Higher Accuracy for Bayesian and Frequentist Inference: Large Sample Theory for Small Sample Likelihood

Recent likelihood theory produces $p$-values that have remarkable accuracy and wide applicability. The calculations use familiar tools such as maximum likelihood values (MLEs), observed information and parameter rescaling. The usual evaluation of such $p$-values is by simulations, and such simulations do verify that the global distribution of the $p$-values is uniform(0, 1), to high accuracy in repeated sampling. The derivation of the $p$-values, however, asserts a stronger statement, that they have a uniform(0, 1) distribution conditionally, given identified precision information provided by the data. We take a simple regression example that involves exact precision information and use large sample techniques to extract highly accurate information as to the statistical position of the data point with respect to the parameter: specifically, we examine various $p$-values and Bayesian posterior survivor $s$-values for validity. With observed data we numerically evaluate the various $p$-values and $s$-values, and we also record the related general formulas. We then assess the numerical values for accuracy using Markov chain Monte Carlo (McMC) methods. We also propose some third-order likelihood-based procedures for obtaining means and variances of Bayesian posterior distributions, again followed by McMC assessment. Finally we propose some adaptive McMC methods to improve the simulation acceptance rates. All these methods are based on asymptotic analysis that derives from the effect of additional data. And the methods use simple calculations based on familiar maximizing values and related informations. The example illustrates the general formulas and the ease of calculations, while the McMC assessments demonstrate the numerical validity of the $p$-values as percentage position of a data point. The example, however, is very simple and transparent, and thus gives little indication that in a wide generality of models the formulas do accurately separate information for almost any parameter of interest, and then do give accurate $p$-value determinations from that information. As illustration an enigmatic problem in the literature is discussed and simulations are recorded; various examples in the literature are cited.Comment: Published in at http://dx.doi.org/10.1214/07-STS240 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Model of Low-pass Filtering of Local Field Potentials in Brain Tissue

Local field potentials (LFPs) are routinely measured experimentally in brain tissue, and exhibit strong low-pass frequency filtering properties, with high frequencies (such as action potentials) being visible only at very short distances ($\approx$10~$\mu m$) from the recording electrode. Understanding this filtering is crucial to relate LFP signals with neuronal activity, but not much is known about the exact mechanisms underlying this low-pass filtering. In this paper, we investigate a possible biophysical mechanism for the low-pass filtering properties of LFPs. We investigate the propagation of electric fields and its frequency dependence close to the current source, i.e. at length scales in the order of average interneuronal distance. We take into account the presence of a high density of cellular membranes around current sources, such as glial cells. By considering them as passive cells, we show that under the influence of the electric source field, they respond by polarisation, i.e., creation of an induced field. Because of the finite velocity of ionic charge movement, this polarization will not be instantaneous. Consequently, the induced electric field will be frequency-dependent, and much reduced for high frequencies. Our model establishes that with respect to frequency attenuation properties, this situation is analogous to an equivalent RC-circuit, or better a system of coupled RC-circuits. We present a number of numerical simulations of induced electric field for biologically realistic values of parameters, and show this frequency filtering effect as well as the attenuation of extracellular potentials with distance. We suggest that induced electric fields in passive cells surrounding neurons is the physical origin of frequency filtering properties of LFPs.Comment: 10 figs, revised tex file and revised fig

On the flexibility of the design of Multiple Try Metropolis schemes

The Multiple Try Metropolis (MTM) method is a generalization of the classical Metropolis-Hastings algorithm in which the next state of the chain is chosen among a set of samples, according to normalized weights. In the literature, several extensions have been proposed. In this work, we show and remark upon the flexibility of the design of MTM-type methods, fulfilling the detailed balance condition. We discuss several possibilities and show different numerical results

Diffusion of hydrogen in crystalline silicon

The coefficient of diffusion of hydrogen in crystalline silicon is calculated using tight-binding molecular dynamics. Our results are in good quantitative agreement with an earlier study by Panzarini and Colombo [Phys. Rev. Lett. 73, 1636 (1994)]. However, while our calculations indicate that long jumps dominate over single hops at high temperatures, no abrupt change in the diffusion coefficient can be observed with decreasing temperature. The (classical) Arrhenius diffusion parameters, as a consequence, should extrapolate to low temperatures.Comment: 4 pages, including 5 postscript figures; submitted to Phys. Rev. B Brief Repor

On Second-Order Monadic Monoidal and Groupoidal Quantifiers

We study logics defined in terms of second-order monadic monoidal and groupoidal quantifiers. These are generalized quantifiers defined by monoid and groupoid word-problems, equivalently, by regular and context-free languages. We give a computational classification of the expressive power of these logics over strings with varying built-in predicates. In particular, we show that ATIME(n) can be logically characterized in terms of second-order monadic monoidal quantifiers

Seismological structure of the 1.8 Ga Trans-Hudson Orogen of North America

Precambrian tectonic processes are debated: what was the nature and scale of orogenic events on the younger, hotter, and more ductile Earth? Northern Hudson Bay records the Paleoproterozoic collision between the Western Churchill and Superior plates—the ∼1.8 Ga Trans-Hudson Orogeny (THO)—and is an ideal locality to study Precambrian tectonic structure. Integrated field, geochronological, and thermobarometric studies suggest that the THO was comparable to the present-day Himalayan-Karakoram-Tibet Orogen (HKTO). However, detailed understanding of the deep crustal architecture of the THO, and how it compares to that of the evolving HKTO, is lacking. The joint inversion of receiver functions and surface wave data provides new Moho depth estimates and shear velocity models for the crust and uppermost mantle of the THO. Most of the Archean crust is relatively thin (∼39 km) and structurally simple, with a sharp Moho; upper-crustal wave speed variations are attributed to postformation events. However, the Quebec-Baffin segment of the THO has a deeper Moho (∼45 km) and a more complex crustal structure. Observations show some similarity to recent models, computed using the same methods, of the HKTO crust. Based on Moho character, present-day crustal thickness, and metamorphic grade, we support the view that southern Baffin Island experienced thickening during the THO of a similar magnitude and width to present-day Tibet. Fast seismic velocities at >10 km below southern Baffin Island may be the result of partial eclogitization of the lower crust during the THO, as is currently thought to be happening in Tibet

Enhancing students’ motivation to learn software engineering programming techniques: a collaborative and social interaction approach

To motivate students to study advanced programming techniques, including the use of architectural styles such as the model–view–controller pattern, we have con-ducted action research upon a project based-learning approach. In addition to collabo-ration, the approach includes students’ searching and analysis of scientific documents and their involvement in communities of practice outside academia. In this paper, we report the findings of second action research cycle, which took place throughout the fourth semester of a six-semester program. As with the previous cycle during the pre-vious academic year, students did not satisfactorily achieve expected learning out-comes. More groups completed the assigned activities, but results continue to reflect poor engagement in the communities of practice and very low performance in other learning tasks. From the collected data we have identified new approaches and recom-mendations for subsequent research.Fundação para a Ciência e Tecnologia (FCT), Portugal, for Ph.D. Grants SFRH/BD/91309/2012 and SFRH/BD/87815/201

Experimental and computational study of trace element distribution between orthopyroxene and anhydrous silicate melts: substitution mechanisms and the effect of iron

Although orthopyroxene (Opx) is present during a wide range of magmatic differentiation processes in the terrestrial and lunar mantle, its effect on melt trace element contents is not well quantified. We present results of a combined experimental and computational study of trace element partitioning between Opx and anhydrous silicate melts. Experiments were performed in air at atmospheric pressure and temperatures ranging from 1,326 to 1,420°C in the system CaO-MgO-A

The Effect of Auditory Distraction on the Useful Field of View in Hearing Impaired Individuals and its implications for driving

This study assessed whether the increased demand of listening in hearing impaired individuals exacerbates the detrimental impact of auditory distraction on a visual task (useful field of view test), relative to normally hearing listeners. Auditory distraction negatively affects this visual task, which is linked with various driving performance outcomes. Hearing impaired and normally hearing participants performed useful field of view testing with and without a simultaneous listening task. They also undertook a cognitive test battery. For all participants, performing the visual and auditory tasks together reduced performance on each respective test. For a number of subtests, hearing impaired participants showed poorer visual task performance, though not to a statistically significant extent. Hearing impaired participants were significantly poorer at a reading span task than normally hearing participants and tended to score lower on the most visually complex subtest of the visual task in the absence of auditory task engagement. Useful field of view performance is negatively affected by auditory distraction, and hearing loss may present further problems, given the reductions in visual and cognitive task performance suggested in this study. Suggestions are made for future work to extend this study, given the practical importance of the findings