Entropy, Statistical Evidence, and Scientific Inference: Evidence Functions in Theory and Applications.

Scope and Goals of the Special Issue: There is a growing realization that despite being the essential tool of modern data-based scientific discovery and model testing, statistics has major problems [...].

Solar photothermochemical alkane reverse combustion.

A one-step, gas-phase photothermocatalytic process for the synthesis of hydrocarbons, including liquid alkanes, aromatics, and oxygenates, with carbon numbers (Cn) up to C13, from CO2 and water is demonstrated in a flow photoreactor operating at elevated temperatures (180-200 °C) and pressures (1-6 bar) using a 5% cobalt on TiO2 catalyst and under UV irradiation. A parametric study of temperature, pressure, and partial pressure ratio revealed that temperatures in excess of 160 °C are needed to obtain the higher Cn products in quantity and that the product distribution shifts toward higher Cn products with increasing pressure. In the best run so far, over 13% by mass of the products were C5+ hydrocarbons and some of these, i.e., octane, are drop-in replacements for existing liquid hydrocarbons fuels. Dioxygen was detected in yields ranging between 64% and 150%. In principle, this tandem photochemical-thermochemical process, fitted with a photocatalyst better matched to the solar spectrum, could provide a cheap and direct method to produce liquid hydrocarbons from CO2 and water via a solar process which uses concentrated sunlight for both photochemical excitation to generate high-energy intermediates and heat to drive important thermochemical carbon-chain-forming reactions.

Ecological change points: The strength of density dependence and the loss of history.

Change points in the dynamics of animal abundances have extensively been recorded in historical time series records. Little attention has been paid to the theoretical dynamic consequences of such change-points. Here we propose a change-point model of stochastic population dynamics. This investigation embodies a shift of attention from the problem of detecting when a change will occur, to another non-trivial puzzle: using ecological theory to understand and predict the post-breakpoint behavior of the population dynamics. The proposed model and the explicit expressions derived here predict and quantify how density dependence modulates the influence of the pre-breakpoint parameters into the post-breakpoint dynamics. Time series transitioning from one stationary distribution to another contain information about where the process was before the change-point, where is it heading and how long it will take to transition, and here this information is explicitly stated. Importantly, our results provide a direct connection of the strength of density dependence with theoretical properties of dynamic systems, such as the concept of resilience. Finally, we illustrate how to harness such information through maximum likelihood estimation for state-space models, and test the model robustness to widely different forms of compensatory dynamics. The model can be used to estimate important quantities in the theory and practice of population recovery.

The Instruments and Capabilities of the Miniature X-Ray Solar Spectrometer (MinXSS) CubeSats.

The Miniature X-ray Solar Spectrometer (MinXSS) CubeSat is the first solar science oriented CubeSat mission flown for the NASA Science Mission Directorate, with the main objective of measuring the solar soft X-ray (SXR) flux and a science goal of determining its influence on Earth's ionosphere and thermosphere. These observations can also be used to investigate solar quiescent, active region, and flare properties. The MinXSS X-ray instruments consist of a spectrometer, called X123, with a nominal 0.15 keV full-width at half-maximum (FWHM) resolution at 5.9 keV and a broadband X-ray photometer, called XP. Both instruments are designed to obtain measurements from 0.5 - 30 keV at a nominal time cadence of 10 s. A description of the MinXSS instruments, performance capabilities, and relation to the Geostationary Operational Environmental Satellite (GOES) 0.1 - 0.8 nm flux is given in this article. Early MinXSS results demonstrate the capability of measuring variations of the solar spectral soft X-ray (SXR) flux between 0.8 - 12 keV from at least GOES A5-M5 ( 5 × 10 - 8 - 5 × 10 - 5 W m - 2 ) levels and of inferring physical properties (temperature and emission measure) from the MinXSS data alone. Moreover, coronal elemental abundances can be inferred, specifically for Fe, Ca, Si, Mg, S, Ar, and Ni, when the count rate is sufficiently high at each elemental spectral feature. Additionally, temperature response curves and emission measure loci demonstrate the MinXSS sensitivity to plasma emission at different temperatures. MinXSS observations coupled with those from other solar observatories can help address some of the most compelling questions in solar coronal physics. Finally, simultaneous observations by MinXSS and the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) can provide the most spectrally complete soft X-ray solar flare photon flux measurements to date.

Diffraction limited focusing and routing of gap plasmons by a metal-dielectric-metal lens.

Passive optical elements can play key roles in photonic applications such as plasmonic integrated circuits. Here we experimentally demonstrate passive gap-plasmon focusing and routing in two-dimensions. This is accomplished using a high numerical-aperture metal-dielectric-metal lens incorporated into a planar-waveguide device. Fabrication via metal sputtering, oxide deposition, electron- and focused-ion- beam lithography, and argon ion-milling is reported on in detail. Diffraction-limited focusing is optically characterized by sampling out-coupled light with a microscope. The measured focal distance and full-width-half-maximum spot size agree well with the calculated lens performance. The surface plasmon polariton propagation length is measured by sampling light from multiple out-coupler slits.

Density-dependent state-space model for population-abundance data with unequal time intervals.

The Gompertz state-space (GSS) model is a stochastic model for analyzing time-series observations of population abundances. The GSS model combines density dependence, environmental process noise, and observation error toward estimating quantities of interest in biological monitoring and population viability analysis. However, existing methods for estimating the model parameters apply only to population data with equal time intervals between observations. In the present paper, we extend the GSS model to data with unequal time intervals, by embedding it within a state-space version of the Ornstein-Uhlenbeck process, a continuous-time model of an equilibrating stochastic system. Maximum likelihood and restricted maximum likelihood calculations for the Ornstein-Uhlenbeck state-space model involve only numerical maximization of an explicit multivariate normal likelihood, and so the extension allows for easy bootstrapping, yielding confidence intervals for model parameters, statistical hypothesis testing of density dependence, and selection among sub-models using information criteria. Ecologists and managers previously drawn to models lacking density dependence or observation error because such models accommodated unequal time intervals (for example, due to missing data) now have an alternative analysis framework incorporating density dependence, process noise, and observation error.

Wildlife mortality from infrastructure collisions: statistical modeling of count data from carcass surveys.

Anthropogenic infrastructure is a mortality source for many vertebrate species. Mortality is often measured using periodic counts of carcasses or remains at infrastructure segments, and bias from carcass removal is estimated via field experiments with wildlife carcasses. We describe a model for combining removal experiment and carcass count data to estimate underlying process parameters using joint likelihood. In the model, the instantaneous number of carcasses present is a stochastic birth-death process with Poisson arrivals (carcass addition) and proportional deaths (removal of carcasses). The approach accommodates modeling heterogeneity in the addition and removal processes using generalized regression. Results of fitting the model to a Greater Sage-Grouse (Centrocercus urophasianus) fence collision data set show that order of magnitude differences in expected carcass counts can be a function of spatial differences in removal and suggest caution for interpretation of many published studies. While the model assumption of negligible detection error may be tenable for some systems, the modeling framework provides a starting point for future state-space versions incorporating detection error.

Is suicide a mental health, public health or societal problem?

PURPOSE OF REVIEW: Suicide is a complex phenomenon wherein multiple parameters intersect: psychological, medical, moral, religious, social, economic and political. Over the decades, however, it has been increasingly and almost exclusively come to be viewed through a biomedical prism. Colonized thus by health and more specifically mental health professionals, alternative and complimentary approaches have been excluded from the discourse. The review questions many basic premises, which have been taken as given in this context, particularly the '90 percent statistic' derived from methodologically flawed psychological autopsy studies. RECENT FINDINGS: An alternative perspective posits that suicide is a societal problem which has been expropriated by health professionals, with little to show for the efficacy of public health interventions such as national suicide prevention plans, which continue to be ritually rolled out despite a consistent record of repeated failures. This view is supported by macro-level data from studies across national borders. SUMMARY: The current framing of suicide as a public health and mental health problem, amenable to biomedical interventions has stifled seminal discourse on the subject. We need to jettison this tunnel vision and move on to a more inclusive approach.

Air impacts from three alternatives for producing JP-8 jet fuel.

UNLABELLED: To increase U.S. petroleum energy independence, the University of Texas at Arlington (UT Arlington) has developed a direct coal liquefaction process which uses a hydrogenated solvent and a proprietary catalyst to convert lignite coal to crude oil. This sweet crude can be refined to form JP-8 military jet fuel, as well as other end products like gasoline and diesel. This paper presents an analysis of air pollutants resulting from using UT Arlington's liquefaction process to produce crude and then JP-8, compared with 2 alternative processes: conventional crude extraction and refining (CCER), and the Fischer-Tropsch process. For each of the 3 processes, air pollutant emissions through production of JP-8 fuel were considered, including emissions from upstream extraction/ production, transportation, and conversion/refining. Air pollutants from the direct liquefaction process were measured using a LandTEC GEM2000 Plus, Draeger color detector tubes, OhioLumex RA-915 Light Hg Analyzer, and SRI 8610 gas chromatograph with thermal conductivity detector. According to the screening analysis presented here, producing jet fuel from UT Arlington crude results in lower levels of pollutants compared to international conventional crude extraction/refining. Compared to US domestic CCER, the UTA process emits lower levels of CO2-e, NO(x), and Hg, and higher levels of CO and SO2. Emissions from the UT Arlington process for producing JP-8 are estimated to be lower than for the Fischer-Tropsch process for all pollutants, with the exception of CO2-e, which were high for the UT Arlington process due to nitrous oxide emissions from crude refining. When comparing emissions from conventional lignite combustion to produce electricity, versus UT Arlington coal liquefaction to make JP-8 and subsequent JP-8 transport, emissions from the UT Arlington process are estimated to be lower for all air pollutants, per MJ of power delivered to the end user. IMPLICATIONS: The United States currently imports two-thirds of its crude oil, leaving its transportation system especially vulnerable to disruptions in international crude supplies. At current use rates, U.S. coal reserves (262 billion short tons, including 23 billion short tons lignite) would last 236 years. Accordingly, the University of Texas at Arlington (UT Arlington) has developed a process that converts lignite to crude oil, at about half the cost of regular crude. According to the screening analysis presented here, producing jet fuel from UT Arlington crude generates lower levels of pollutants compared to international conventional crude extraction/refining (CCER).

Analysis and comparison of inertinite-derived adsorbent with conventional adsorbents.

UNLABELLED: To increase U.S. petroleum energy-independence, the University of Texas at Arlington (UT Arlington) has developed a coal liquefaction process that uses a hydrogenated solvent and a proprietary catalyst to convert lignite coal to crude oil. This paper reports on part of the environmental evaluation of the liquefaction process: the evaluation of the solid residual from liquefying the coal, called inertinite, as a potential adsorbent for air and water purification. Inertinite samples derived from Arkansas and Texas lignite coals were used as test samples. In the activated carbon creation process, inertinite samples were heated in a tube furnace (Lindberg, Type 55035, Arlington, UT) at temperatures ranging between 300 and 850 degrees C for time spans of 60, 90, and 120 min, using steam and carbon dioxide as oxidizing gases. Activated inertinite samples were then characterized by ultra-high-purity nitrogen adsorption isotherms at 77 K using a high-speed surface area and pore size analyzer (Quantachrome, Nova 2200e, Kingsville, TX). Surface area and total pore volume were determined using the Brunauer Emmet, and Teller method, for the inertinite samples, as well as for four commercially available activated carbons (gas-phase adsorbents Calgon Fluepac-B and BPL 4 x 6; liquid-phase adsorbents Filtrasorb 200 and Carbsorb 30). In addition, adsorption isotherms were developed for inertinite and the two commercially available gas-phase carbons, using methyl ethyl ketone (MEK) as an example compound. Adsorption capacity was measured gravimetrically with a symmetric vapor sorption analyzer (VTI, Inc., Model SGA-100, Kingsville, TX). Also, liquid-phase adsorption experiments were conducted using methyl orange as an example organic compound. The study showed that using inertinite from coal can be beneficially reused as an adsorbent for air or water pollution control, although its surface area and adsorption capacity are not as high as those for commercially available activated carbons. IMPLICATIONS: The United States currently imports two-thirds of its crude oil, leaving its transportation system especially vulnerable to disruptions in international crude supplies. UT Arlington has developed a liquefaction process that converts coal, abundant in the United States, to crude oil. This work demonstrated that the undissolvable solid coal residual from the liquefaction process, called inertinite, can be converted to an activated carbon adsorbent. Although its surface area and adsorption capacity are not as high as those for commercially available carbons, the inertinite source material would be available at no cost, and its beneficial reuse would avoid the need for disposal.

Higher-energy composite fermion levels in the fractional quantum Hall effect.

Even though composite fermions in the fractional quantum Hall liquid are well established, it is not yet known up to what energies they remain intact. We probe the high-energy spectrum of the 1/3 liquid directly by resonant inelastic light scattering, and report the observation of a large number of new collective modes. Supported by our theoretical calculations, we associate these with transitions across two or more composite fermions levels. The formation of quasiparticle levels up to high energies is direct evidence for the robustness of topological order in the fractional quantum Hall effect.

Replicated sampling increases efficiency in monitoring biological populations.

Observation or sampling error in population monitoring can cause serious degradation of the inferences, such as estimates of trend or risk, that ecologists and managers frequently seek to make with time-series observations of population abundances. We show that replicating the sampling process can considerably improve the information obtained from population monitoring. At each sampling time the sampling method would be repeated, either simultaneously or within a short time. In this study we examine the potential value of replicated sampling to population monitoring using a density-dependent population model. We modify an existing population time-series model, the Gompertz state-space model, to incorporate replicated sampling, and we develop maximum-likelihood and restricted maximum-likelihood estimates of model parameters. Depending on sampling protocols, replication may or may not entail substantial extra cost. Some sampling programs already have replicated samples, but the samples are aggregated or pooled into one estimate of population abundance; such practice of aggregating samples, according to our model, loses considerable information about model parameters. The gains from replicated sampling are realized in substantially improved statistical inferences about model parameters, especially inferences for sorting out the contributions of process noise and observation error to observed population variability.

Hierarchical models in ecology: confidence intervals, hypothesis testing, and model selection using data cloning.

Hierarchical statistical models are increasingly being used to describe complex ecological processes. The data cloning (DC) method is a new general technique that uses Markov chain Monte Carlo (MCMC) algorithms to compute maximum likelihood (ML) estimates along with their asymptotic variance estimates for hierarchical models. Despite its generality, the method has two inferential limitations. First, it only provides Wald-type confidence intervals, known to be inaccurate in small samples. Second, it only yields ML parameter estimates, but not the maximized likelihood values used for profile likelihood intervals, likelihood ratio hypothesis tests, and information-theoretic model selection. Here we describe how to overcome these inferential limitations with a computationally efficient method for calculating likelihood ratios via data cloning. The ability to calculate likelihood ratios allows one to do hypothesis tests, construct accurate confidence intervals and undertake information-based model selection with hierarchical models in a frequentist context. To demonstrate the use of these tools with complex ecological models, we reanalyze part of Gause's classic Paramecium data with state-space population models containing both environmental noise and sampling error. The analysis results include improved confidence intervals for parameters, a hypothesis test of laboratory replication, and a comparison of the Beverton-Holt and the Ricker growth forms based on a model selection index.

Another look at the eigenvalues of a population matrix model.

Population matrix models are important tools in resource management, in part because they are used to calculate the finite rate of growth ("dominant eigenvalue"). But understanding how a population matrix model converts life history traits into the finite rate of growth can be tricky. We introduce interactive software ("IsoPOPd") that uses the characteristic equation to display how vital rates (survival and fertility) contribute to the finite rate of growth. Higher-order interactions among vital rates complicate the linkage between a management intervention and a population's growth rate. We illustrate the use of the software for investigating the consequences of three management interventions in a 3-stage model of white-tailed deer (Odocoileus virginianus). The software is applicable to any species with 2- or 3-stages, but the mathematical concepts underlying the software are applicable to a population matrix model of any size. The IsoPOPd software is available at: https://cwhl.vet.cornell.edu/tools/isopopd.

Errors in Statistical Inference Under Model Misspecification: Evidence, Hypothesis Testing, and AIC.

The methods for making statistical inferences in scientific analysis have diversified even within the frequentist branch of statistics, but comparison has been elusive. We approximate analytically and numerically the performance of Neyman-Pearson hypothesis testing, Fisher significance testing, information criteria, and evidential statistics (Royall, 1997). This last approach is implemented in the form of evidence functions: statistics for comparing two models by estimating, based on data, their relative distance to the generating process (i.e., truth) (Lele, 2004). A consequence of this definition is the salient property that the probabilities of misleading or weak evidence, error probabilities analogous to Type 1 and Type 2 errors in hypothesis testing, all approach 0 as sample size increases. Our comparison of these approaches focuses primarily on the frequency with which errors are made, both when models are correctly specified, and when they are misspecified, but also considers ease of interpretation. The error rates in evidential analysis all decrease to 0 as sample size increases even under model misspecification. Neyman-Pearson testing on the other hand, exhibits great difficulties under misspecification. The real Type 1 and Type 2 error rates can be less, equal to, or greater than the nominal rates depending on the nature of model misspecification. Under some reasonable circumstances, the probability of Type 1 error is an increasing function of sample size that can even approach 1! In contrast, under model misspecification an evidential analysis retains the desirable properties of always having a greater probability of selecting the best model over an inferior one and of having the probability of selecting the best model increase monotonically with sample size. We show that the evidence function concept fulfills the seeming objectives of model selection in ecology, both in a statistical as well as scientific sense, and that evidence functions are intuitive and easily grasped. We find that consistent information criteria are evidence functions but the MSE minimizing (or efficient) information criteria (e.g., AIC, AICc, TIC) are not. The error properties of the MSE minimizing criteria switch between those of evidence functions and those of Neyman-Pearson tests depending on models being compared.

Data cloning: easy maximum likelihood estimation for complex ecological models using Bayesian Markov chain Monte Carlo methods.

We introduce a new statistical computing method, called data cloning, to calculate maximum likelihood estimates and their standard errors for complex ecological models. Although the method uses the Bayesian framework and exploits the computational simplicity of the Markov chain Monte Carlo (MCMC) algorithms, it provides valid frequentist inferences such as the maximum likelihood estimates and their standard errors. The inferences are completely invariant to the choice of the prior distributions and therefore avoid the inherent subjectivity of the Bayesian approach. The data cloning method is easily implemented using standard MCMC software. Data cloning is particularly useful for analysing ecological situations in which hierarchical statistical models, such as state-space models and mixed effects models, are appropriate. We illustrate the method by fitting two nonlinear population dynamics models to data in the presence of process and observation noise.

Experimental support of the scaling rule for demographic stochasticity.

A scaling rule of ecological theory, accepted but lacking experimental confirmation, is that the magnitude of fluctuations in population densities due to demographic stochasticity scales inversely with the square root of population numbers. This supposition is based on analyses of models exhibiting exponential growth or stable equilibria. Using two quantitative measures, we extend the scaling rule to situations in which population densities fluctuate due to nonlinear deterministic dynamics. These measures are applied to populations of the flour beetle Tribolium castaneum that display chaotic dynamics in both 20-g and 60-g habitats. Populations cultured in the larger habitat exhibit a clarification of the deterministic dynamics, which follows the inverse square root rule. Lattice effects, a deterministic phenomenon caused by the discrete nature of individuals, can cause deviations from the scaling rule when population numbers are small. The scaling rule is robust to the probability distribution used to model demographic variation among individuals.

Plant facilitation of a belowground predator.

Interest in facilitative predator plant interactions has focused upon above-ground systems. Underground physical conditions are distinctive, however, and we provide evidence that bush lupine, Lupinus arboreus, facilitates the survival of the predatory nematode Heterorhabditis marelatus. Because H. marelatus is prone to desiccation and lupines maintain a zone of moist soil around their taproots even during dry periods, we hypothesized that dry-season nematode survival under lupines might be higher than in the surrounding grasslands. We performed field surveys and measured nematode survival in lupine and grassland rhizospheres under wet- and dry-season conditions. Nematodes survived the crucial summer period better under lupines than in grasslands; however, this advantage disappeared in wet, winter soils. Modeling the probability of nematode population extinction showed that, while even large nematode cohorts were likely to go extinct in grasslands, even small cohorts in lupine rhizospheres were likely to survive until the arrival of the next prey generation. Because this nematode predator has a strong top-down effect on lupine survival via its effect on root-boring larvae of the ghost moth Hepialus californicus, this facilitative interaction may enable a belowground trophic cascade. Similar cases of predator facilitation in seasonally stressful environments are probably common in nature.

How Hives Collapse: Allee Effects, Ecological Resilience, and the Honey Bee.

We construct a mathematical model to quantify the loss of resilience in collapsing honey bee colonies due to the presence of a strong Allee effect. In the model, recruitment and mortality of adult bees have substantial social components, with recruitment enhanced and mortality reduced by additional adult bee numbers. The result is an Allee effect, a net per-individual rate of hive increase that increases as a function of adult bee numbers. The Allee effect creates a critical minimum size in adult bee numbers, below which mortality is greater than recruitment, with ensuing loss of viability of the hive. Under ordinary and favorable environmental circumstances, the critical size is low, and hives remain large, sending off viably-sized swarms (naturally or through beekeeping management) when hive numbers approach an upper stable equilibrium size (carrying capacity). However, both the lower critical size and the upper stable size depend on many parameters related to demographic rates and their enhancement by bee sociality. Any environmental factors that increase mortality, decrease recruitment, or interfere with the social moderation of these rates has the effect of exacerbating the Allee effect by increasing the lower critical size and substantially decreasing the upper stable size. As well, the basin of attraction to the upper stable size, defined by the model potential function, becomes narrower and shallower, indicating the loss of resilience as the hive becomes subjected to increased risk of falling below the critical size. Environmental effects of greater severity can cause the two equilibria to merge and the basin of attraction to the upper stable size to disappear, resulting in collapse of the hive from any initial size. The model suggests that multiple proximate causes, among them pesticides, mites, pathogens, and climate change, working singly or in combinations, could trigger hive collapse.

Hierarchical competition models with the Allee effect II: the case of immigration.

This is part II of an earlier paper that dealt with hierarchical models with the Allee effect but with no immigration. In this paper, we greatly simplify the proofs in part I and provide a proof of the global dynamics of the non-hyperbolic cases that were previously conjectured. Then, we show how immigration to one of the species or to both would, drastically, change the dynamics of the system. It is shown that if the level of immigration to one or to both species is above a specified level, then there will be no extinction region where both species go to extinction.