Validating the reported random errors of ACE‐FTS measurements

In order to validate the reported precision of space‐based atmospheric composition measurements, validation studies often focus on measurements in the tropical stratosphere, where natural variability is weak. The scatter in tropical measurements can then be used as an upper limit on single‐profile measurement precision. Here we introduce a method of quantifying the scatter of tropical measurements which aims to minimize the effects of short‐term atmospheric variability while maintaining large enough sample sizes that the results can be taken as representative of the full data set. We apply this technique to measurements of O3, HNO3, CO, H2O, NO, NO2, N2O, CH4, CCl2F2, and CCl3F produced by the Atmospheric Chemistry Experiment–Fourier Transform Spectrometer (ACE‐FTS). Tropical scatter in the ACE‐FTS retrievals is found to be consistent with the reported random errors (RREs) for H2O and CO at altitudes above 20 km, validating the RREs for these measurements. Tropical scatter in measurements of NO, NO2, CCl2F2, and CCl3F is roughly consistent with the RREs as long as the effect of outliers in the data set is reduced through the use of robust statistics. The scatter in measurements of O3, HNO3, CH4, and N2O in the stratosphere, while larger than the RREs, is shown to be consistent with the variability simulated in the Canadian Middle Atmosphere Model. This result implies that, for these species, stratospheric measurement scatter is dominated by natural variability, not random error, which provides added confidence in the scientific value of single‐profile measurements.

Analysis of the variability of auditory brainstem response components through linear regression

(ABR) is of fundamental importance to the investiga- tion of the auditory system behavior, though its in- terpretation has a subjective nature because of the manual process employed in its study and the clinical experience required for its analysis. When analyzing the ABR, clinicians are often interested in the identi- fication of ABR signal components referred to as Jewett waves. In particular, the detection and study of the time when these waves occur (i.e., the wave la- tency) is a practical tool for the diagnosis of disorders affecting the auditory system. In this context, the aim of this research is to compare ABR manual/visual analysis provided by different examiners. Methods: The ABR data were collected from 10 normal-hearing subjects (5 men and 5 women, from 20 to 52 years). A total of 160 data samples were analyzed and a pair- wise comparison between four distinct examiners was executed. We carried out a statistical study aiming to identify significant differences between assessments provided by the examiners. For this, we used Linear Regression in conjunction with Bootstrap, as a me- thod for evaluating the relation between the responses given by the examiners. Results: The analysis sug- gests agreement among examiners however reveals differences between assessments of the variability of the waves. We quantified the magnitude of the ob- tained wave latency differences and 18% of the inves- tigated waves presented substantial differences (large and moderate) and of these 3.79% were considered not acceptable for the clinical practice. Conclusions: Our results characterize the variability of the manual analysis of ABR data and the necessity of establishing unified standards and protocols for the analysis of these data. These results may also contribute to the validation and development of automatic systems that are employed in the early diagnosis of hearing loss.

The prevalence and nature of prescribing and monitoring errors in English general practice – a retrospective case note review

Objective To determine the prevalence and nature of prescribing and monitoring errors in general practices in England. Design Retrospective case note review of unique medication items prescribed over a 12 month period to a 2% random sample of patients. Mixed effects logistic regression was used to analyse the data. Setting Fifteen general practices across three primary care trusts in England. Data sources Examination of 6048 unique prescription items prescribed over the previous 12 months for 1777 patients. Main outcome measures Prevalence of prescribing and monitoring errors, and severity of errors, using validated definitions. Results Prescribing and/or monitoring errors were detected in 4.9% (296/6048) of all prescription items (95% confidence interval 4.4 - 5.5%). The vast majority of errors were of mild to moderate severity, with 0.2% (11/6048) of items having a severe error. After adjusting for covariates, patient-related factors associated with an increased risk of prescribing and/or monitoring errors were: age less than 15 (Odds Ratio (OR) 1.87, 1.19 to 2.94, p=0.006) or greater than 64 years (OR 1.68, 1.04 to 2.73, p=0.035), and higher numbers of unique medication items prescribed (OR 1.16, 1.12 to 1.19, p<0.001). Conclusion Prescribing and monitoring errors are common in English general practice, although severe errors are unusual. Many factors increase the risk of error. Having identified the most common and important errors, and the factors associated with these, strategies to prevent future errors should be developed based on the study findings.

Random Prism: a noise-tolerant alternative to Random Forests

Ensemble learning can be used to increase the overall classification accuracy of a classifier by generating multiple base classifiers and combining their classification results. A frequently used family of base classifiers for ensemble learning are decision trees. However, alternative approaches can potentially be used, such as the Prism family of algorithms that also induces classification rules. Compared with decision trees, Prism algorithms generate modular classification rules that cannot necessarily be represented in the form of a decision tree. Prism algorithms produce a similar classification accuracy compared with decision trees. However, in some cases, for example, if there is noise in the training and test data, Prism algorithms can outperform decision trees by achieving a higher classification accuracy. However, Prism still tends to overfit on noisy data; hence, ensemble learners have been adopted in this work to reduce the overfitting. This paper describes the development of an ensemble learner using a member of the Prism family as the base classifier to reduce the overfitting of Prism algorithms on noisy datasets. The developed ensemble classifier is compared with a stand-alone Prism classifier in terms of classification accuracy and resistance to noise.

A nonparametric ensemble transform method for Bayesian inference

Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian inference is implemented. Sequential Monte Carlo methods rely on importance sampling combined with a resampling step, while EnKFs utilize a linear transformation of Monte Carlo samples based on the classic Kalman filter. While EnKFs have proven to be quite robust even for small ensemble sizes, they are not consistent since their derivation relies on a linear regression ansatz. In this paper, we propose another transform method, which does not rely on any a priori assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables. © 2013, Society for Industrial and Applied Mathematics

Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.

Influence of dietary protein intake and glycemic index on the association between TCF7L2 HapA and weight gain

BACKGROUND: Genetic polymorphisms of transcription factor 7-like 2 (TCF7L2) have been associated with type 2 diabetes and BMI. OBJECTIVE: The objective was to investigate whether TCF7L2 HapA is associated with weight development and whether such an association is modulated by protein intake or by the glycemic index (GI). DESIGN: The investigation was based on prospective data from 5 cohort studies nested within the European Prospective Investigation into Cancer and Nutrition. Weight change was followed up for a mean (±SD) of 6.8 ± 2.5 y. TCF7L2 rs7903146 and rs10885406 were successfully genotyped in 11,069 individuals and used to derive HapA. Multiple logistic and linear regression analysis was applied to test for the main effect of HapA and its interaction with dietary protein or GI. Analyses from the cohorts were combined by random-effects meta-analysis. RESULTS: HapA was associated neither with baseline BMI (0.03 ± 0.07 BMI units per allele; P = 0.6) nor with annual weight change (8.8 ± 11.7 g/y per allele; P = 0.5). However, a previously shown positive association between intake of protein, particularly of animal origin, and subsequent weight change in this population proved to be attenuated by TCF7L2 HapA (P-interaction = 0.01). We showed that weight gain becomes independent of protein intake with an increasing number of HapA alleles. Substitution of protein with either fat or carbohydrates showed the same effects. No interaction with GI was observed. CONCLUSION: TCF7L2 HapA attenuates the positive association between animal protein intake and long-term body weight change in middle-aged Europeans but does not interact with the GI of the diet.

Genetic polymorphisms in the hypothalamic pathway in relation to subsequent weight change--the DiOGenes study

BACKGROUND: Single nucleotide polymorphisms (SNPs) in genes encoding the components involved in the hypothalamic pathway may influence weight gain and dietary factors may modify their effects. AIM: We conducted a case-cohort study to investigate the associations of SNPs in candidate genes with weight change during an average of 6.8 years of follow-up and to examine the potential effect modification by glycemic index (GI) and protein intake. METHODS AND FINDINGS: Participants, aged 20-60 years at baseline, came from five European countries. Cases ('weight gainers') were selected from the total eligible cohort (n = 50,293) as those with the greatest unexplained annual weight gain (n = 5,584). A random subcohort (n = 6,566) was drawn with the intention to obtain an equal number of cases and noncases (n = 5,507). We genotyped 134 SNPs that captured all common genetic variation across the 15 candidate genes; 123 met the quality control criteria. Each SNP was tested for association with the risk of being a 'weight gainer' (logistic regression models) in the case-noncase data and with weight gain (linear regression models) in the random subcohort data. After accounting for multiple testing, none of the SNPs was significantly associated with weight change. Furthermore, we observed no significant effect modification by dietary factors, except for SNP rs7180849 in the neuromedin β gene (NMB). Carriers of the minor allele had a more pronounced weight gain at a higher GI (P = 2 x 10⁻⁷). CONCLUSIONS: We found no evidence of association between SNPs in the studied hypothalamic genes with weight change. The interaction between GI and NMB SNP rs7180849 needs further confirmation.

The stochastic component in choice and regression to the mean

In this article, we illustrate experimentally an important consequence of the stochastic component in choice behaviour which has not been acknowledged so far. Namely, its potential to produce ‘regression to the mean’ (RTM) effects. We employ a novel approach to individual choice under risk, based on repeated multiple-lottery choices (i.e. choices among many lotteries), to show how the high degree of stochastic variability present in individual decisions can distort crucially certain results through RTM effects. We demonstrate the point in the context of a social comparison experiment.

On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.

Elastic net orthogonal forward regression

An efficient two-level model identification method aiming at maximising a model׳s generalisation capability is proposed for a large class of linear-in-the-parameters models from the observational data. A new elastic net orthogonal forward regression (ENOFR) algorithm is employed at the lower level to carry out simultaneous model selection and elastic net parameter estimation. The two regularisation parameters in the elastic net are optimised using a particle swarm optimisation (PSO) algorithm at the upper level by minimising the leave one out (LOO) mean square error (LOOMSE). There are two elements of original contributions. Firstly an elastic net cost function is defined and applied based on orthogonal decomposition, which facilitates the automatic model structure selection process with no need of using a predetermined error tolerance to terminate the forward selection process. Secondly it is shown that the LOOMSE based on the resultant ENOFR models can be analytically computed without actually splitting the data set, and the associate computation cost is small due to the ENOFR procedure. Consequently a fully automated procedure is achieved without resort to any other validation data set for iterative model evaluation. Illustrative examples are included to demonstrate the effectiveness of the new approaches.

Association between Mediterranean and Nordic diet scores and changes in weight and waist circumference: influence of FTO and TCF7L2 loci

BACKGROUND: Several studies have shown that adherence to the Mediterranean Diet measured by using the Mediterranean diet score (MDS) is associated with lower obesity risk. The newly proposed Nordic Diet could hold similar beneficial effects. Because of the increasing focus on the interaction between diet and genetic predisposition to adiposity, studies should consider both diet and genetics. OBJECTIVE: We investigated whether FTO rs9939609 and TCF7L2 rs7903146 modified the association between the MDS and Nordic diet score (NDS) and changes in weight (Δweight), waist circumference (ΔWC), and waist circumference adjusted for body mass index (BMI) (ΔWCBMI). DESIGN: We conducted a case-cohort study with a median follow-up of 6.8 y that included 11,048 participants from 5 European countries; 5552 of these subjects were cases defined as individuals with the greatest degree of unexplained weight gain during follow-up. A randomly selected subcohort included 6548 participants, including 5496 noncases. Cases and noncases were compared in analyses by using logistic regression. Continuous traits (ie, Δweight, ΔWC, and ΔWCBMI) were analyzed by using linear regression models in the random subcohort. Interactions were tested by including interaction terms in models. RESULTS: A higher MDS was significantly inversely associated with case status (OR: 0.98; 95% CI: 0.96, 1.00), ΔWC (β = -0.010 cm/y; 95% CI: -0.020, -0.001 cm/y), and ΔWCBMI (β = -0.008; 95% CI:-0.015, -0.001) per 1-point increment but not Δweight (P = 0.53). The NDS was not significantly associated with any outcome. There was a borderline significant interaction between the MDS and TCF7L2 rs7903146 on weight gain (P = 0.05), which suggested a beneficial effect of the MDS only in subjects who carried 1 or 2 risk alleles. FTO did not modify observed associations. CONCLUSIONS: A high MDS is associated with a lower ΔWC and ΔWCBMI, regardless of FTO and TCF7L2 risk alleles. For Δweight, findings were less clear, but the effect may depend on the TCF7L2 rs7903146 variant. The NDS was not associated with anthropometric changes during follow-up.

Meta-analysis of relationships between enteric methane yield and milk fatty acid profile in dairy cattle

Various studies have indicated a relationship between enteric methane (CH4) production and milk fatty acid (FA) profiles of dairy cattle. However, the number of studies investigating such a relationship is limited and the direct relationships reported are mainly obtained by variation in CH4 production and milk FA concentration induced by dietary lipid supplements. The aim of this study was to perform a meta-analysis to quantify relationships between CH4 yield (per unit of feed and unit of milk) and milk FA profile in dairy cattle and to develop equations to predict CH4 yield based on milk FA profile of cows fed a wide variety of diets. Data from 8 experiments encompassing 30 different dietary treatments and 146 observations were included. Yield of CH4 measured in these experiments was 21.5 ± 2.46 g/kg of dry matter intake (DMI) and 13.9 ± 2.30 g/ kg of fat- and protein-corrected milk (FPCM). Correlation coefficients were chosen as effect size of the relationship between CH4 yield and individual milk FA concentration (g/100 g of FA). Average true correlation coefficients were estimated by a random-effects model. Milk FA concentrations of C6:0, C8:0, C10:0, C16:0, and C16:0-iso were significantly or tended to be positively related to CH4 yield per unit of feed. Concentrations of trans-6+7+8+9 C18:1, trans-10+11 C18:1, cis- 11 C18:1, cis-12 C18:1, cis-13 C18:1, trans-16+cis-14 C18:1, and cis-9,12 C18:2 in milk fat were significantly or tended to be negatively related to CH4 yield per unit of feed. Milk FA concentrations of C10:0, C12:0, C14:0-iso, C14:0, cis-9 C14:1, C15:0, and C16:0 were significantly or tended to be positively related to CH4 yield per unit of milk. Concentrations of C4:0, C18:0, trans-10+11 C18:1, cis-9 C18:1, cis-11 C18:1, and cis- 9,12 C18:2 in milk fat were significantly or tended to be negatively related to CH4 yield per unit of milk. Mixed model multiple regression and a stepwise selection procedure of milk FA based on the Bayesian information criterion to predict CH4 yield with milk FA as input (g/100 g of FA) resulted in the following prediction equations: CH4 (g/kg of DMI) = 23.39 + 9.74 × C16:0- iso – 1.06 × trans-10+11 C18:1 – 1.75 × cis-9,12 C18:2 (R2 = 0.54), and CH4 (g/kg of FPCM) = 21.13 – 1.38 × C4:0 + 8.53 × C16:0-iso – 0.22 × cis-9 C18:1 – 0.59 × trans-10+11 C18:1 (R2 = 0.47). This indicated that milk FA profile has a moderate potential for predicting CH4 yield per unit of feed and a slightly lower potential for predicting CH4 yield per unit of milk. Key words: methane , milk fatty acid profile , metaanalysis , dairy cattle

Nonlinear identification using orthogonal forward regression with nested optimal regularization

An efficient data based-modeling algorithm for nonlinear system identification is introduced for radial basis function (RBF) neural networks with the aim of maximizing generalization capability based on the concept of leave-one-out (LOO) cross validation. Each of the RBF kernels has its own kernel width parameter and the basic idea is to optimize the multiple pairs of regularization parameters and kernel widths, each of which is associated with a kernel, one at a time within the orthogonal forward regression (OFR) procedure. Thus, each OFR step consists of one model term selection based on the LOO mean square error (LOOMSE), followed by the optimization of the associated kernel width and regularization parameter, also based on the LOOMSE. Since like our previous state-of-the-art local regularization assisted orthogonal least squares (LROLS) algorithm, the same LOOMSE is adopted for model selection, our proposed new OFR algorithm is also capable of producing a very sparse RBF model with excellent generalization performance. Unlike our previous LROLS algorithm which requires an additional iterative loop to optimize the regularization parameters as well as an additional procedure to optimize the kernel width, the proposed new OFR algorithm optimizes both the kernel widths and regularization parameters within the single OFR procedure, and consequently the required computational complexity is dramatically reduced. Nonlinear system identification examples are included to demonstrate the effectiveness of this new approach in comparison to the well-known approaches of support vector machine and least absolute shrinkage and selection operator as well as the LROLS algorithm.

Estimation of Gaussian process regression model using probability distance measures

A new class of parameter estimation algorithms is introduced for Gaussian process regression (GPR) models. It is shown that the integration of the GPR model with probability distance measures of (i) the integrated square error and (ii) Kullback–Leibler (K–L) divergence are analytically tractable. An efficient coordinate descent algorithm is proposed to iteratively estimate the kernel width using golden section search which includes a fast gradient descent algorithm as an inner loop to estimate the noise variance. Numerical examples are included to demonstrate the effectiveness of the new identification approaches.