Given Level Of Precision Research Articles

Nested Simulation for Conditional Value-at-Risk with Discrete Losses

Nested simulation has been an active area of research in recent years, with an important application in portfolio risk measurement. While majority of the literature has been focusing on the continuous case where portfolio loss is assumed to follow a continuous distribution, monetary losses of a portfolio in practice are usually measured in discrete units, oftentimes due to the practical consideration of meaningful decimal places for a given level of precision in risk measurement. In this paper, we study a nested simulation procedure for estimating conditional Value-at-Risk (CVaR), a popular risk measure, in the case where monetary losses of the portfolio take discrete values. Tailored to the discrete nature of portfolio losses, we propose a rounded estimator and show that when the portfolio loss follows a sub-Gaussian distribution or has a sufficiently high-order moment, the mean squared error (MSE) of the resulting CVaR estimator decays to zero at a rate close to [Formula: see text], much faster than the rate of the CVaR estimator in the continuous case which is [Formula: see text], where [Formula: see text] denotes the sampling budget required by the nested simulation procedure. Performance of the proposed estimator is demonstrated using numerical examples.

D-Optimal Designs for Binary and Weighted Linear Regression Models: One Design Variable

D-optimality is a well-known concept in experimental design that seeks to select an optimal set of design points to estimate the unknown parameters of a statistical model with a minimum variance. In this paper, we focus on proving a conjecture made by Ford, Torsney and Wu regarding the existence of a class of D-optimal designs for binary and weighted linear regression models. Our concentration is on models with one design variable. The conjecture states that, for any given level of precision, there exists a two-level factorial design that is D-optimal for these models. To prove this conjecture, we use an intuitive approach that explores various link functions in the generalised linear model context to establish the veracity of the conjecture. We also present explicit and clear plots of various functions wherever deemed necessary and appropriate to further strengthen the proofs. Our results establish the existence of D-optimal designs for binary and weighted linear regression models with one design variable, which have important implications for the efficient design of experiments in various fields. These findings contribute to the development of optimal experimental designs for studying binary and weighted linear regression models and provide a foundation for future research in this area.

Genetic identification and reiterated captures suggest that the Astyanax mexicanus El Pachón cavefish population is closed and declining.

The sizes of Astyanax mexicanus blind cavefish populations of North-East Mexico are demographic parameters of great importance for investigating a variety of ecological, evolutionary, and conservation issues. However, few estimates have been obtained. For these mobile animals living in an environment difficult to explore as a whole, methods based on capture-mark-recapture are appropriate, but their feasibility and interpretation of results depend on several assumptions that must be carefully examined. Here, we provide evidence that minimally invasive genetic identification from captures at different time intervals (three days and three years) can give insights into cavefish population size dynamics as well as other important demographic parameters of interest. We also provide tools to calibrate sampling and genotyping efforts necessary to reach a given level of precision. Our results suggest that the El Pachón cave population is currently very small, of an order of magnitude of a few hundreds of individuals, and is distributed in a relatively isolated area. The probable decline in population size in the El Pachón cave since the last census in 1971 raises serious conservation issues.

Use of the DermaBlade for Debridement of Hypergranulatory Wound Tissue.

Use of the DermaBlade for Debridement of Hypergranulatory Wound Tissue.

Prediction with data from designed experimentation

The intent of this study was to understand via simulation how data from designed experimentation for linear models can succeed in the prediction of individual values despite its relatively small size which renders data splitting for validation purposes nonviable. Another intent was to emphasize why, for a given level of precision, designed experimentation requires far many more runs for the prediction of individual values than it does for its more mundane use of mean prediction, and how this required number of runs can be determined via simulation as a function of the model validation method used. The results showed that prediction with designed data can be successful given its low tendency to overfitting and that model reduction can be detrimental to prediction which contrasts with the pursuit of a bias-variance tradeoff with undesigned data. As designed data increasingly resembles undesigned data, either by containing factors that have zero influence in the response, having high correlation among factors levels, and/or having small n to p ratio, model reduction becomes increasingly necessary for prediction.

The Reliability of Fluorescence Z-Scan Analysis in the Complex Environment of the Living Cell

Fluorescence z-scan analysis aims to fit the intensity traces recorded while moving a two-photon excitation volume vertically through a cell in order to identify the vertical concentration profile of a fluorescent species. Z-scan analysis has proved able to quantify delicate PM-protein binding interactions as well as sub-resolution partitioning of proteins due to the actin cortex. Despite recent progress, questions remain regarding the reliability and applicability of z-scan analysis in the complex environment of the living cell. In high precision z-scan applications, obtaining a good quality of fit is critical to ensuring that experimental results remain uncontaminated by fluorescent features outside the scope of the z-scan modeling. However, a statistical method to robustly assess the quality of fit in z-scan analysis has been lacking. To address these issues, we provide control data validating core aspects of the z-scan method at high precision and demonstrate the potential for error when applying the method without rigorous quality of fit controls. We propose a conceptual framework for estimating the amplitude of errors in z-scan analysis due to fluorescent features that may not be included in the z-scan fit model. We apply this framework to analyze the potential for microvilli structures, abundant in some cell lines, to perturb z-scan measurements and we outline data quality controls that contain the potential for error. This work provides a foundation supporting the use of simple stratified layers to model concentration profiles within the living cell together with checks that identify when such simplified models may be inapplicable for a given level of precision. This work has been supported by grants from the National Institutes of Health (R01 GM064589, R01 GM098550, RO1 GM124279).

Dynamic Kolmogorov Approach to RNN Universality

Feed-Forward Neural Networks are known to be universal approximators, meaning that they can approach any measurable function at any given level of precision, provided that their hidden layer is large enough. However, such property does not ensure practical convergence via training, and certain types of problems have been found to be best solved via other neural structures. Time-series analysis, for example, has been frequently associated with Recurrent Neural Networks or more recently LSTM architectures. However, are those endowed with the same universality as FFNN? Given that RNN universality has already been proven on measurable dynamic systems, this paper shows that any multivariate continuous function can be written as a dynamic system uploaded once per variable, thanks to the Kolmogorov Representation Theorem, hence concluding to the continuous universality of RNN architectures.

Most Likely Optimal Subsampled Markov Chain Monte Carlo

Markov Chain Monte Carlo (MCMC) requires to evaluate the full data likelihood at different parameter values iteratively and is often computationally infeasible for large data sets. This paper proposes to approximate the log-likelihood with subsamples taken according to nonuniform subsampling probabilities, and derives the most likely optimal (MLO) subsampling probabilities for better approximation. Compared with existing subsampled MCMC algorithm with equal subsampling probabilities, the MLO subsampled MCMC has a higher estimation efficiency with the same subsampling ratio. The authors also derive a formula using the asymptotic distribution of the subsampled log-likelihood to determine the required subsample size in each MCMC iteration for a given level of precision. This formula is used to develop an adaptive version of the MLO subsampled MCMC algorithm. Numerical experiments demonstrate that the proposed method outperforms the uniform subsampled MCMC.

Multi-vibration information fusion for detection of HVCB faults using CART and D–S evidence theory

The condition of a high-voltage circuit breaker (HVCB) may have a major effect on a power system. In the practical application of artificial intelligence, many advanced technologies have been applied to the assessment of the state of health of a HVCB or the identification of a fault. To date, most related research related to the improvement of a feature extraction process or a classification method intended to attain a higher level of precision have been based on a single sensor. However, any method that relies on data from a single sensor cannot exceed a given level of precision. Most studies have neglected to consider whether the information provided by a single vibration signal is sufficient and effective. Therefore, this study proposes a multi-vibration Information joint diagnosis method to improve the diagnosis of HVCB faults. The procedure has two key steps: 1) the basic probability assigns an acquisition using a classification and regression tree (CART); and 2) a combination rule design based on the Gini index in the CART. By comparing the results of eight typical classifiers and three traditional fusion methods in a case of HVCB system, the validity and superiority of the proposed method has been verified.

Variation in canopy structure, leaf area, light interception and light use efficiency among Eucalyptus clones

Differences in growth rates between Eucalyptus clones depend on differences in the acquisition of resources, and the efficiency of using resources to produce carbohydrates and grow wood. We examined differences in canopy structure, light interception, and light use efficiency for the 18 TECHS clones in a common garden experiment in Brazil. The degree of clumping within canopies varied substantially among clones, leading to large differences in both leaf area and light interception per unit of leaf area. Two methods of determining plot-level leaf area index (LP-80 and LAI-2000) were moderately well correlated (R2 = 0.4), but both methods underestimated actual leaf area index (determined by destructive sampling) by about one-third. Completely overcast sky conditions increased accuracy of leaf area estimates, reducing variation among measurements within plots and lowering the number of samples needed to obtain a given level of precision. Genotypes with high leaf area clumping also had higher leaf angle inclinations than genotypes with lower clumping. The apparent light interception coefficient (k) averaged 0.56 for the LP-80, and 0.47 for the LAI-2000. The range of k estimates differed by up to 2-fold among clones, underscoring the limited generality of light extinction coefficients. Light interception ranged from about 70 to 95% of incoming light, and leaf area index accounted for only 30% of the pattern in light interception among clones. Differences in stemwood production were influenced more strongly by clonal differences in efficiency of light use (stemwood production per unit of light intercepted) than by differences in leaf area or light interception. The efficiency of producing wood per unit of light intercepted spanned a two-fold range, with higher efficiencies for more productive clones. We suggest that production ecology studies focus more on measurements of light interception than on leaf area, avoiding issues about difficult-to-measure features of crown and canopy structures. The additional step of characterizing light use efficiency would also be very important.

Precision of retardance autocalibration in full-Stokes division-of-focal-plane imaging polarimeters.

We investigate the validity domain and precision of retardance autocalibration in full-Stokes imaging polarimeters based on a linear division-of-focal-plane polarization camera. We demonstrate that the level of precision of autocalibration in these systems gets worse as the degree of linear polarization of input Stokes vector approaches zero. Autocalibration is impossible when the input is purely circular or totally unpolarized. In all other cases, reaching a given level of precision requires a higher signal-to-noise ratio as the input gets closer to circular or unpolarized.

Influence of transect length and downed woody debris abundance on precision of the line-intersect sampling method

BackgroundAccurate downed woody debris (DWD) volume or mass estimates are needed for numerous applications such as fuel loading, forest carbon, and biodiversity/habitat assessments. The line-intersect sampling (LIS) method of inventorying DWD is widely used in forest inventories and ecological studies because it is time-efficient and unbiased. Despite its widespread use, the appropriate transect length needed to achieve a desired precision at a particular location has received relatively little attention.MethodsWe conducted intensive LIS sampling at 33 locations representing eight mature or old-growth forest types in northeastern USA, providing a range of forest conditions and DWD volumes (from 17 to 323 m3∙ha− 1). We used these empirical field data to test, through simulations, the effect of increasing transect length (up to 340 m at each location) on precision of associated LIS volume estimates. Importantly, we used a novel application of copula models to account for within-transect spatial autocorrelation of DWD volumes during our simulations, thereby properly addressing variance estimates.ResultsAs expected, precision consistently improved with increasing cumulative transect length, and locations with lower DWD volumes required longer transects to achieve a given level of precision. We developed models relating precision, transect length, and DWD volume that allows us to gauge a suitable LIS transect length for desired precision levels.ConclusionsLIS provides an attractive method for estimating DWD volume for a given localized area of interest. For the forest types sampled here, and for the particular copula model framework employed, transect lengths of ca. 120 m provide a reasonable level of precision, ranging from 18% to 60% coefficients of variation.

The number of repeated observations needed to estimate the habitual physical activity of an individual to a given level of precision.

Physical activity behavior varies naturally from day to day, from week to week and even across seasons. In order to assess the habitual level of physical activity of a person, the person must be monitored for long enough so that the level can be identified, taking into account this natural within-person variation. An important question, and one whose answer has implications for study- and survey design, epidemiological research and population surveillance, is, for how long does an individual need to be monitored before such a habitual level or pattern can be identified to a desired level of precision? The aim of this study was to estimate the number of repeated observations needed to identify the habitual physical activity behaviour of an individual to a given degree of precision. A convenience sample of 50 Swedish adults wore accelerometers during four consecutive weeks. The number of days needed to come within 5–50% of an individual's usual physical activity 95% of the time was calculated. To get an idea of the uncertainty of the estimates all statistical estimates were bootstrapped 2000 times. The mean number of days of measurement needed for the observation to, with 95% confidence, be within 20% of the habitual physical activity of an individual is highest for vigorous physical activity, for which 182 days are needed. For sedentary behaviour the equivalent number of days is 2.4. To capture 80% of the sample to within ±20% of their habitual level of physical activity, 3.4 days is needed if sedentary behavior is the outcome of interest, and 34.8 days for MVPA. The present study shows that for analyses requiring accurate data at the individual level a longer measurement collection period than the traditional 7-day protocol should be used. In addition, the amount of MVPA was negatively associated with the number of days required to identify the habitual physical activity level indicating that the least active are also those whose habitual physical activity level is the most difficult to identify. These results could have important implications for researchers whose aim is to analyse data on an individual level. Before recommendations regarding an appropriate monitoring protocol are updated, the present study should be replicated in different populations.

Stochastic Matrix-Free Equilibration

We present a novel method for approximately equilibrating a matrix using only multiplication by the matrix and its transpose. Our method is based on convex optimization and projected stochastic gradient descent, using an unbiased estimate of a gradient obtained by a randomized method. Our method provably converges in expectation and empirically gets good results with a small number of iterations. We show how the method can be applied as a preconditioner for matrix-free iterative algorithms, substantially reducing the iterations required to reach a given level of precision. We also derive a novel connection between equilibration and condition number, showing that equilibration minimizes an upper bound on the condition number over all choices of row and column scalings.

Harmony Search algorithm: a variant with Self-regulated Fretwidth

This article presents a novel modification of the Harmony Search (HS) algorithm that is able to self-tune as the search progress. This adaptive behavior is independent of total iterations. Moreover, it requires less iterations and provides more precision than other variants of HS. Its effectiveness and performance was assessed, comparing our data against four well known and recent modifications of HS: IHS (Improved Harmony Search, 2007), ABHS (Adjustable Bandwidth Harmony Search, 2014), PAHS (Parameter Adaptive Harmony Search, 2014), and IGHS (Intelligent Global Harmony Search, 2014). Unlike other works, we did not analyze the data for a given number of iterations. Instead, we ran each algorithm until it achieved a given level of precision, and analyzed the number of iterations it required. Our test benchmark contained 30 standard test functions distributed like this: 11 unimodal, 8 multimodal with fixed dimensions, and 11 multimodal with variable dimensions. The latter also included a function whose optima was located at a different coordinate in each dimension. The search domain for each function was fixed according to the literature, though we also executed tests regarding the effect of varying it. We carried out a parameter sweep to find adequate values for each parameter of our proposed algorithm, analyzing 100 independent runs for 648 different combinations. Data confirm the implemented procedure outperformed the other variants for problems in 2D and in 5D. Scaling the test functions to 10D, 30D, and 50D reduced the convergence rate of the implemented procedure, but it still outperformed IHS, ABHS, and PAHS. In some cases (e.g. Schwefel function in 30D), the Self-regulated Fretwidth Harmony Search algorithm (SFHS) was found to be the fastest approach. It was also found that IGHS performs well for optimization problems whose optima is located at the same coordinates in all dimensions, but not as well in other scenarios. Our proposed algorithm (SFHS) is not hindered by this. SFHS was able to achieve full convergence for a test function with optima located at different coordinates, even in 50D and while exploring a search domain of [–1250, 1250]. SFHS is able to achieve a more precise solution than HS (several orders of smaller magnitude), and so it stands as a good improvement over HS, as well as over the tested variants (IHS, ABHS, PAHS, IGHS). Still, our proposed method exhibited some limitations, such as requiring more parameters than other variants, being unable to converge 100% of the times for all high dimensional functions, and sometimes needing several iterations to converge. In the first case, we think this allows for more freedom in the evolution of parameters. In the second case, we consider it can be addressed by replicating the self-tuning behavior to the remaining parameters. In the final aspect, we estimate that accelerating the evolution of SFHS could prove a very useful strategy. Regarding other optimization strategies, we ran tests in up to 30 dimensions, and compared our data against the Firefly algorithm. We found that our proposed method retains 100% convergence rate, while the convergence rate of Firefly drops drastically (in some cases), even yielding 0% at 30 dimensions.

Guidelines for constructing allometric models for the prediction of woody biomass: How many individuals to harvest?

The recent development of biomass markets and carbon trading has led to increasing interest in obtaining accurate estimates of woody biomass production. Aboveground woody biomass (B) is often estimated indirectly using allometric models, where representative individuals are harvested and weighed, and regression analyses used to generalise the relationship between individual mass and more readily measured non‐destructive attributes such as plant height and stem diameter (D). To satisfy regulatory requirements and/or to provide market confidence, allometric models must be based on sufficient data to ensure predictions are accurate, whilst at the same time being practically and financially achievable.Using computer resampling experiments and allometric models of the formB=aDbthe trade‐off between increasing the sample size of individuals to construct an allometric model and the accuracy of the resulting biomass predictions was assessed. A range of algorithms for selecting individuals across the stem diameter size‐class range were also explored. The results showed marked variability across allometric models in the required number of individuals to satisfy a given level of precision. A range of 17–95 individuals were required to achieve biomass predictions with a standard deviation within 5% of the mean for the best performing stem diameter selection algorithm, while 25–166 individuals were required for the poorest. This variability arises from (a) inherent uncertainty in the relationship between diameter and biomass across allometric models, and (b) differences between the diameter size‐class distribution of individuals used to construct a model, and the diameter size‐class distribution of the population to which the model is applied.Allometric models are a key component of quantifying land‐based sequestration activities, but despite their importance little attention has been given to ensuring the methods used in their development will yield sufficiently accurate biomass predictions. The results from this study address this gap and will be of use in guiding the development of new allometric models; in assessing the suitability of existing allometric models; and in facilitating the estimation of uncertainty in biomass predictions.

Memory-Efficient Fast Shortest Path Estimation in Large Social Networks

As the sizes of contemporary social networks surpass billions of users, so grows the need for fast graph algorithms to analyze them. A particularly important basic operation is the computation of shortest paths between nodes. Classical exact algorithms for this problem are prohibitively slow on large graphs, which motivates the development of approximate methods. Of those, landmark-based methods have been actively studied in recent years. Landmark-based estimation methods start by picking a fixed set of landmark nodes, precomputing the distance from each node in the graph to each landmark, and storing the precomputed distances in a data structure. Prior work has shown that the number of landmarks required to achieve a given level of precision grows with the size of the graph. Simultaneously, the size of the data structure is proportional to the product of the size of the graph and the number of landmarks. In this work we propose an alternative landmark-based distance estimation approach that substantially reduces space requirements by means of pruning: computing distances from each node to only a small subset of the closest landmarks. We evaluate our method on the DBLP, Orkut, Twitter and Skype social networks and demonstrate that the resulting estimation algorithms are comparable in query time and potentially superior in approximation quality to equivalent non-pruned landmark-based methods, while requiring less memory or disk space.

Analog synthetic biology

We analyse the pros and cons of analog versus digital computation in living cells. Our analysis is based on fundamental laws of noise in gene and protein expression, which set limits on the energy, time, space, molecular count and part-count resources needed to compute at a given level of precision. We conclude that analog computation is significantly more efficient in its use of resources than deterministic digital computation even at relatively high levels of precision in the cell. Based on this analysis, we conclude that synthetic biology must use analog, collective analog, probabilistic and hybrid analog–digital computational approaches; otherwise, even relatively simple synthetic computations in cells such as addition will exceed energy and molecular-count budgets. We present schematics for efficiently representing analog DNA–protein computation in cells. Analog electronic flow in subthreshold transistors and analog molecular flux in chemical reactions obey Boltzmann exponential laws of thermodynamics and are described by astoundingly similar logarithmic electrochemical potentials. Therefore, cytomorphic circuits can help to map circuit designs between electronic and biochemical domains. We review recent work that uses positive-feedback linearization circuits to architect wide-dynamic-range logarithmic analog computation in Escherichia coli using three transcription factors, nearly two orders of magnitude more efficient in parts than prior digital implementations.

An efficient approach to ab initio Monte Carlo simulation.

We present a Nested Markov chain Monte Carlo (NMC) scheme for building equilibrium averages based on accurate potentials such as density functional theory. Metropolis sampling of a reference system, defined by an inexpensive but approximate potential, was used to substantially decorrelate configurations at which the potential of interest was evaluated, thereby dramatically reducing the number needed to build ensemble averages at a given level of precision. The efficiency of this procedure was maximized on-the-fly through variation of the reference system thermodynamic state (characterized here by its inverse temperature β(0)), which was otherwise unconstrained. Local density approximation results are presented for shocked states of argon at pressures from 4 to 60 GPa, where-depending on the quality of the reference system potential-acceptance probabilities were enhanced by factors of 1.2-28 relative to unoptimized NMC. The optimization procedure compensated strongly for reference potential shortcomings, as evidenced by significantly higher speedups when using a reference potential of lower quality. The efficiency of optimized NMC is shown to be competitive with that of standard ab initio molecular dynamics in the canonical ensemble.

Rigorous benchmarking in reasonable time

Experimental evaluation is key to systems research. Because modern systems are complex and non-deterministic, good experimental methodology demands that researchers account for uncertainty. To obtain valid results, they are expected to run many iterations of benchmarks, invoke virtual machines (VMs) several times, or even rebuild VM or benchmark binaries more than once. All this repetition costs time to complete experiments. Currently, many evaluations give up on sufficient repetition or rigorous statistical methods, or even run benchmarks only in training sizes. The results reported often lack proper variation estimates and, when a small difference between two systems is reported, some are simply unreliable. In contrast, we provide a statistically rigorous methodology for repetition and summarising results that makes efficient use of experimentation time. Time efficiency comes from two key observations. First, a given benchmark on a given platform is typically prone to much less non-determinism than the common worst-case of published corner-case studies. Second, repetition is most needed where most uncertainty arises (whether between builds, between executions or between iterations). We capture experimentation cost with a novel mathematical model, which we use to identify the number of repetitions at each level of an experiment necessary and sufficient to obtain a given level of precision. We present our methodology as a cookbook that guides researchers on the number of repetitions they should run to obtain reliable results. We also show how to present results with an effect size confidence interval. As an example, we show how to use our methodology to conduct throughput experiments with the DaCapo and SPEC CPU benchmarks on three recent platforms.