Bohmian arrival time is less than Kijowski's one if and only if the wave packet leads to position probability backflow through x. Otherwise the two average arrival times coincide.Comment: 9 page

Evaluating Microarray-based Classifiers: An Overview

For the last eight years, microarray-based class prediction has been the subject of numerous publications in medicine, bioinformatics and statistics journals. However, in many articles, the assessment of classification accuracy is carried out using suboptimal procedures and is not paid much attention. In this paper, we carefully review various statistical aspects of classifier evaluation and validation from a practical point of view. The main topics addressed are accuracy measures, error rate estimation procedures, variable selection, choice of classifiers and validation strategy

Temporal Ordering in Quantum Mechanics

We examine the measurability of the temporal ordering of two events, as well as event coincidences. In classical mechanics, a measurement of the order-of-arrival of two particles is shown to be equivalent to a measurement involving only one particle (in higher dimensions). In quantum mechanics, we find that diffraction effects introduce a minimum inaccuracy to which the temporal order-of-arrival can be determined unambiguously. The minimum inaccuracy of the measurement is given by dt=1/E where E is the total kinetic energy of the two particles. Similar restrictions apply to the case of coincidence measurements. We show that these limitations are much weaker than limitations on measuring the time-of-arrival of a particle to a fixed location.Comment: New section added, arguing that order-of-arrival can be measured more accurately than time-of-arrival. To appear in Journal of Physics