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.

The Endothelial Sample Size Analysis in Corneal Specular Microscopy Clinical Examinations

Purpose: To evaluate endothelial cell sample size and statistical error in corneal specular microscopy (CSM) examinations. Methods: One hundred twenty examinations were conducted with 4 types of corneal specular microscopes: 30 with each BioOptics, CSO, Konan, and Topcon corneal specular microscopes. All endothelial image data were analyzed by respective instrument software and also by the Cells Analyzer software with a method developed in our lab(US Patent). A reliability degree (RD) of 95% and a relative error (RE) of 0.05 were used as cut-off values to analyze images of the counted endothelial cells called samples. The sample size mean was the number of cells evaluated on the images obtained with each device. Only examinations with RE<0.05 were considered statistically correct and suitable for comparisons with future examinations. The Cells Analyzer software was used to calculate the RE and customized sample size for all examinations. Results: Bio-Optics: sample size, 97 +/- 22 cells; RE, 6.52 +/- 0.86; only 10% of the examinations had sufficient endothelial cell quantity (RE<0.05); customized sample size, 162 +/- 34 cells. CSO: sample size, 110 +/- 20 cells; RE, 5.98 +/- 0.98; only 16.6% of the examinations had sufficient endothelial cell quantity (RE<0.05); customized sample size, 157 +/- 45 cells. Konan: sample size, 80 +/- 27 cells; RE, 10.6 +/- 3.67; none of the examinations had sufficient endothelial cell quantity (RE>0.05); customized sample size, 336 +/- 131 cells. Topcon: sample size, 87 +/- 17 cells; RE, 10.1 +/- 2.52; none of the examinations had sufficient endothelial cell quantity (RE>0.05); customized sample size, 382 +/- 159 cells. Conclusions: A very high number of CSM examinations had sample errors based on Cells Analyzer software. The endothelial sample size (examinations) needs to include more cells to be reliable and reproducible. The Cells Analyzer tutorial routine will be useful for CSM examination reliability and reproducibility.

Calculation of the variance in surveys of the economic climate

Public opinion surveys have become progressively incorporated into systems of official statistics. Surveys of the economic climate are usually qualitative because they collect opinions of businesspeople and/or experts about the long-term indicators described by a number of variables. In such cases the responses are expressed in ordinal numbers, that is, the respondents verbally report, for example, whether during a given trimester the sales or the new orders have increased, decreased or remained the same as in the previous trimester. These data allow to calculate the percent of respondents in the total population (results are extrapolated), who select every one of the three options. Data are often presented in the form of an index calculated as the difference between the percent of those who claim that a given variable has improved in value and of those who claim that it has deteriorated. As in any survey conducted on a sample the question of the measurement of the sample error of the results has to be addressed, since the error influences both the reliability of the results and the calculation of the sample size adequate for a desired confidence interval. The results presented here are based on data from the Survey of the Business Climate (Encuesta de Clima Empresarial) developed through the collaboration of the Statistical Institute of Catalonia (Institut d’Estadística de Catalunya) with the Chambers of Commerce (Cámaras de Comercio) of Sabadell and Terrassa.

Amostragem para diagnose do estado nutricional e avaliação da fertilidade do solo em caramboleiras

Para a realização de uma análise confiável, a etapa mais sensível e que merece extremo cuidado é a amostragem do tecido vegetal e do solo. A amostra mais adequada é aquela que representa o melhor possível a área de estudo, exigindo um mínimo de plantas amostradas para atender a esse objetivo e com o menor número possível de amostras simples coletadas. Assim, o presente trabalho procurou dimensionar o número de plantas a serem amostradas para a diagnose do estado nutricional, bem como o número de amostras simples necessárias para formar a amostra composta, para fins de avaliação da fertilidade do solo cultivado com caramboleiras. O estudo foi realizado em um pomar comercial de caramboleiras, no município de Vista Alegre do Alto (SP), empregando-se amostragem aleatória, coletando-se a sexta folha a partir do ápice do ramo da caramboleira, na altura mediana da frutífera, no florescimento da cultura, em 40 plantas. Foram coletadas, também, 30 amostras simples de solo, em zigue-zague, nas linhas da cultura, com o auxílio de um trado tipo holandês, nas camadas de 0 a 0,2 m e 0,2 a 0,4 m. Considerando-se aceitável um erro amostral de 10%, 21 plantas de carambola seriam suficientes para as determinações químicas foliares de macronutrientes. Já para os micronutrientes, seriam necessárias, no mínimo, 52 plantas amostradas. O aumento do número de amostras simples reduziu o erro porcentual na estimativa da média desejada, permitindo a recomendação de 14 e 17 amostras simples nas camadas de 0 a 0,2 m e 0,2 a 0,4 m (erro = 20%), respectivamente.

Tamanho da amostra foliar para avaliação do estado nutricional de goiabeiras com e sem irrigação

The ideal size precision of the foliar sample determines manual work optimization, and also diminishes inherent errors in diagnosis reports of nutritional state. This work aimed to determine the size of the foliar samples and the sample error variation in guava plantations submitted to two hydric cultivations for the nutritional state diagnosis of this fruit. The work included two studies, both under an entirely randomized experimental design. Study 1 was carried out in an orchard under unirrigated cultivation with four treatments and six repetitions that consisted of leaf collection in 5, 10, 20 and 40 plants. Study 2 was carried out in an orchard under irrigated cultivation with five treatments and 10 repetitions that consisted of leaf collection in 10, 20, 30, 40 and 50 guava plants. It was concluded that in unirrigated orchards it is necessary to sample leaves in 40 plants in order to keep the macronutrients sample error between 5 to 10%. For the micronutrients, on the other hand, at least 40 plants were necessary and, if Fe and Zn were considered, the sample must be even larger. In irrigated orchards, leaves deriving from 10 plants were enough to keep the sample error between 5 to 10%. However, considering the micronutrients, it was necessary to sample 20 guava plants.

Amostragem de folhas em cafeeiro para fins de diagnose do estado nutricional

Pós-graduação em Agronomia (Ciência do Solo) - FCAV

Improving sample representativeness in environmental studies: a major component for the uncertainty budget

For environmental quality assessment, INAA has been applied for determining chemical elements in small (200 mg) and large (200 g) samples of leaves from 200 trees. By applying the Ingamells` constant, the expected percent standard deviation was estimated in 0.9-2.2% for 200 mg samples. Otherwise, for composite samples (200 g), expected standard deviation varied from 0.5 to 10% in spite of analytical uncertainties ranging from 2 to 30%. Results thereby suggested the expression of the degree of representativeness as a source of uncertainty, contributing for increasing of the reliability of environmental studies mainly in the case of composite samples.

Osmolarity effects on observed insect cell size after baculovirus infection are avoided using growth medium for sample dilution

Rates of cell size increase are an important measure of success during the baculovirus infection process. Batch and fed batch cultures sustain large fluctuations in osmolarity that can affect the measured cell volume if this parameter is not considered during the sizing protocol. Where osmolarity differences between the sizing diluent and the culture broth exist, biased measurements of size are obtained as a result of the cell osmometer response. Spodoptera frugiperda (Sf9) cells are highly sensitive to volume change when subjected to a change in osmolarity. Use of the modified protocol with culture supernatants for sample dilution prior to sizing removed the observed error during measurement.

Pleural fluid: Are temperature and storage time critical preanalytical error factors in biochemical analyses?

Background: Biochemical analysis of fluid is the primary laboratory approach hi pleural effusion diagnosis. Standardization of the steps between collection and laboratorial analyses are fundamental to maintain the quality of the results. We evaluated the influence of temperature and storage time on sample stability. Methods: Pleural fluid from 30 patients was submitted to analyses of proteins, albumin, lactic dehydrogenase (LDH), cholesterol, triglycerides, and glucose. Aliquots were stored at 21 degrees, 4 degrees, and-20 degrees C, and concentrations were determined after 1, 2, 3, 4, 7, and 14 days. LDH isoenzymes were quantified in 7 random samples. Results: Due to the instability of isoenzymes 4 and 5, a decrease in LDH was observed in the first 24 h in samples maintained at -20 degrees C and after 2 days when maintained at 4 degrees C. Aside from glucose, all parameters were stable for up to at least day 4 when stored at room temperature or 4 degrees C. Conclusions: Temperature and storage time are potential preanalytical errors in pleural fluid analyses, mainly if we consider the instability of glucose and LDH. The ideal procedure is to execute all the tests immediately after collection. However, most of the tests can be done in refrigerated sample;, excepting LDH analysis. (C) 2010 Elsevier B.V. All rights reserved.

Strabismus, visual acuity, and uncorrected refractive error in Portuguese children aged 6 to 11 years

Introduction: Visual anomalies that affect school-age children represent an important public health problem. Data on the prevalence are lacking in Portugal but is needed for planning vision services. This study was conducted to determine the prevalence of strabismus, decreased visual acuity, and uncorrected refractive error in Portuguese children aged 6 to 11 years. Methods and materials: A cross-sectional study was carried out on a sample of 672 school-age children (7.69 ± 1.19 years). Children received an orthoptic assessment (visual acuity, ocular alignment, and ocular movements) and non-cycloplegic autorefraction. Results: After orthoptic assessment, 13.8% of children were considered abnormal (n = 93). Manifest strabismus was found in 4% of the children. Rates of esotropia (2.1%) were slightly higher than exotropia (1.8%). Strabismus rates were not statistically significant different per sex (p = 0.681) and grade (p = 0.228). Decreased visual acuity at distance was present in 11.3% of children. Visual acuity ≤20/66 (0.5 logMAR) was found in 1.3% of the children. We also found that 10.3% of children had an uncorrected refractive error. Conclusions: Strabismus affects a small proportion of the Portuguese school-age children. Decreased visual acuity and uncorrected refractive error affected a significant proportion of school-age children. New policies need to be developed to address this public health problem.

Assessing usual dietary intake in complex sample design surveys: the National Dietary Survey

The National Cancer Institute (NCI) method allows the distributions of usual intake of nutrients and foods to be estimated. This method can be used in complex surveys. However, the user must perform additional calculations, such as balanced repeated replication (BRR), in order to obtain standard errors and confidence intervals for the percentiles and mean from the distribution of usual intake. The objective is to highlight adaptations of the NCI method using data from the National Dietary Survey. The application of the NCI method was exemplified analyzing the total energy (kcal) and fruit (g) intake, comparing estimations of mean and standard deviation that were based on the complex design of the Brazilian survey with those assuming simple random sample. Although means point estimates were similar, estimates of standard error using the complex design increased by up to 60% compared to simple random sample. Thus, for valid estimates of food and energy intake for the population, all of the sampling characteristics of the surveys should be taken into account because when these characteristics are neglected, statistical analysis may produce underestimated standard errors that would compromise the results and the conclusions of the survey.

Evaluation of Spatial interpolation techniques for mapping climate variables with low sample density: a case study using a new gridded dataset of Bangladesh

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.

Parametric and semiparametric estimation of sample selection models: an empirical application to the female labour force in Portugal

This comment corrects the errors in the estimation process that appear in Martins (2001). The first error is in the parametric probit estimation, as the previously presented results do not maximize the log-likelihood function. In the global maximum more variables become significant. As for the semiparametric estimation method, the kernel function used in Martins (2001) can take on both positive and negative values, which implies that the participation probability estimates may be outside the interval [0,1]. We have solved the problem by applying local smoothing in the kernel estimation, as suggested by Klein and Spady (1993).

Restriction site-associated DNA sequencing, genotyping error estimation and de novo assembly optimization for population genetic inference.

Restriction site-associated DNA sequencing (RADseq) provides researchers with the ability to record genetic polymorphism across thousands of loci for nonmodel organisms, potentially revolutionizing the field of molecular ecology. However, as with other genotyping methods, RADseq is prone to a number of sources of error that may have consequential effects for population genetic inferences, and these have received only limited attention in terms of the estimation and reporting of genotyping error rates. Here we use individual sample replicates, under the expectation of identical genotypes, to quantify genotyping error in the absence of a reference genome. We then use sample replicates to (i) optimize de novo assembly parameters within the program Stacks, by minimizing error and maximizing the retrieval of informative loci; and (ii) quantify error rates for loci, alleles and single-nucleotide polymorphisms. As an empirical example, we use a double-digest RAD data set of a nonmodel plant species, Berberis alpina, collected from high-altitude mountains in Mexico.

Restriction site-associated DNA sequencing, genotyping error estimation and de novo assembly optimization for population genetic inference.

Restriction site-associated DNA sequencing (RADseq) provides researchers with the ability to record genetic polymorphism across thousands of loci for nonmodel organisms, potentially revolutionizing the field of molecular ecology. However, as with other genotyping methods, RADseq is prone to a number of sources of error that may have consequential effects for population genetic inferences, and these have received only limited attention in terms of the estimation and reporting of genotyping error rates. Here we use individual sample replicates, under the expectation of identical genotypes, to quantify genotyping error in the absence of a reference genome. We then use sample replicates to (i) optimize de novo assembly parameters within the program Stacks, by minimizing error and maximizing the retrieval of informative loci; and (ii) quantify error rates for loci, alleles and single-nucleotide polymorphisms. As an empirical example, we use a double-digest RAD data set of a nonmodel plant species, Berberis alpina, collected from high-altitude mountains in Mexico.