Fitting Effective Diffusion Models to Data Associated with a "Glassy Potential": Estimation, Classical Inference Procedures and Some Heuristics

A variety of researchers have successfully obtained the parameters of low dimensional diffusion models using the data that comes out of atomistic simulations. This naturally raises a variety of questions about efficient estimation, goodness-of-fit tests, and confidence interval estimation. The first part of this article uses maximum likelihood estimation to obtain the parameters of a diffusion model from a scalar time series. I address numerical issues associated with attempting to realize asymptotic statistics results with moderate sample sizes in the presence of exact and approximated transition densities. Approximate transition densities are used because the analytic solution of a transition density associated with a parametric diffusion model is often unknown.I am primarily interested in how well the deterministic transition density expansions of Ait-Sahalia capture the curvature of the transition density in (idealized) situations that occur when one carries out simulations in the presence of a "glassy" interaction potential. Accurate approximation of the curvature of the transition density is desirable because it can be used to quantify the goodness-of-fit of the model and to calculate asymptotic confidence intervals of the estimated parameters. The second part of this paper contributes a heuristic estimation technique for approximating a nonlinear diffusion model. A "global" nonlinear model is obtained by taking a batch of time series and applying simple local models to portions of the data. I demonstrate the technique on a diffusion model with a known transition density and on data generated by the Stochastic Simulation Algorithm.Comment: 30 pages 10 figures Submitted to SIAM MMS (typos removed and slightly shortened

Minimax Estimation of Nonregular Parameters and Discontinuity in Minimax Risk

When a parameter of interest is nondifferentiable in the probability, the existing theory of semiparametric efficient estimation is not applicable, as it does not have an influence function. Song (2014) recently developed a local asymptotic minimax estimation theory for a parameter that is a nondifferentiable transform of a regular parameter, where the nondifferentiable transform is a composite map of a continuous piecewise linear map with a single kink point and a translation-scale equivariant map. The contribution of this paper is two fold. First, this paper extends the local asymptotic minimax theory to nondifferentiable transforms that are a composite map of a Lipschitz continuous map having a finite set of nondifferentiability points and a translation-scale equivariant map. Second, this paper investigates the discontinuity of the local asymptotic minimax risk in the true probability and shows that the proposed estimator remains to be optimal even when the risk is locally robustified not only over the scores at the true probability, but also over the true probability itself. However, the local robustification does not resolve the issue of discontinuity in the local asymptotic minimax risk

A genome-wide investigation of the worldwide invader Sargassum muticum shows high success albeit (almost) no genetic diversity

Twenty years of genetic studies of marine invaders have shown that successful invaders are often characterized by native and introduced populations displaying similar levels of genetic diversity. This pattern is presumably due to high propagule pressure and repeated introductions. The opposite pattern is reported in this study of the brown seaweed, Sargassum muticum, an emblematic species for circumglobal invasions. Albeit demonstrating polymorphism in the native range, microsatellites failed to detect any genetic variation over 1,269 individuals sampled from 46 locations over the Pacific-Atlantic introduction range. Single-nucleotide polymorphisms (SNPs) obtained from ddRAD sequencing revealed some genetic variation, but confirmed severe founder events in both the Pacific and Atlantic introduction ranges. Our study thus exemplifies the need for extreme caution in interpreting neutral genetic diversity as a proxy for invasive potential. Our results confirm a previously hypothesized transoceanic secondary introduction from NE Pacific to Europe. However, the SNP panel unexpectedly revealed two additional distinct genetic origins of introductions. Also, conversely to scenarios based on historical records, southern rather than northern NE Pacific populations could have seeded most of the European populations. Finally, the most recently introduced populations showed the lowest selfing rates, suggesting higher levels of recombination might be beneficial at the early stage of the introduction process (i.e., facilitating evolutionary novelties), whereas uniparental reproduction might be favored later in sustainably established populations (i.e., sustaining local adaptation).Agence Nationale de la Recherche - ANR-10-BTBR-04; European Regional Development Fund; Fundacao para a Ciencia e a Tecnologia - SFRH/BPD/107878/2015, UID/Multi/04326/2016, UID/Multi/04326/2019; Brittany Region;info:eu-repo/semantics/publishedVersio

Comparison of Information Structures and Completely Positive Maps

A theorem of Blackwell about comparison between information structures in classical statistics is given an analogue in the quantum probabilistic setup. The theorem provides an operational interpretation for trace-preserving completely positive maps, which are the natural quantum analogue of classical stochastic maps. The proof of the theorem relies on the separation theorem for convex sets and on quantum teleportation.Comment: 12 pages. Substantial changes. Accepted for publication in Journal of Physics

Fisher information and asymptotic normality in system identification for quantum Markov chains

This paper deals with the problem of estimating the coupling constant $\theta$ of a mixing quantum Markov chain. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal (Gaussian) distribution, and we give the explicit expressions of its mean and variance. In particular we obtain a simple estimator of $\theta$ whose classical Fisher information can be optimized over different choices of measured observables. We then show that the quantum state of the output together with the system, is itself asymptotically Gaussian and compute its quantum Fisher information which sets an absolute bound to the estimation error. The classical and quantum Fisher informations are compared in a simple example. In the vicinity of $\theta=0$ we find that the quantum Fisher information has a quadratic rather than linear scaling in output size, and asymptotically the Fisher information is localised in the system, while the output is independent of the parameter.Comment: 10 pages, 2 figures. final versio

Simulating the Multi-Epoch Direct Detection Technique to Isolate the Thermal Emission of the Non-Transiting Hot Jupiter HD187123B

We report the 6.5$\sigma$ detection of water from the hot Jupiter HD187123b with a Keplerian orbital velocity $K_p$ of 53 $\pm$ 13 km/s. This high confidence detection is made using a multi-epoch, high resolution, cross correlation technique, and corresponds to a planetary mass of 1.4$^{+0.5}_{-0.3}$ $M_J$ and an orbital inclination of 21 $\pm$ 5$^{\circ}$. The technique works by treating the planet/star system as a spectroscopic binary and obtaining high signal-to-noise, high resolution observations at multiple points across the planet's orbit to constrain the system's binary dynamical motion. All together, seven epochs of Keck/NIRSPEC $L$-band observations were obtained, with five before the instrument upgrade and two after. Using high resolution SCARLET planetary and PHOENIX stellar spectral models, along with a line-by-line telluric absorption model, we were able to drastically increase the confidence of the detection by running simulations that could reproduce, and thus remove, the non-random structured noise in the final likelihood space well. The ability to predict multi-epoch results will be extremely useful for furthering the technique. Here, we use these simulations to compare three different approaches to combining the cross correlations of high resolution spectra and find that the Zucker 2003 log(L) approach is least affected by unwanted planet/star correlation for our HD187123 data set. Furthermore, we find that the same total S/N spread across an orbit in many, lower S/N epochs rather than fewer, higher S/N epochs could provide a more efficient detection. This work provides a necessary validation of multi-epoch simulations which can be used to guide future observations and will be key to studying the atmospheres of further separated, non-transiting exoplanets.Comment: Accepted to AJ, 14 pages, 10 figure

The singular continuous diffraction measure of the Thue-Morse chain

The paradigm for singular continuous spectra in symbolic dynamics and in mathematical diffraction is provided by the Thue-Morse chain, in its realisation as a binary sequence with values in $\{\pm 1\}$. We revisit this example and derive a functional equation together with an explicit form of the corresponding singular continuous diffraction measure, which is related to the known representation as a Riesz product.Comment: 6 pages, 1 figure; revised and improved versio

Demonstration project on epilepsy in Brazil - Outcome assessment

Purpose: To assess the outcome of patients with epilepsy treated at primary care health units under the framework of the demonstration project on epilepsy in Brazil, part of the WHO/ILAE/IBE Global Campaign Against Epilepsy. Method. We assessed the outcome of patients treated at four primary health units. The staff of the health units underwent information training in epilepsy. The outcome assessment was based on: 1) reduction of seizure frequency, 2) subjective perception from the patient's and the physician's point of view, 3) reduction of absenteeism, 4) social integration (school and work), and 5) sense of independence. Results: A total of 181 patients (93 women - 51%) with a mean age of 38 (range from 2 to 86) years were studied. The mean follow-up was 26 months (range from 1 to 38 months, 11 patients had follow-up of less than 12 months). Seizure frequency was assessed based on a score system, ranging from 0 (no seizure in the previous 24 months) to 7 (> 10 seizure/day). The baseline median seizure-frequency score was 3 (one to three seizures per month). At the end of the study the median seizure-frequency score was 1 (one to three seizures per year). The patients' and relatives' opinions were that in the majority (59%) the health status had improved a lot, some (19%) had improved a little, 20% experienced no change and in 2% the health status was worse. With regard to absenteeism, social integration and sense of independence, there were some modest improvements only. Discussion: The development of a model of epilepsy treatment at primary health level based on the existing health system, with strategic measures centred on the health care providers and the community, has proved to be effective providing important reductions in seizure frequency, as well as in general well being. This model can be applied nationwide, as the key elements already exist provided that strategic measures are put forward in accordance with local health providers and managers