On probability-based inference under data missing by design

Whether a statistician wants to complement a probability model for observed data with a prior distribution and carry out fully probabilistic inference, or base the inference only on the likelihood function, may be a fundamental question in theory, but in practice it may well be of less importance if the likelihood contains much more information than the prior. Maximum likelihood inference can be justified as a Gaussian approximation at the posterior mode, using flat priors. However, in situations where parametric assumptions in standard statistical models would be too rigid, more flexible model formulation, combined with fully probabilistic inference, can be achieved using hierarchical Bayesian parametrization. This work includes five articles, all of which apply probability modeling under various problems involving incomplete observation. Three of the papers apply maximum likelihood estimation and two of them hierarchical Bayesian modeling. Because maximum likelihood may be presented as a special case of Bayesian inference, but not the other way round, in the introductory part of this work we present a framework for probability-based inference using only Bayesian concepts. We also re-derive some results presented in the original articles using the toolbox equipped herein, to show that they are also justifiable under this more general framework. Here the assumption of exchangeability and de Finetti's representation theorem are applied repeatedly for justifying the use of standard parametric probability models with conditionally independent likelihood contributions. It is argued that this same reasoning can be applied also under sampling from a finite population. The main emphasis here is in probability-based inference under incomplete observation due to study design. This is illustrated using a generic two-phase cohort sampling design as an example. The alternative approaches presented for analysis of such a design are full likelihood, which utilizes all observed information, and conditional likelihood, which is restricted to a completely observed set, conditioning on the rule that generated that set. Conditional likelihood inference is also applied for a joint analysis of prevalence and incidence data, a situation subject to both left censoring and left truncation. Other topics covered are model uncertainty and causal inference using posterior predictive distributions. We formulate a non-parametric monotonic regression model for one or more covariates and a Bayesian estimation procedure, and apply the model in the context of optimal sequential treatment regimes, demonstrating that inference based on posterior predictive distributions is feasible also in this case.

A note on sampling chironomids for RNA-based studies of natural populations that retains critical morphological vouchers

The rapid uptake of transcriptomic approaches in freshwater ecology has seen a wealth of data produced concerning the ways in which organisms interact with their environment on a molecular level. Typically, such studies focus either at the community level and so don’t require species identifications, or on laboratory strains of known species identity or natural populations of large, easily identifiable taxa. For chironomids, impediments still exist for applying these technologies to natural populations because they are small-bodied and often require time-consuming secondary sorting of stream material and morphological voucher preparation to confirm species diagnosis. These procedures limit the ability to maintain RNA quantity and quality in such organisms because RNA degrades rapidly and gene expression can be altered rapidly in organisms; thereby limiting the inclusion of such taxa in transcriptomic studies. Here, we demonstrate that these limitations can be overcome and outline an optimised protocol for collecting, sorting and preserving chironomid larvae that enables retention of both morphological vouchers and RNA for subsequent transcriptomics purposes. By ensuring that sorting and voucher preparation are completed within <4 hours after collection and that samples are kept cold at all times, we successfully retained both RNA and morphological vouchers from all specimens. Although not prescriptive in specific methodology, we anticipate that this paper will assist in promoting transcriptomic investigations of the sublethal impact on chironomid gene expression of changes to aquatic environments.

Optimal adaptive sequential spatial sampling of soil using pair-copulas

A spatial sampling design that uses pair-copulas is presented that aims to reduce prediction uncertainty by selecting additional sampling locations based on both the spatial configuration of existing locations and the values of the observations at those locations. The novelty of the approach arises in the use of pair-copulas to estimate uncertainty at unsampled locations. Spatial pair-copulas are able to more accurately capture spatial dependence compared to other types of spatial copula models. Additionally, unlike traditional kriging variance, uncertainty estimates from the pair-copula account for influence from measurement values and not just the configuration of observations. This feature is beneficial, for example, for more accurate identification of soil contamination zones where high contamination measurements are located near measurements of varying contamination. The proposed design methodology is applied to a soil contamination example from the Swiss Jura region. A partial redesign of the original sampling configuration demonstrates the potential of the proposed methodology.

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

Sampling frequency affects estimates of annual nitrous oxide fluxes

Quantifying nitrous oxide (N(2)O) fluxes, a potent greenhouse gas, from soils is necessary to improve our knowledge of terrestrial N(2)O losses. Developing universal sampling frequencies for calculating annual N(2)O fluxes is difficult, as fluxes are renowned for their high temporal variability. We demonstrate daily sampling was largely required to achieve annual N(2)O fluxes within 10% of the best estimate for 28 annual datasets collected from three continents, Australia, Europe and Asia. Decreasing the regularity of measurements either under- or overestimated annual N(2)O fluxes, with a maximum overestimation of 935%. Measurement frequency was lowered using a sampling strategy based on environmental factors known to affect temporal variability, but still required sampling more than once a week. Consequently, uncertainty in current global terrestrial N(2)O budgets associated with the upscaling of field-based datasets can be decreased significantly using adequate sampling frequencies.

The Noether-Lefschetz theorem for the divisor class group

Let X be a normal projective threefold over a field of characteristic zero and vertical bar L vertical bar be a base-point free, ample linear system on X. Under suitable hypotheses on (X, vertical bar L vertical bar), we prove that for a very general member Y is an element of vertical bar L vertical bar, the restriction map on divisor class groups Cl(X) -> Cl(Y) is an isomorphism. In particular, we are able to recover the classical Noether-Lefschetz theorem, that a very general hypersurface X subset of P-C(3) of degree >= 4 has Pic(X) congruent to Z.

Autonomous greenhouse gas sampling using multiple robotic boats

Accurately quantifying total greenhouse gas emissions (e.g. methane) from natural systems such as lakes, reservoirs and wetlands requires the spatial-temporal measurement of both diffusive and ebullitive (bubbling) emissions. Traditional, manual, measurement techniques provide only limited localised assessment of methane flux, often introducing significant errors when extrapolated to the whole-of-system. In this paper, we directly address these current sampling limitations and present a novel multiple robotic boat system configured to measure the spatiotemporal release of methane to atmosphere across inland waterways. The system, consisting of multiple networked Autonomous Surface Vehicles (ASVs) and capable of persistent operation, enables scientists to remotely evaluate the performance of sampling and modelling algorithms for real-world process quantification over extended periods of time. This paper provides an overview of the multi-robot sampling system including the vehicle and gas sampling unit design. Experimental results are shown demonstrating the system’s ability to autonomously navigate and implement an exploratory sampling algorithm to measure methane emissions on two inland reservoirs.

Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform

The images of Hermite and Laguerre-Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterized. These are used to characterize the image of Schwartz class of rapidly decreasing functions f on R-n and C-n under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for the windowed (short-time) Fourier transform is proved.

Studies on Aerosol Particle Emission, Sampling and Authenticity

Emissions of coal combustion fly ash through real scale ElectroStatic Precipitators (ESP) were studied in different coal combustion and operation conditions. Sub-micron fly-ash aerosol emission from a power plant boiler and the ESP were determined and consequently the aerosol penetration, as based on electrical mobility measurements, thus giving thereby an indication for an estimate on the size and the maximum extent that the small particles can escape. The experimentals indicate a maximum penetration of 4% to 20 % of the small particles, as counted on number basis instead of the normally used mass basis, while simultaneously the ESP is operating at a nearly 100% collection efficiency on mass basis. Although the size range as such seems to appear independent of the coal, of the boiler or even of the device used for the emission control, the maximum penetration level on the number basis depends on the ESP operating parameters. The measured emissions were stable during stable boiler operation for a fired coal, and the emissions seemed each to be different indicating that the sub-micron size distribution of the fly-ash could be used as a specific characteristics for recognition, for instance for authenticity, provided with an indication of known stable operation. Consequently, the results on the emissions suggest an optimum particle size range for environmental monitoring in respect to the probability of finding traces from the samples. The current work embodies also an authentication system for aerosol samples for post-inspection from any macroscopic sample piece. The system can comprise newly introduced new devices, for mutually independent use, or, for use in a combination with each other, as arranged in order to promote the sampling operation length and/or the tag selection diversity. The tag for the samples can be based on naturally occurring measures and/or added measures of authenticity in a suitable combination. The method involves not only military related applications but those in civil industries as well. Alternatively to the samples, the system can be applied to ink for note printing or other monetary valued papers, but also in a filter manufacturing for marking fibrous filters.

Psychoacoustic sampling as a reliable, non-invasive method to monitor orthopteran species diversity in tropical forests

We evaluated trained listener-based acoustic sampling as a reliable and non-invasive method for rapid assessment of ensiferan species diversity in tropical evergreen forests. This was done by evaluating the reliability of identification of species and numbers of calling individuals using psychoacoustic experiments in the laboratory and by comparing psychoacoustic sampling in the field with ambient noise recordings made at the same time. The reliability of correct species identification by the trained listener was 100% for 16 out of 20 species tested in the laboratory. The reliability of identifying the numbers of individuals correctly was 100% for 13 out of 20 species. The human listener performed slightly better than the instrument in detecting low frequency and broadband calls in the field, whereas the recorder detected high frequency calls with greater probability. To address the problem of pseudoreplication during spot sampling in the field, we monitored the movement of calling individuals using focal animal sampling. The average distance moved by calling individuals for 17 out of 20 species was less than 1.5 m in half an hour. We suggest that trained listener-based sampling is preferable for crickets and low frequency katydids, whereas broadband recorders are preferable for katydid species with high frequency calls for accurate estimation of ensiferan species richness and relative abundance in an area.

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.

Repeated random sampling in year 5

As an extension to an activity introducing Year 5 students to the practice of statistics, the software TinkerPlots made it possible to collect repeated random samples from a finite population to informally explore students’ capacity to begin reasoning with a distribution of sample statistics. This article provides background for the sampling process and reports on the success of students in making predictions for the population from the collection of simulated samples and in explaining their strategies. The activity provided an application of the numeracy skill of using percentages, the numerical summary of the data, rather than graphing data in the analysis of samples to make decisions on a statistical question. About 70% of students made what were considered at least moderately good predictions of the population percentages for five yes–no questions, and the correlation between predictions and explanations was 0.78.

A novel fractional sampling offset estimation in an OFDM system

The Orthogonal Frequency Division Multiplexing (OFDM) is a form of Multi-Carrier Modulation where the data stream is transmitted over a number of carriers which are orthogonal to each other i.e. the carrier spacing is selected such that each carrier is located at the zeroes of all other carriers in the spectral domain. This paper proposes a new novel sampling offset estimation algorithm for an OFDM system in order to receive the OFDM data symbols error-free over the noisy channel at the receiver and to achieve fine timing synchronization between the transmitter and the receiver. The performance of this algorithm has been studied in AWGN, ADSL and SUI channels successfully.