Sensitivity and out-of-sample error in continuous time data assimilation

Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically though, these two requirements cannot both be met at the same time–tracking the observations is not possible without the trajectory deviating from the proposed model equations, while adherence to the model requires deviations from the observations. Thus, data assimilation faces a trade-off. In this contribution, the sensitivity of the data assimilation with respect to perturbations in the observations is identified as the parameter which controls the trade-off. A relation between the sensitivity and the out-of-sample error is established, which allows the latter to be calculated under operational conditions. A minimum out-of-sample error is proposed as a criterion to set an appropriate sensitivity and to settle the discussed trade-off. Two approaches to data assimilation are considered, namely variational data assimilation and Newtonian nudging, also known as synchronization. Numerical examples demonstrate the feasibility of the approach.

Evaluating raw ensembles with the continuous ranked probability score

The continuous ranked probability score (CRPS) is a frequently used scoring rule. In contrast with many other scoring rules, the CRPS evaluates cumulative distribution functions. An ensemble of forecasts can easily be converted into a piecewise constant cumulative distribution function with steps at the ensemble members. This renders the CRPS a convenient scoring rule for the evaluation of ‘raw’ ensembles, obviating the need for sophisticated ensemble model output statistics or dressing methods prior to evaluation. In this article, a relation between the CRPS score and the quantile score is established. The evaluation of ‘raw’ ensembles using the CRPS is discussed in this light. It is shown that latent in this evaluation is an interpretation of the ensemble as quantiles but with non-uniform levels. This needs to be taken into account if the ensemble is evaluated further, for example with rank histograms.

A framework for adapting survey design through time for wildlife population assessment

Sampling strategies for monitoring the status and trends in wildlife populations are often determined before the first survey is undertaken. However, there may be little information about the distribution of the population and so the sample design may be inefficient. Through time, as data are collected, more information about the distribution of animals in the survey region is obtained but it can be difficult to incorporate this information in the survey design. This paper introduces a framework for monitoring motile wildlife populations within which the design of future surveys can be adapted using data from past surveys whilst ensuring consistency in design-based estimates of status and trends through time. In each survey, part of the sample is selected from the previous survey sample using simple random sampling. The rest is selected with inclusion probability proportional to predicted abundance. Abundance is predicted using a model constructed from previous survey data and covariates for the whole survey region. Unbiased design-based estimators of status and trends and their variances are derived from two-phase sampling theory. Simulations over the short and long-term indicate that in general more precise estimates of status and trends are obtained using this mixed strategy than a strategy in which all of the sample is retained or all selected with probability proportional to predicted abundance. Furthermore the mixed strategy is robust to poor predictions of abundance. Estimates of status are more precise than those obtained from a rotating panel design.

The sample autocorrelation function and the detection of long-memory processes

The detection of long-range dependence in time series analysis is an important task to which this paper contributes by showing that whilst the theoretical definition of a long-memory (or long-range dependent) process is based on the autocorrelation function, it is not possible for long memory to be identified using the sum of the sample autocorrelations, as usually defined. The reason for this is that the sample sum is a predetermined constant for any stationary time series; a result that is independent of the sample size. Diagnostic or estimation procedures, such as those in the frequency domain, that embed this sum are equally open to this criticism. We develop this result in the context of long memory, extending it to the implications for the spectral density function and the variance of partial sums of a stationary stochastic process. The results are further extended to higher order sample autocorrelations and the bispectral density. The corresponding result is that the sum of the third order sample (auto) bicorrelations at lags h,k≥1, is also a predetermined constant, different from that in the second order case, for any stationary time series of arbitrary length.

Probability of survival in a random exchange economy with dependent agents

In this paper I analyze the general equilibrium in a random Walrasian economy. Dependence among agents is introduced in the form of dependency neighborhoods. Under the uncertainty, an agent may fail to survive due to a meager endowment in a particular state (direct effect), as well as due to unfavorable equilibrium price system at which the value of the endowment falls short of the minimum needed for survival (indirect terms-of-trade effect). To illustrate the main result I compute the stochastic limit of equilibrium price and probability of survival of an agent in a large Cobb-Douglas economy.

Bayesian ranking and slection of fishing boat efficiencies

The steadily accumulating literature on technical efficiency in fisheries attests to the importance of efficiency as an indicator of fleet condition and as an object of management concern. In this paper, we extend previous work by presenting a Bayesian hierarchical approach that yields both efficiency estimates and, as a byproduct of the estimation algorithm, probabilistic rankings of the relative technical efficiencies of fishing boats. The estimation algorithm is based on recent advances in Markov Chain Monte Carlo (MCMC) methods— Gibbs sampling, in particular—which have not been widely used in fisheries economics. We apply the method to a sample of 10,865 boat trips in the US Pacific hake (or whiting) fishery during 1987–2003. We uncover systematic differences between efficiency rankings based on sample mean efficiency estimates and those that exploit the full posterior distributions of boat efficiencies to estimate the probability that a given boat has the highest true mean efficiency.

From ensemble forecasts to predictive distribution functions

The translation of an ensemble of model runs into a probability distribution is a common task in model-based prediction. Common methods for such ensemble interpretations proceed as if verification and ensemble were draws from the same underlying distribution, an assumption not viable for most, if any, real world ensembles. An alternative is to consider an ensemble as merely a source of information rather than the possible scenarios of reality. This approach, which looks for maps between ensembles and probabilistic distributions, is investigated and extended. Common methods are revisited, and an improvement to standard kernel dressing, called ‘affine kernel dressing’ (AKD), is introduced. AKD assumes an affine mapping between ensemble and verification, typically not acting on individual ensemble members but on the entire ensemble as a whole, the parameters of this mapping are determined in parallel with the other dressing parameters, including a weight assigned to the unconditioned (climatological) distribution. These amendments to standard kernel dressing, albeit simple, can improve performance significantly and are shown to be appropriate for both overdispersive and underdispersive ensembles, unlike standard kernel dressing which exacerbates over dispersion. Studies are presented using operational numerical weather predictions for two locations and data from the Lorenz63 system, demonstrating both effectiveness given operational constraints and statistical significance given a large sample.

Online data processing consent under EU law: a theoretical framework and empirical evidence from the UK

This article analyses the results of an empirical study on the 200 most popular UK-based websites in various sectors of e-commerce services. The study provides empirical evidence on unlawful processing of personal data. It comprises a survey on the methods used to seek and obtain consent to process personal data for direct marketing and advertisement, and a test on the frequency of unsolicited commercial emails (UCE) received by customers as a consequence of their registration and submission of personal information to a website. Part One of the article presents a conceptual and normative account of data protection, with a discussion of the ethical values on which EU data protection law is grounded and an outline of the elements that must be in place to seek and obtain valid consent to process personal data. Part Two discusses the outcomes of the empirical study, which unveils a significant departure between EU legal theory and practice in data protection. Although a wide majority of the websites in the sample (69%) has in place a system to ask separate consent for engaging in marketing activities, it is only 16.2% of them that obtain a consent which is valid under the standards set by EU law. The test with UCE shows that only one out of three websites (30.5%) respects the will of the data subject not to receive commercial communications. It also shows that, when submitting personal data in online transactions, there is a high probability (50%) of incurring in a website that will ignore the refusal of consent and will send UCE. The article concludes that there is severe lack of compliance of UK online service providers with essential requirements of data protection law. In this respect, it suggests that there is inappropriate standard of implementation, information and supervision by the UK authorities, especially in light of the clarifications provided at EU level.

An effective approach for land-cover classification from airborne lidar fused with co-registered data

Airborne lidar provides accurate height information of objects on the earth and has been recognized as a reliable and accurate surveying tool in many applications. In particular, lidar data offer vital and significant features for urban land-cover classification, which is an important task in urban land-use studies. In this article, we present an effective approach in which lidar data fused with its co-registered images (i.e. aerial colour images containing red, green and blue (RGB) bands and near-infrared (NIR) images) and other derived features are used effectively for accurate urban land-cover classification. The proposed approach begins with an initial classification performed by the Dempster–Shafer theory of evidence with a specifically designed basic probability assignment function. It outputs two results, i.e. the initial classification and pseudo-training samples, which are selected automatically according to the combined probability masses. Second, a support vector machine (SVM)-based probability estimator is adopted to compute the class conditional probability (CCP) for each pixel from the pseudo-training samples. Finally, a Markov random field (MRF) model is established to combine spatial contextual information into the classification. In this stage, the initial classification result and the CCP are exploited. An efficient belief propagation (EBP) algorithm is developed to search for the global minimum-energy solution for the maximum a posteriori (MAP)-MRF framework in which three techniques are developed to speed up the standard belief propagation (BP) algorithm. Lidar and its co-registered data acquired by Toposys Falcon II are used in performance tests. The experimental results prove that fusing the height data and optical images is particularly suited for urban land-cover classification. There is no training sample needed in the proposed approach, and the computational cost is relatively low. An average classification accuracy of 93.63% is achieved.

Some implications of a sample of practical Turing tests

A series of imitation games involving 3-participant (simultaneous comparison of two hidden entities) and 2-participant (direct interrogation of a hidden entity) were conducted at Bletchley Park on the 100th anniversary of Alan Turing’s birth: 23 June 2012. From the ongoing analysis of over 150 games involving (expert and non-expert, males and females, adults and child) judges, machines and hidden humans (foils for the machines), we present six particular conversations that took place between human judges and a hidden entity that produced unexpected results. From this sample we focus on features of Turing’s machine intelligence test that the mathematician/code breaker did not consider in his examination for machine thinking: the subjective nature of attributing intelligence to another mind.

Sparse probability density function estimation using the minimum integrated square error

We develop a new sparse kernel density estimator using a forward constrained regression framework, within which the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Our main contribution is to derive a recursive algorithm to select significant kernels one at time based on the minimum integrated square error (MISE) criterion for both the selection of kernels and the estimation of mixing weights. The proposed approach is simple to implement and the associated computational cost is very low. Specifically, the complexity of our algorithm is in the order of the number of training data N, which is much lower than the order of N2 offered by the best existing sparse kernel density estimators. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with comparable accuracy to those of the classical Parzen window estimate and other existing sparse kernel density estimators.

The probability of sale and price premiums in withdrawn auctioned properties

This paper examines the impact of the auction process of residential properties that whilst unsuccessful at auction sold subsequently. The empirical analysis considers both the probability of sale and the premium of the subsequent sale price over the guide price, reserve and opening bid. The findings highlight that the final achieved sale price is influenced by key price variables revealed both prior to and during the auction itself. Factors such as auction participation, the number of individual bidders and the number of bids are significant in a number of the alternative specifications.

A fast algorithm for sparse probability density function construction

A new sparse kernel density estimator is introduced. Our main contribution is to develop a recursive algorithm for the selection of significant kernels one at time using the minimum integrated square error (MISE) criterion for both kernel selection. The proposed approach is simple to implement and the associated computational cost is very low. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with competitive accuracy to existing kernel density estimators.

Insights into the molecular architecture of a peptide nanotube using FTIR and solid-state NMR spectroscopic measurements on an aligned sample

The self-assembly of proteins and peptides into b-sheet-rich amyloid fibers is a process that has gained notoriety because of its association with human diseases and disorders. Spontaneous self-assembly of peptides into nonfibrillar supramolecular structures can also provide a versatile and convenient mechanism for the bottom-up design of biocompatible materials with functional properties favoring a wide range of practical applications.[1] One subset of these fascinating and potentially useful nanoscale constructions are the peptide nanotubes, elongated cylindrical structures with a hollow center bounded by a thin wall of peptide molecules.[2] A formidable challenge in optimizing and harnessing the properties of nanotube assemblies is to gain atomistic insight into their architecture, and to elucidate precisely how the tubular morphology is constructed from the peptide building blocks. Some of these fine details have been elucidated recently with the use of magic-angle-spinning (MAS) solidstate NMR (SSNMR) spectroscopy.[3] MAS SSNMR measurements of chemical shifts and through-space interatomic distances provide constraints on peptide conformation (e.g., b-strands and turns) and quaternary packing. We describe here a new application of a straightforward SSNMR technique which, when combined with FTIR spectroscopy, reports quantitatively on the orientation of the peptide molecules within the nanotube structure, thereby providing an additional structural constraint not accessible to MAS SSNMR.