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

Early Huntington's disease affects movements in transformed sensorimotor mappings

This study examined the effect of transformed visual feedback on movement control in Huntington’s disease (HD). Patients in the early stages of HD and controls performed aiming movements towards peripheral targets on a digitizing tablet using an indirect visual control of movement through a monitor and emphasizing precision. In a baseline condition, HD patients were slower but showed few precision problems in aiming. When visual feedback was inverted in both vertical and horizontal axes, patients showed problems in initial and terminal phases of movement where feedback is most critical. When visual feedback was inverted along a single axis as in a mirror-inversion, HD patients showed large deviations and over-corrections before adaptation. Adaptation was similar in both groups. These results suggest that HD impairs on-line error correction in novel movements

Impact of primary and secondary machinery tracks on fine root growth of sugar maple after selection cutting

Selection cutting, where approximately 30% of the trees are removed every 30 years, is the main silvicultural treatment used in temperate deciduous forests of Quebec (Canada). Concerns have been raised that the use of heavy machinery is creating soil disturbances that are negatively affecting the growth and survival of remaining trees. The aim of the study was to determine if heavy machinery is affecting the growth, morphology, and architecture of sugar maple (Acer saccharum Marsh.) fine roots in and around machinery tracks left after selection logging. The study site, a sugar maple dominated stand, was located in southern Quebec. Root ingrowth bags and standard root cores were used to compare fine root growth, morphology, and architecture in and around machinery tracks one year after logging. Fine root growth of maple was reduced fivefold in both primary (multiple trip) and secondary (only one trip) machinery tracks compared with the control. There was a nonstatistical reduction in fine root growth within 1 m of the tracks. Because machinery tracks cover between 15% and 25% of a stand after selection logging, such reduction in fine root growth could be significant for the growth and survival of the remaining mature maple trees

On the Nature of Ultracool White Dwarfs: Not so Cool Afterall

A recent analysis of the 100 pc white dwarf sample in the SDSS footprint demonstrated for the first time the existence of a well defined ultracool -- or IR-faint -- white dwarf sequence in the Hertzsprung-Russell diagram. Here we take advantage of this discovery to enlarge the IR-faint white dwarf sample threefold. We expand our selection to the entire Pan-STARRS survey footprint as well as the Montreal White Dwarf Database 100 pc sample, and identify 37 candidates with strong flux deficits in the optical. We present follow-up Gemini optical spectroscopy of 30 of these systems, and confirm all of them as IR-faint white dwarfs. We identify an additional set of 33 objects as candidates based on their colors and magnitudes. We present a detailed model atmosphere analysis of all 70 newly identified IR-faint white dwarfs together with 35 previously known objects reported in the literature. We discuss the physics of model atmospheres and show that the key physical ingredient missing in our previous generation of model atmospheres was the high-density correction to the He-minus free-free absorption coefficient. With new model atmospheres calculated for the purpose of this analysis, we now obtain significantly higher effective temperatures and larger stellar masses for these IR-faint white dwarfs than the Teff and M values reported in previous analyses, thus solving a two decade old problem. In particular, we identify in our sample a group of ultramassive white dwarfs in the Debye cooling phase with stellar parameters never measured before.Comment: Accepted for publication in The Astrophysical Journal (33 pages, 21 figures

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

Evolutionary Trajectories are Contingent on Mitonuclear Interactions

Critical mitochondrial functions, including cellular respiration, rely on frequently interacting components expressed from both the mitochondrial and nuclear genomes. The fitness of eukaryotic organisms depends on a tight collaboration between both genomes. In the face of an elevated rate of evolution in mtDNA, current models predict that the maintenance of mitonuclear compatibility relies on compensatory evolution of the nuclear genome. Mitonuclear interactions would therefore exert an influence on evolutionary trajectories. One prediction from this model is that the same nuclear genome evolving with different mitochondrial haplotypes would follow distinct molecular paths toward higher fitness. To test this prediction, we submitted 1,344 populations derived from 7 mitonuclear genotypes of Saccharomyces cerevisiae to >300 generations of experimental evolution in conditions that either select for a mitochondrial function or do not strictly require respiration for survival. Performing high-throughput phenotyping and whole-genome sequencing on independently evolved individuals, we identified numerous examples of gene-level evolutionary convergence among populations with the same mitonuclear background. Phenotypic and genotypic data on strains derived from this evolution experiment identify the nuclear genome and the environment as the main determinants of evolutionary divergence, but also show a modulating role for the mitochondrial genome exerted both directly and via interactions with the two other components. We finally recapitulated a subset of prominent loss-of-function alleles in the ancestral backgrounds and confirmed a generalized pattern of mitonuclear-specific and highly epistatic fitness effects. Together, these results demonstrate how mitonuclear interactions can dictate evolutionary divergence of populations with identical starting nuclear genotypes

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