The marginalization paradox and the formal Bayes' law

It has recently been shown that the marginalization paradox (MP) can be resolved by interpreting improper inferences as probability limits. The key to the resolution is that probability limits need not satisfy the formal Bayes' law, which is used in the MP to deduce an inconsistency. In this paper, I explore the differences between probability limits and the more familiar pointwise limits, which do imply the formal Bayes' law, and show how these differences underlie some key differences in the interpretation of the MP.Comment: Presented at Maxent 2007, Saratoga Springs, NY, July 200

A classical explanation of quantization

In the context of our recently developed emergent quantum mechanics, and, in particular, based on an assumed sub-quantum thermodynamics, the necessity of energy quantization as originally postulated by Max Planck is explained by means of purely classical physics. Moreover, under the same premises, also the energy spectrum of the quantum mechanical harmonic oscillator is derived. Essentially, Planck's constant h is shown to be indicative of a particle's "zitterbewegung" and thus of a fundamental angular momentum. The latter is identified with quantum mechanical spin, a residue of which is thus present even in the non-relativistic Schroedinger theory.Comment: 20 pages; version accepted for publication in Foundations of Physic

Causal evidence that intrinsic beta frequency is relevant for enhanced signal propagation in the motor system as shown through rhythmic TMS

Correlative evidence provides support for the idea that brain oscillations underpin neural computations. Recent work using rhythmic stimulation techniques in humans provide causal evidence but the interactions of these external signals with intrinsic rhythmicity remain unclear. Here, we show that sensorimotor cortex precisely follows externally applied rhythmic TMS (rTMS) stimulation in the beta-band but that the elicited responses are strongest at the intrinsic individual beta-peak-frequency. While these entrainment effects are of short duration, even subthreshold rTMS pulses propagate through the network and elicit significant cortico-spinal coupling, particularly when stimulated at the individual beta-frequency. Our results show that externally enforced rhythmicity interacts with intrinsic brain rhythms such that the individual peak frequency determines the effect of rTMS. The observed downstream spinal effect at the resonance frequency provides evidence for the causal role of brain rhythms for signal propagation

Einstein, incompleteness, and the epistemic view of quantum states

Does the quantum state represent reality or our knowledge of reality? In making this distinction precise, we are led to a novel classification of hidden variable models of quantum theory. Indeed, representatives of each class can be found among existing constructions for two-dimensional Hilbert spaces. Our approach also provides a fruitful new perspective on arguments for the nonlocality and incompleteness of quantum theory. Specifically, we show that for models wherein the quantum state has the status of something real, the failure of locality can be established through an argument considerably more straightforward than Bell's theorem. The historical significance of this result becomes evident when one recognizes that the same reasoning is present in Einstein's preferred argument for incompleteness, which dates back to 1935. This fact suggests that Einstein was seeking not just any completion of quantum theory, but one wherein quantum states are solely representative of our knowledge. Our hypothesis is supported by an analysis of Einstein's attempts to clarify his views on quantum theory and the circumstance of his otherwise puzzling abandonment of an even simpler argument for incompleteness from 1927.Comment: 18 pages, 8 figures, 1 recipe for cupcakes; comments welcom

Comparison of Statistical Algorithms for the Detection of Infectious Disease Outbreaks in Large Multiple Surveillance Systems

A large-scale multiple surveillance system for infectious disease outbreaks has been in operation in England and Wales since the early 1990s. Changes to the statistical algorithm at the heart of the system were proposed and the purpose of this paper is to compare two new algorithms with the original algorithm. Test data to evaluate performance are created from weekly counts of the number of cases of each of more than 2000 diseases over a twenty-year period. The time series of each disease is separated into one series giving the baseline (background) disease incidence and a second series giving disease outbreaks. One series is shifted forward by twelve months and the two are then recombined, giving a realistic series in which it is known where outbreaks have been added. The metrics used to evaluate performance include a scoring rule that appropriately balances sensitivity against specificity and is sensitive to variation in probabilities near 1. In the context of disease surveillance, a scoring rule can be adapted to reflect the size of outbreaks and this was done. Results indicate that the two new algorithms are comparable to each other and better than the algorithm they were designed to replace

Using GIS to create synthetic disease outbreaks

BACKGROUND: The ability to detect disease outbreaks in their early stages is a key component of efficient disease control and prevention. With the increased availability of electronic health-care data and spatio-temporal analysis techniques, there is great potential to develop algorithms to enable more effective disease surveillance. However, to ensure that the algorithms are effective they need to be evaluated. The objective of this research was to develop a transparent user-friendly method to simulate spatial-temporal disease outbreak data for outbreak detection algorithm evaluation. A state-transition model which simulates disease outbreaks in daily time steps using specified disease-specific parameters was developed to model the spread of infectious diseases transmitted by person-to-person contact. The software was developed using the MapBasic programming language for the MapInfo Professional geographic information system environment. RESULTS: The simulation model developed is a generalised and flexible model which utilises the underlying distribution of the population and incorporates patterns of disease spread that can be customised to represent a range of infectious diseases and geographic locations. This model provides a means to explore the ability of outbreak detection algorithms to detect a variety of events across a large number of stochastic replications where the influence of uncertainty can be controlled. The software also allows historical data which is free from known outbreaks to be combined with simulated outbreak data to produce files for algorithm performance assessment. CONCLUSION: This simulation model provides a flexible method to generate data which may be useful for the evaluation and comparison of outbreak detection algorithm performance