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Computer intensive statistical methods: validation, model selection and bootstrap
... Unfortunately, the condition of independence does not hold with time series data, as chronologically ordered observations are almost always serially correlated in time (one exception is white noise). To our knowledge, there is not currently a standard way of performing CV for time series data, but two useful CV procedures that deal with the issue of serial dependence in temporal data can be found in Arlot, Celisse, et al. [37,38]. Essentially, the modified CV procedure proposed by Arlot, Celisse, et al. [37] chooses the training and validation sets in such a way that the effects of serial correlation are minimized, while [38] proposes a procedure called forward validation, which exclusively uses the most recent training examples as validation data. ...
... To our knowledge, there is not currently a standard way of performing CV for time series data, but two useful CV procedures that deal with the issue of serial dependence in temporal data can be found in Arlot, Celisse, et al. [37,38]. Essentially, the modified CV procedure proposed by Arlot, Celisse, et al. [37] chooses the training and validation sets in such a way that the effects of serial correlation are minimized, while [38] proposes a procedure called forward validation, which exclusively uses the most recent training examples as validation data. CV error produced by the forward validation procedure would be a good approximation to unknown prediction error since the short-term future behavior of a time series tends to be similar to that of its most recently recorded observations. ...
This paper reviews the application of Artificial Neural Network (ANN) models to time series prediction tasks. We begin by briefly introducing some basic concepts and terms related to time series analysis, and by outlining some of the most popular ANN architectures considered in the literature for time series forecasting purposes: Feed Forward Neural Networks, Radial Basis Function Networks, Recurrent Neural Networks and Self Organizing Maps; we analyze the strengths and weaknesses of these architectures in the context of time series modeling. We then summarize some recent time series ANN modeling applications found in the literature, focusing mainly on the previously outlined architectures; in our opinion, these summarized techniques constitute a representative sample of the research and development efforts made in this field. We aim to provide the general reader with a good perspective on how ANNs have been employed for time series modeling and forecasting tasks. Finally, we comment on possible new research directions in this area.
... Este procedimiento y la confirmación del modelo estructural se ha desarrollado con el software IBM ® SPSS ® Amos 24.0.0. Para comprobar la validez convergente se utilizaron los tres criterios planteados por Hair et al. (1999): la confiabilidad de los ítems de cada constructo (carga factorial), la varianza promedio extraída (VPE) y la confiabilidad del constructo, usándose los índices de ajuste sugeridos por Fornell y Larcker (1981), Hair et al. (1999), Hjorth (1994) y Nunnally (1978) para evaluar la adecuación del modelo -carga factorial > 0,7, VPE > 0,5 y confiabilidad del constructo > 0,7-(tabla 4). ...
... This procedure and the confirmation of the structural model were carried out using IBM ® SPSS ® Amos 24.0.0 software. To check convergent validity the three criteria proposed by Hair et al., (1999) were used: the reliability of the items of each construct (factor loadings), the average variance extracted (AVE), and the reliability of the construct, using the fit indices suggested by Fornell and Larcker (1981), Hair et al., (1999), Hjorth (1994) and Nunnally (1978) to assess model fit -factor loadings >0.7, AVE >0.5 and construct reliability >0.7 -( Table 4). ...
Los trabajos que asocian presupuestos participativos e ingresos fiscales son escasos siendo, además, inexistentes los que tratan de encontrar una relación de causalidad potencial entre participar en este tipo de procesos e incrementar el cumplimiento tributario de los individuos. Por ello, con el presente trabajo se pretende dar un pequeño paso hacia adelante aportando evidencia empírica a este respecto. Partiendo de 530 cuestionarios de un municipio que cuenta con una determinada trayectoria participativa, y mediante un sistema de ecuaciones estructurales, se demuestra cómo el hecho de participar activamente en un proceso de presupuestos participativos podría dar lugar a una mayor conciencia fiscal.
... Next, we wanted the best-fitting, " final " model for each species, and we wanted it to be robust to the kinds of data variations that are inherent in field work. We accomplished this using bootstrapped data sets (Hjorth 1994), which we created using SPSS (SPSS for Windows, Version 16.0, Chicago, SPSS Inc., through IBM SPSS Statistics for Windows, Version 22.0, Armonk, New York, IBM Corp.) by randomly choosing 387 sample plots with replacement after each choice. Bootstrapped data sets introduce nothing extraneous; data are varied using the data itself (Hjorth 1994) (see Mancke and Gavin (2000) for more discussion about this). ...
... We accomplished this using bootstrapped data sets (Hjorth 1994), which we created using SPSS (SPSS for Windows, Version 16.0, Chicago, SPSS Inc., through IBM SPSS Statistics for Windows, Version 22.0, Armonk, New York, IBM Corp.) by randomly choosing 387 sample plots with replacement after each choice. Bootstrapped data sets introduce nothing extraneous; data are varied using the data itself (Hjorth 1994) (see Mancke and Gavin (2000) for more discussion about this). For each species, we fitted the 12 candidate models to each of 50 bootstrapped data sets, creating 600 fitted models. ...
Nearly half of the amphibian species in northeastern North America rely on vernal pools as their primary breeding habitat. The problem is that, because vernal pools are small and isolated, they are often left unmonitored and unprotected. A primary threat to both amphibians and vernal pools is habitat destruction and fragmentation, but our knowledge of the species-specific impacts of habitat loss and fragmentation on all phases of the amphibian life cycle are still rudimentary. The wood frog (Lithobates sylvaticus) was the focus of this research because it is considered the most common vernal pool indicator in Pennsylvania. The objectives of this study were to investigate the effect of road proximity on vernal pool hydrology and water chemistry, reproductive effort of wood frogs (i.e., numbers of egg masses deposited), and upland movement patterns of wood frogs. These parameters were compared between three isolated pools (> 1000 m from the nearest road) and two pools in a fragmented habitat (< 100 m from two roads) within a Pennsylvania state park. This study indicates that, although road proximity did not have a significant effect on vernal pool water chemistry and egg mass abundance was greater in the fragmented location, habitat fragmentation by roads did have a significant effect on the movement patterns of wood frogs in surrounding terrestrial habitat. At the isolated site where there were no barriers to movement, wood frogs were distributed randomly around the pools. However, wood frogs in the fragmented location were trapped at a lower frequency near roads than expected by chance, indicating that the presence of roads may reduce the amount of upland habitat utilized by adult wood frogs. Although this was a small and localized study, the results indicate the challenging nature of conserving species with complex life cycles in human dominated landscapes and highlight the importance of considering life-cycle and species-specific habitat requirements when designing vernal pool conservation plans.
... In order to explore the possibility of using wavelet-derived metrics as early predictors for clinical outcomes, we utilized a linear support vector machine (SVM) classifier (Cristianini and Shawe Taylor, 2000) with leave-one-out cross-validation (LOOCV) (Hjorth, 1994). SVM is a commonly used algorithm in machine learning for pattern recognition and data classification, while LOOCV is a special case of leave-k-out cross validation when k is equal to one (Shao, 1993). ...
... In order to explore the possibility of using wavelet-derived metrics as early predictors for clinical outcomes, we utilized a linear support vector machine (SVM) classifier (Cristianini and Shawe-Taylor, 2000) with leave-one-out cross-validation (LOOCV) (Hjorth, 1994). SVM is a commonly used algorithm in machine learning for pattern recognition and data classification, while LOOCV is a special case of leave-k-out cross validation when k is equal to one (Shao, 1993 ). ...
Cerebral autoregulation represents the physiological mechanisms that keep brain perfusion relatively constant in the face of changes in blood pressure and thus plays an essential role in normal brain function. This study assessed cerebral autoregulation in nine newborns with moderate-to-severe hypoxic–ischemic encephalopathy (HIE). These neonates received hypothermic therapy during the first 72 h of life while mean arterial pressure (MAP) and cerebral tissue oxygenation saturation (SctO2) were continuously recorded. Wavelet coherence analysis, which is a time-frequency domain approach, was used to characterize the dynamic relationship between spontaneous oscillations in MAP and SctO2. Wavelet-based metrics of phase, coherence and gain were derived for quantitative evaluation of cerebral autoregulation. We found cerebral autoregulation in neonates with HIE was time-scale-dependent in nature. Specifically, the spontaneous changes in MAP and SctO2 had in-phase coherence at time scales of less than 80 min (< 0.0002 Hz in frequency), whereas they showed anti-phase coherence at time scales of around 2.5 h (~ 0.0001 Hz in frequency). Both the in-phase and anti-phase coherence appeared to be related to worse clinical outcomes. These findings suggest the potential clinical use of wavelet coherence analysis to assess dynamic cerebral autoregulation in neonatal HIE during hypothermia.
... For prediction of optimum number of PLS components, bootstrap technique [25, 26] was used. This technique is based on dividing the original training set to two-thirds (bootstrap training set) and one-third (bootstrap test set). ...
... For a data set X (í µí°¼ × í µí°½) of an output vector c, SVR models aim to find a multivariate regression function í µí±(í µí±¥) that depends on X to predict a desired response (e.g., concentration of a chemical compound ) from an object (e.g., a spectrum). SVR model equations are illustrated in literature262728 and the summary equation can be given as follows: ...
A comparison between partial least squares regression and support vector regression chemometric models is introduced in this study. The two models are implemented to analyze cefoperazone sodium in presence of its reported impurities, 7-aminocephalosporanic acid and 5-mercapto-1-methyl-tetrazole, in pure powders and in pharmaceutical formulations through processing UV spectroscopic data. For best results, a 3-factor 4-level experimental design was used, resulting in a training set of 16 mixtures containing different ratios of interfering moieties. For method validation, an independent test set consisting of 9 mixtures was used to test predictive ability of established models.The introduced results show the capability of the two proposed models to analyze cefoperazone in presence of its impurities 7-aminocephalosporanic acid and 5-mercapto-1-methyl-tetrazole with high trueness and selectivity (101.87 ± 0.708 and 101.43 ± 0.536 for PLSR and linear SVR, resp.). Analysis results of drug products were statistically compared to a reported HPLC method showing no significant difference in trueness and precision, indicating the capability of the suggested multivariate calibration models to be reliable and adequate for routine quality control analysis of drug product. SVR offers more accurate results with lower prediction error compared to PLSR model; however, PLSR is easy to handle and fast to optimize.
... It is assumed that responses are independent, and the random noise vector is zero-mean, uncorrelated and follows normal distribution. This last assumption also means that the residuals from any fitted model (difference between predictions and actual observations) should not show an identifiable structure [38,39]. Therefore, before making inferences using regression models, one should perform residual analysis. ...
... This is because the purpose of this phase was to avoid ''overfitting " models to the in-house data. This bias-variance tradeoff is common in statistical predictive modeling [39]. Finally, to classify the comprehensive data obtained in this study, a variant of k-means clustering method was applied using combined NDT results. ...
... However, as we will see, this is almost the same as BMA with some appropriate model priors, and when C is taken to be BIC or some other criterion based on penalized likelihood (see Noble, 2000). One aspect of model uncertainty which however drew a lot of attention among frequentists lately is the selection bias inherent in any model estimation preceded by model selection using the same data set (see Miller, 1990;Pötscher, 1991;Breiman, 1992;Chatfield, 1995;Hjorth, 1994;Efron, 2000). The reason why selection bias arises is that the actual population parameters estimated are not those of the true model, but rather those constrained by all the possible samples that would have produced the model actually selected, given the model selection procedure. ...
... The universal bootstrap approach of Efron and Gong (1983) does not lead to the improved predictions even if it allows one to correct for the prediction bias in terms of the naïve R 2 . Breiman (1992), Breiman and Spector (1992), and Hjorth (1994) showed how to account for model selection bias when making model selection, which only establishes a more complicated procedure for selecting a single model. After you make the finial selection the same issues of model selection bias arise. ...
... Lastly, in scenario 4, both sizes of historical and prospective datasets are fixed. These diverse approaches collectively fall under the umbrella term forward validation [16,17]. ...
This study delves into the multifaceted nature of cross-validation (CV) techniques in machine learning model evaluation and selection, underscoring the challenge of choosing the most appropriate method due to the plethora of available variants. It aims to clarify and standardize terminology such as sets, groups, folds, and samples pivotal in the CV domain, and introduces an exhaustive compilation of advanced CV methods like leave-one-out, leave-p-out, Monte Carlo, grouped, stratified, and time-split CV within a hold-out CV framework. Through graphical representations, the paper enhances the comprehension of these methodologies, facilitating more informed decision making for practitioners. It further explores the synergy between different CV strategies and advocates for a unified approach to reporting model performance by consolidating essential metrics. The paper culminates in a comprehensive overview of the CV techniques discussed, illustrated with practical examples, offering valuable insights for both novice and experienced researchers in the field.
... AUROC is the most common metric used in ERP BCIs. If we wish to determine the classification performance offline, we often use cross-validation [Hjorth, 2017]. Cross-validation separates a set into k-folds, and uses k-1 folds as training set while 1 fold as testing data. ...
Brain-Computer Interfaces (BCIs) are systems that enable a person to manipulate an external device with only brain activity, often using ElectroEncephaloGraphgy (EEG). Although there is great medical potential (communication and mobility assistance, as well as neuro-rehabilitation of those who lost motor functions), BCIs are rarely used outside of laboratories. This is mostly due to users’ variability from their brain morphologies to their changeable psychological states, making it impossible to create one system that works with high success for all. The success of a BCI depends tremendously on the user’s ability to focus to give mental commands, and the machine’s ability to decode such mental commands. Most approaches consist in either designing more intuitive and immersive interfaces to assist the users to focus, or enhancing the machine decoding properties. The latest advances in machine decoding are enabling adaptive machines that try to adjust to the changeable EEG during the BCI task. This thesis is unifying the adaptive machine decoding approaches and the interface design through the creation of adaptive and optimal BCI tasks according to user states and traits. Its purpose is to improve the performance and usability of BCIs and enable their use outside of laboratories. To such end, we first created a taxonomy for adaptive BCIs to account for the various changeable factors of the system. Then, we showed that by adapting the task difficulty we can influence a state of flow, i.e., an optimal state of immersion, control and pleasure. which in turn correlates with BCI performance. Furthermore, we have identified the user traits that can benefit from particular types of task difficulties. This way we have prior knowledge that can guide the task adaptation process, specific to each user trait. As we wish to create a generic adaptation rule that works for all users, we use a probabilistic Bayesian model, called Active Inference used in neuroscience to computationally model brain behavior. When we provide such probabilistic model to the machine, it becomes adaptive in such a way that it mimics brain behavior. That way, we can achieve an automatic co-adaptive BCI and potentially get a step closer into using BCIs in our daily lives.
... The accuracy of the prediction by the models was evaluated using five-fold cross-validation [45]. In each run of cross-validation, the training set included 80% of HEB lines, randomly selected per HEB family, while the remaining 20% of HEB lines were assigned to build the test set. ...
Like other crop species, barley, the fourth most important crop worldwide, suffers from the genetic bottleneck effect, where further improvements in performance through classical breeding methods become difficult. Therefore, indirect selection methods are of great interest. Here, genomic prediction (GP) based on 33,005 SNP markers and, alternatively, metabolic prediction (MP) based on 128 metabolites with sampling at two different time points in one year, were applied to predict multi-year agronomic traits in the nested association mapping (NAM) population HEB-25. We found prediction abilities of up to 0.93 for plant height with SNP markers and of up to 0.61 for flowering time with metabolites. Interestingly, prediction abilities in GP increased after reducing the number of incorporated SNP markers. The estimated effects of GP and MP were highly concordant, indicating MP as an interesting alternative to GP, being able to reflect a stable genotype-specific metabolite profile. In MP, sampling at an early developmental stage outperformed sampling at a later stage. The results confirm the value of GP for future breeding. With MP, an interesting alternative was also applied successfully. However, based on our results, usage of MP alone cannot be recommended in barley. Nevertheless, MP can assist in unravelling physiological pathways for the expression of agronomically important traits.
... We split our data set into K non-overlapping subsets (folds). According to [21], we set K to 5, to avoid overestimating the true expected error. Next, we trained four different types of classifiers: Linear Discriminant Analysis (LDA), SVM, Naive Bayes (NB), and K-nearest-neighbors (KNN) on 150 normal and abnormal gait samples from our data set. ...
... This criteria estimates the quality of each model based on a trade-off between the goodness of fit and model complexity (Burnham and Anderson, 2002). The candidate models were also created with the help of cross-validation (Hjorth, 1994). The other reason for using cross-validation was to overcome problems arising from small sizes (see Green, 1991 for details). ...
Executive summary
Project Background
Water levels of Rainy River have been regulated using different rule-curves since 1949. The present rule curves (2000RC) dictating target water levels will soon be reviewed by the International Joint Commission according to effects on many parameters like including shoreline properties, fisheries, and socio-economic indicators.
Study objectives
Walleye and Lake Sturgeon are the primary sport fish in Rainy River. Rainy River provides important spawning grounds for both of these species. Heinrich and Friday (2014) mentioned four spawning sites for Lake Sturgeon in the main-stem of Rainy River. Payer (1987) tagged over 10 000 Walleyes in Lake of the Woods and observed that a large portion of them spawned in Rainy River.
The present project integrates a large amount of knowledge from other studies and aims to quantify the effects of historical water-level regulations on some key species of Rainy River: Lake Sturgeon and Walleye. We used 2D habitat modeling to evaluate the impact of different water-level management plans on these biological indicators.
We first developed an Integrated Ecosystem Response Model (IERM) based on a computation grid covering Rainy River from International Falls dam to about 2 km downstream from the Black River outlet with a 10 m resolution. The grid was developed from a Digital Elevation Model (DEM) to which we coupled hydrological and biological information. This process integrated several habitat models concerning key faunal species potentially sensitive to water-level management. The habitat models used quarter-monthly (QM) time steps to analyze four long-term water-levels series representing measured levels, as well as simulated levels based on natural conditions (absence of water-level management) and two sets of rule-curves (2000RC and 1970RC). Each water level-time series ranges from 1950 to 2012 (1950 to 2014 for the measured one) and simulated series were generated through hydrologic response models using measured inflows over the entire period.
We developed spatially explicit 2D models to quantify areas of suitable habitat for the two species. These models are based on scientific knowledge from the literature and logistic regressions comparing environmental variables (water depth, velocity, bottom slope, etc.) in the presence and in the absence of each taxon to predict their probability of occurrence at each grid node. The models were also bounded by various relevant processes (air or water temperature, ice-out date, etc.) to predict suitable habitat for each modeled species.
Results
Lake Sturgeon
Results from the Lake Sturgeon spawning habitat model suggest that the 2000RC increased the amount of suitable spawning habitat compared to the 1970RC. Still, under natural conditions, the mean surface area of habitat suitable to spawning Lake Sturgeon would have been slightly greater than under any regulated time series. This suggests that a RC closer to natural condition would marginally increase the surface area of spawning habitat.
Walleye
The 2D model suggests that the Walleye spawning conditions improved under the 2000RC compared to the 1970RC. This was caused by smaller river discharge variations during the Walleye spawning and egg incubation period. Interestingly, Natural water levels would provide more favorable spawning conditions than any past regulated water levels in Rainy River.
Recommendations
To preserve optimal conditions for Lake Sturgeon spawning, relatively stable river discharges at International Fall must be targeted during the spawning and egg incubation period. Large discharge variations during this critical period may results in egg exposure to air or their washing off from spawning areas. Also, stable river discharge during the Walleye spawning period would provide them with more spawning habitat. Such a scenario involves that discharge remain stable from the onset of spawning until eggs hatch to ensure that eggs are constantly maintained in a suitable environment.
It is not essential to maximize the amount of suitable spawning grounds every year to maintain a healthy fish population. Lake Sturgeon and Walleye would still reproduce should water levels be lower in spring or river discharges be too variable, but recruitment would then be inferior. One year of good reproduction every 3 to 5 years should be adequate to maintain stable population size for these two species. However, we regard water stability during spawning and egg incubation period as critical, since large discharge variations could results in the complete loss of a year-class. Such a loss could have long-term effects on population dynamics by reducing the number of spawning adults in the following years.
... Second, the dose-response relationship is unknown prior to the study, leading to model uncertainty. This problem is often underestimated, although ignoring model uncertainty can lead to highly undesirable effects (Chatfield (1995), Draper (1995), Hjorth (1994). Third, data from dose-finding studies are usually highly variable. ...
Dose-finding studies are frequently conducted to evaluate the effect of different doses or concentration levels of a compound on a response of interest. Applications include the investigation of a new medicinal drug, a herbicide or fertilizer, a molecular entity, an
environmental toxin, or an industrial chemical. In pharmaceutical drug development, dosefinding studies are of critical importance because of regulatory requirements that marketed doses are safe and provide clinically relevant efficacy. Motivated by a dose-finding study in
moderate persistent asthma, we propose response-adaptive designs addressing two major challenges in dose-finding studies: uncertainty about the dose-response models and large variability in parameter estimates. To allocate new cohorts of patients in an ongoing study,
we use optimal designs that are robust under model uncertainty. In addition, we use
a Bayesian shrinkage approach to stabilize the parameter estimates over the successive
interim analyses used in the adaptations. This allows us to calculate updated parameter
estimates and model probabilities that can then be used to calculate the optimal design
for subsequent cohorts. The resulting designs are hence robust with respect to model misspecification and additionally can efficiently adapt to the information accrued in an ongoing study. We focus on adaptive designs for estimating the minimum effective dose, although alternative optimality criteria or mixtures thereof could be used, enabling the design to address multiple objectives. In an extensive simulation study, we investigate the operating characteristics of the proposed methods under a variety of scenarios discussed by
the clinical team to design the aforementioned clinical study.
... The common point of these data sets is that their important error rate in test phase without any kind of data pre-processing is about 10% or above with reference and robust classifiers such as 1-nearest neighbour (1-NN) [2] [5] or C4.5 [19]. In relation to the experimental design we have followed a stratified 4-fold cross validation [13], whereby the data set is divided into four parts and subsequently a partition is the test set and the three remaining ones are pooled as the training data. On the other hand, for the assessment of the classification models we have chosen the accuracy [15] and roc [8] measures. ...
This paper presents a novel procedure to apply in a sequential way two data preparation techniques from a different nature such as data cleansing and feature selection. For the former we have experienced with a partial removal of outliers via inter-quartile range whereas for the latter we have chosen relevant attributes with two widespread feature subset selectors like CFS (Correlation-based Feature Selection) and CNS (Consistency-based Feature Selection), which are founded on correlation and consistency measures, respectively. Empirical results on seven difficult binary and multi-class data sets, that is, with a test error rate of at least a 10%, according to accuracy, with C4.5 or 1-nearest neighbour classifiers without any kind of prior data pre-processing are outlined. Non-parametric statistical tests assert that the meeting of the aforementioned two data preparation strategies using a correlation measure for feature selection with C4.5 algorithm is significant better, measured with roc measure, than the single application of the data cleansing approach. Last but not least, a weak and not very powerful learner like PART achieved promising results with the new proposal based on a consistency measure and is able to compete with the best configuration of C4.5. To sum up, bearing in mind the new approach, for roc measure PART classifier with a consistency metric behaves slightly better than C4.5 and a correlation measure.
... For the number of generations, four kind of values were defined (100, 300, 500 and 1000) and in regard to the maximum number of neurons in the hidden layer the range [4][5][6][7][8][9][10][11][12]were considered. In relation to the experimental design we have followed a three-fold stratified cross validation (Hjorth, 1993), whereby data set is divided into three parts and subsequently a partition is the test set and the two remaining ones are pooled as the training data. For stochastic algorithms, for each cross validation fold we perform 30 iterations and since we have three folds the results are averaged from 90 runs in order to get a good reliability level. ...
This paper presents a quality enhancement of the selected features by a hybrid filter-based jointly on feature ranking and feature subset selection (FR-FSS) using a consistency-based measure via merging new features which are obtained applying other FR-FSS evaluated with a correlation metric. The goal is to overcome the accuracy of a neural network classifier containing product units as hidden nodes combined with a feature selection pre-processing step by means of a single consistency-based FR-FSS filter. Neural models are trained with a refined evolutionary programming approach called two-stage evolutionary algorithm. The experimentation has been carried out in eight complex classification problems, seven out of them from UCI (University of California at Irvine) repository and one real-world problem, with high test error rates (around 20%) with powerful classifiers such as 1-nearest neighbour or C4.5. Non-parametric statistical tests revealed that the new proposal significantly improves the accuracy of the neural models.
... The experimental design used in this chapter has been a stratified four-fold cross vali- dation [38]. The primary idea of the four-fold cross validation procedure is to divide the full data set in four partitions of the same size; each one is used as a test set and the remaining are used as a train set. ...
Digital forensics research includes several stages. Once we have collected the data the last goal is to obtain a model in order to predict the output with unseen data. We focus on supervised machine learning techniques. This chapter performs an experimental study on a forensics data task for multi-class classification including several types of methods such as decision trees, bayes classifiers, based on rules, artificial neural networks and based on nearest neighbors. The classifiers have been evaluated with two performance measures: accuracy and Cohen's kappa. The followed experimental design has been a 4-fold cross validation with thirty repetitions for non-deterministic algorithms in order to obtain reliable results, averaging the results from 120 runs. A statistical analysis has been conducted in order to compare each pair of algorithms by means of t-tests using both the accuracy and Cohen's kappa metrics.
... We use leave-one-out cross-validation to evaluate the spatiotemporal interpolation errors for the ozone dataset. This cross-validation process removes one of the n observation points and uses the remaining n − 1 points to estimate its value; and this process is repeated at each observation point [15]. The observation points are the points with measured original values. ...
This paper investigates spatiotemporal interpolation methods for the application of air pollution assessment. The air pollutant of interest in this paper is fine particulate matter PM2.5. The choice of the time scale is investigated when applying the shape function-based method. It is found that the measurement scale of the time dimension has an impact on the interpolation results. Based upon the comparison between the accuracies of interpolation results, the most effective time scale out of four experimental ones was selected for performing the PM2.5 interpolation. The paper also evaluates the population exposure to the ambient air pollution of PM 2.5 at the county-level in the contiguous U.S. in 2009. The interpolated county-level PM2.5 has been linked to 2009 population data and the population with a risky PM2.5 exposure has been estimated. The risky PM2.5 exposure means the PM2.5 concentration exceeding the National Ambient Air Quality Standards. The geographic distribution of the counties with a risky PM2.5 exposure is visualized. This work is essential to understanding the associations between ambient air pollution exposure and population health outcomes. Copyright © 2011, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.
... In the classical cross-validation, all n 2 pairs of training sets are mutually disjoint (and so are testing sets) and hence folds are dependent, whereas in the bootstrapping instead of repeatedly analyzing subsets of data set, one repeatedly analyzes the subsamples (with replacement) of the data. For more information see (Hjorth, 1994; Weiss and Kulikowski, 1991; Fu et al., 2005). We introduce the following notation. ...
Typically, the n-fold cross-validation is used both to: (1) estimate the generalization properties of a model of fixed complexity, (2) choose from a family of models of different complexities, the one with the best complexity, given a data set of certain size. Obviously, it is a time-consuming procedure. A different approach — the Structural Risk Minimization is based on generalization bounds of learning machines given by Vapnik (Vapnik, 1995a; Vapnik, 1995b). Roughly speaking, SRM is O(n) times faster than n-fold cross-validation but less accurate. We state and prove theorems, which show the probabilistic relationship between the two approaches. In particular, we show what epsilon-difference between the two, one may expect without actually performing the crossvalidation. We conclude the paper with results of experiments confronting the probabilistic bounds we derived.
... Resonemanget utvecklas lätt för att även innefatta en modell med fler parametrar. [14] Låt ...
... With cross-validation [Hjorth, 1994], the PTF reliability is assessed by (1) drawing a random subsample from the data set, (2) developing a PTF for the subsample, (3) testing the accuracy of the PTF against the data left after subsampling. This process is repeated several times. ...
Pedotransfer functions (PTFs) express relationships between soil properties from soil surveys and soil parameters needed in applications such as modeling or soil quality assessment. The accuracy and the reliability of PTFs vary and depend on the selection of the PTF equation, the availability of soil properties used in the PTF, the homogeneity of the data set, and the scale at which the data were collected. Artificial neural networks and the group method of data handling may generate more accurate PTFs than statistical regression. Soil structure parameters in PTFs improve their accuracy. The accuracy of PTFs increases when a preliminary data grouping is made and separate PTFs are developed for each group. Cross-validation is helpful in assessing whether the grouping will improve the reliability. PTFs are generally reliable in regions different from the region of development when the soil-forming factors are similar in the two regions, or when the region of development comprises a wide range of soils. Model sensitivity analysis or error propagation analysis is needed to define the required PTF accuracy. Aggregating soil data up to soil association level is helpful when PTFs are used in crop modeling at the regional scale. The accuracy of crop simulations with a PTF increases with the temporal scale of the modeling. Development of scale-dependent PTFs is a promising avenue of future research.
... A variety of computational methods have been examined including resampling, bootstrapping, and jackknifing (e.g., Faraway, 1992;Hjorth, 1994). Faraway (1992) wrote a program to simulate the data-analytic actions in a regression analysis. ...
... The accuracy of the prediction of flowering time by GWAS and the two genomic prediction approaches were evaluated using five-fold cross-validations [77]. In each run of crossvalidation, the estimation set included 80% of HEB lines, randomly selected per HEB family, while the remaining 20% of HEB lines were assigned to build the test set. ...
Background
Barley, globally the fourth most important cereal, provides food and beverages for humans
and feed for animal husbandry. Maximizing grain yield under varying climate conditions
largely depends on the optimal timing of flowering. Therefore, regulation of flowering time is
of extraordinary importance to meet future food and feed demands. We developed the first
barley nested association mapping (NAM) population, HEB-25, by crossing 25 wild barleys
with one elite barley cultivar, and used it to dissect the genetic architecture of flowering time.
Results
Upon cultivation of 1,420 lines in multi-field trials and applying a genome-wide association
study, eight major quantitative trait loci (QTL) were identified as main determinants to
control flowering time in barley. These QTL accounted for 64% of the cross-validated
proportion of explained genotypic variance (pG). The strongest single QTL effect
corresponded to the known photoperiod response gene Ppd-H1. After sequencing the
causative part of Ppd-H1, we differentiated twelve haplotypes in HEB-25, whereof the
strongest exotic haplotype accelerated flowering time by 11 days compared to the elite barley
haplotype. Applying a whole genome prediction model including main effects and epistatic
interactions allowed predicting flowering time with an unmatched accuracy of 77% of crossvalidated
pG.
Conclusions
The elaborated causal models represent a fundamental step to explain flowering time in
barley. In addition, our study confirms that the exotic biodiversity present in HEB-25 is a
valuable toolbox to dissect the genetic architecture of important agronomic traits and to
replenish the elite barley breeding pool with favorable, trait-improving exotic alleles.
... The fact that selection was data-based is often ignored in the subsequent analysis and leads to invalid inferences. Literature on this topic includes but is not limited to Bancroft [5] for pre-test estimators, Breiman [6], Hjorth [7], Chatfield [8], Draper [9], Buckland et al. [10], Zucchini [11], Candolo et al. [12], Hjort and Claeskens [13], Efron [14], Leeb and Pötscher [15], Longford [17], Claeskens and Hjort [4], Schomaker et al. [18], Zucchini et al. [19], Liu and Yang [20] , Nguefack- Tsague and Zucchini [21], Nguefack-Tsague et al. [26], and Nguefack-Tsague [22,23,24,25]. Bayesian model averaging can be found in Hoeting et al. [27] and Wasserman [28]. ...
Model averaging is an alternative to model selection and involves assigning weights to different models. A natural question that arises is whether there is an optimal weighting scheme. Various authors have shown their existence in others methodological frameworks. This paper investigates the derivation of optimal weights for model averaging using square error loss. It is shown that though these weights may exist in theory and depend on model parameters; once estimated they are no longer optimal. It is demonstrated using an example of linear regression that model averaging estimators with these estimated weights are unlikely to outperform post-model selection and others model averaging estimators. We provide a theoretical justification for this phenomenon.
... Therefore, bootstrap does not belong in the appraisal of the theory, but rather it is involved in the estimation of the accuracy of the description. Its proper place is among the tests discussed in Section 5, or rather after them since the bootstrap procedure in itself does not care (Hjorth, 1994) about the fulfillment of the hypothesis P 0 A Ω. If ^ P is within the resulting confidence intervals, we may be confident that Θ did not introduce important systematic errors or bias. Because of the limitations of the experimental protocol discussed above, it is advisable in this work to perform parametric bootstrap, analysing Θðpdatað ^ P ÞÞ. ...
... The duration for the training dataset is from 1 to 8 weeks prior to Feb. 10, 2014. We evaluated the forecast error by a cross-validation mechanism for time series data proposed by Hijorth [12]. The original method by Hijorth computes a weighted sum of one-step-ahead forecasts by rolling the origin when more data is available. ...
With the increasing number of geographically dis-tributed scientific collaborations and the growing sizes of scientific data, it has become challenging for users to achieve the best possible network performance on a shared network. We have developed a model to forecast expected bandwidth utilization on high-bandwidth wide area networks. The forecast model can improve the efficiency of resource utilization and scheduling of data movements on high-bandwidth networks to accommodate ever increasing data volume for large-scale scientific data ap-plications. A univariate forecast model is developed with STL and ARIMA on SNMP path utilization data. Compared with traditional approach such as Box-Jenkins methodology to train the ARIMA model, our forecast model reduces computation time by 83.2%. It also shows resilience against abrupt network usage changes. Its forecast errors are within the standard deviation of the monitored measurements. Keywords—Forecasting, Network, Time series analysis I. INTRODUCTION With advances in large scale experiments and simulations, the data volume of scientific applications has rapidly grown. Even with advances in network technology, it has become more challenging to efficiently coordinate network resources and to achieve best possible network performance on a shared network. It is also challenging to build a forecast model for network bandwidth utilization with accurate and fine-grained prediction due to the computational complexities. To support efficient resource management and scheduling data movement for ever increasing data volume in extreme-scale scientific applications, we have developed an analytical model in order to characterize and forecast
This study examines the impact of dysfunctional follower behavior on organizational performance in state-owned enterprises (SOEs). Data from a cross-sectional survey design based on 315 responses were analyzed using structural equation modeling, which allowed the formulation of several recommendations. First, the evidence suggests that managers seeking to increase organizational performance should not devote many resources to addressing employees' political deviance. Second, managers aiming to increase or maintain organizational performance in SOEs should devote more time and resources to establishing policies that control employee ownership deviance. Third, managers aiming to increase or maintain organizational performance in SOEs should devote more time and resources to establishing measures to control employee personal aggression.
The water heating technologies capable of replacing the electric shower (ChE), with gains of physical and economic efficiency, are solutions recommended by organisms worldwide. These are routes sought by economies such as Australia, the US, China and Brazil, particularly those using thermosyphon and hybrid solar power. The present research turned to the review of the literature on the experiments of water and energy efficiency of six water heating systems, with estimates for vertical sets in the intertropical zone. The literature is focused, fundamentally, on the thermal, economic and material viability of the systems, but incipient regarding ecoefficiencies. The review aimed to identify the main trends and involved 107 articles, books and book chapters, 28 dissertations, 06 theses, 04 standards and a federal report, from the Portal of Journals of Capes since 2000. Five trends were identified: 1) commercial, focused on construction, hotels and resorts; 2) residential, oriented to building systems; 3) social, aimed at condominiums of social interest, popular and rural villages; 4) economic, centered on budgetary constraints; 5) computational, focused on optimization, software, control and uncertainties. A methodology was developed to calculate the accounting and opportunity costs of the systems, water and energy efficiencies, when inserted in the ecological macrosystem, considering CO2 emissions equivalent to the local energy matrix configuration, in four scenarios: with and without water waste, with and without greenhouse effect. An Economics-Eco-Efficiency Index (EEI) was created to hierarchize systems. In descending order, in a scenario without water waste and considering the greenhouse effect, in Bahia: 1º) Low-cost solar heating systems (SAS) with polyvinyl chloride and polypropylene board, EEI 50%, distinguishing itself from PVC for having a greater energy efficiency and to cause less greenhouse effect; 2nd) Conventional SAS, EEI 36%; 3º) Heat Pump, EEI 24%; 4) Flex Heat Pump, EEI 15%. Extending the scope of the inferences, the input variables received probabilistic treatments and uncertainty evaluation, propagated to the total accumulated costs, unit and IEE. By the principle of maximum entropy, different distributions of the inputs generated stochastic outputs with 1e + 6 Monte Carlo Simulations (SMC), using R programming and Oracle® Crystal Ball software, whose averages and medians were equal or smaller that the deterministic results or equal, given the probability of being smaller the number of people, baths / day, pipe length. The hierarchy has not changed. ChE obtained zero EEI, having the lowest energy efficiency. Acquisition and maintenance of ChE are cheap, but it operates more cost-effectively through the use of electricity and, for this reason, is more deleterious in the environment. The SAS were more adequate in the Northeast of Brazil, with low auxiliary energy consumption, minimizing upstream CO2 emissions. The ecological and macroeconomic potential of low-cost SAS is unique in every intertropical region. The heat pump is effective and requires scale to be accessible.
Keywords: Water Heating Systems. Economicity. Eco-efficiency. Ecological Macrosystem. Uncertainty.
Recent progress in metabolomics has been aided by the development of analysis techniques such as gas and liquid chromatography coupled with mass spectrometry (GC-MS and LC-MS) and nuclear magnetic resonance (NMR) spectroscopy. The vast quantities of data produced by these techniques has resulted in an increase in the use of machine algorithms that can aid in the interpretation of this data, such as principal components analysis (PCA) and partial least squares (PLS). Techniques such as these can be applied to biomarker discovery, interlaboratory comparison, and clinical diagnoses. However, there is a lingering question whether the results of these studies can be applied to broader sets of clinical data, usually taken from different data sources. In this work, we address this question by creating a metabolomics workflow that combines a previously published consensus analysis procedure (https://doi.org/10.1016/j.chemolab.2016.12.010) with PCA and PLS models using uncertainty analysis based on bootstrapping. This workflow is applied to NMR data that come from an interlaboratory comparison study using synthetic and biologically obtained metabolite mixtures. The consensus analysis identifies trusted laboratories, whose data are used to create classification models that are more reliable than without. With uncertainty analysis, the reliability of the classification can be rigorously quantified, both for data from the original set and from new data that the model is analyzing.
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This chapter aims to outline the basic concepts underlying genomic selection (GS) in hybrid breeding. First, the concepts of dominance, heterosis, combining ability and heterotic groups are presented as a special feature of hybrid breeding, giving special attention to the breeding method of recurrent reciprocal selection. Subsequently, the cross-validated predictability is introduced as an evaluation criterion for the performance of GS and the relatedness between estimation and prediction sets is presented as its fundamental influential factor in hybrid breeding. Consequently, cross-validation schemes which consider different levels of relatedness according to particular breeding scenarios are illustratively explained. Later, classical mixed models and Bayesian GS approaches modeling dominance and additive effects receive special treatment in this chapter. Even though classical mixed models are in principle not suited for all genetic architectures, it seems they are preferred because of their relatively straightforward understanding and implementation plus their considerable robust performance. Moreover, modeling dominance in addition to additive effects seems to be beneficial when dominance effects are expected to have an important influence on predicted traits. GS models efficiently accommodating epistasis are available, but they have not received the attention needed to properly evaluate their advantages and limitations for hybrid performance prediction. Furthermore, other GS approaches are briefly introduced. Finally, the implementation of GS as a tool to assist hybrid breeding is dissected as an optimization problem, giving later emphasis to the model recalibration after implementing GS for the early stages of a breeding program.
The concern of society about food nowadays extends to the several aspects linked to food consumption encompassing nutritional value, health, safety, and quality, as well as ethics, sustainability, tradition, communication, marketing, and so on. The increased information available to the consumers, the awareness of the impact of diet on healthiness, and the issues brought by globalization of the food market on one hand and the institution of the Common Market (European Union (EU) countries) and its regulations on the other hand have progressively changed the leading paradigms in food science and the essential topics for the food industry. Undoubtedly, ‘quality’ is a primary criterion to access the market. However, quality is a multifaceted concept including both aspects, the set of identifiable features of a product and accountability, trustiness linked to it. Thus, quality is usually an integrated measure of several characteristics deliberately produced (sophistication, adulteration, counterfeit, appearance, etc.) or not (purity, contamination, degradation, etc.) and also of the subjective consumer's perception of the worth of the product (to which issues such as terroir, authenticity, origin, and production practice contribute). In this context, quality control and authentication require a step beyond traditional chemical analysis and characterization, which focuses mainly on single classes of constituents/properties, moving to fingerprinting, fast, nondestructive techniques. In this perspective, the role of chemometrics is of paramount importance to efficiently extract the relevant information and by providing tailored tools that allow exploratory data analysis, graphical representation, and validation of the models during all steps of data processing as well as efficient storage, retrieval, and sharing of information.
Raman spectroscopy has demonstrated great potential in the study of biological molecules in a variety of biomedical applications. But slow data acquisition due to weak Raman signals from these molecules has prevented its wide use especially in an imaging setup. We propose a novel method to reconstruct the entire Raman spectrum from a few narrow- band measurements based on Wiener estimation. This method has been tested on Raman spectra from individual cells and shown fast speed and excellent accuracy. This method represents a new direction to speed up Raman data acquisition in an imaging setup to investigate fast changing phenomena.
Model selection uncertainty would occur if we selected a model based on one data set and subsequently applied it for statistical inferences, because the "correct" model would not be selected with certainty. When the selection and inference are based on the same dataset, some additional problems arise due to the correlation of the two stages (selection and inference). In this paper model selection uncertainty is considered and model averaging is proposed. The proposal is related to the theory of James and Stein of estimating more than three parameters from independent normal observations. We suggest that a model averaging scheme taking into account the selection procedure could be more appropriate than model selection alone. Some properties of this model averaging estimator are investigated; in particular we show using Stein's results that it is a minimax estimator and can outperform Stein-type estimators.
In this text, the authors present a study on estimating the lost gas during the retrieval process of coal sample within wellbores. A new method is proposed because the traditional ones often give inaccurate predictions. To this end, the major sources of errors with those routine methods are first discussed briefly, and modifications are made accordingly in the present method to improve the accuracy of prediction. This new method takes into account these aspects: (1) Both the advection and diffusion effects are included in the proposed flow equation; (2) the present model uses the actual shape of the core sample (say, a cylinder) rather than a simplified 1D spherical object; and (3) a fully numerical scheme is developed in which the actual retrieval history is used to specify the boundary conditions of the core sample. When the relevant sorption isothermal curve for the coal is known, the proposed model contains three parameters to be determined, which refer to the effective permeability, the effective diffusion coefficient, and the initial gas content or the initial gas pressure. The three parameters are determined through best matching the experimental data with the aid of an artificial-neural-network (ANN) technique. Two application examples are presented in this study. One is with a benchmark laboratory test, and the other is with a standard field case studied by means of an established method. It is shown with the two examples that the present method can give accurate predictions for the lost gas volume concerned, and offers some important advantages that the traditional ones do not have.
The purpose of kinetic analysis of living matter is to obtain quantitative measures of the rate of molecular reactions. Quantitative approaches were uncommon in biology and medicine prior to the second half of the 19th century and only slowly gained ground against traditionally qualitative considerations. The competition between quantitative and qualitative perspectives is felt even today.
IntroductionData ScalingMultivariate Methods of Data ReductionStrategies for Data PreprocessingBibliography
Oftmals erweist sich bei der Aufstellung von Erklärungsmodellen die Auswahl der am besten geeigneten Spezifikation als nicht einfach. Im Regelfall stehen verschiedene Modellvarianten und Variablensätze zur Auswahl. Die Beurteilung, welche Kombination die beste Erklärungsgüte besitzt, ist dabei diffizil (Breiman und Spector 1992). In der Regel wird darauf vertraut, anhand der Residual-Methode den Datenfit der einzelnen Varianten zu beurteilen. Orientiert man sich dabei lediglich an dem Datenfit unter Benutzung eines einzelnen Datensatzes, so kann es zum so genannten „overfitting“ kommen. Dabei wird der Fehler des Modells systematisch unterschätzt. In Abbildung 34.1 wird dieses Phänomen grafisch dargestellt.
The paper presents a least squares framework for divisive clustering. Two popular divisive clustering methods, Bisecting K-Means and Principal Direction Division, appear to be versions of the same least squares approach. The PDD recently has been enhanced with a stopping criterion taking into account the minima of the corresponding one-dimensional density function (dePDDP method). We extend this approach to Bisecting K-Means by projecting the data onto random directions and compare thus modified methods. It appears the dePDDP method is superior at datasets with relatively small numbers of clusters, whatever cluster intermix, whereas our version of Bisecting K-Means is superior at greater cluster numbers with noise entities added to the cluster structure.
Model selection uncertainty would occur if we selected a model based on one data set and subsequently applied it for statistical inferences, because the "correct" model would not be selected with certainty. When the selection and inference are based on the same dataset, some additional problems arise due to the correlation of the two stages (selection and inference). In this paper model selection uncertainty is considered and model averaging is proposed. The proposal is related to the theory of James and Stein of estimating more than three parameters from independent normal observations. We suggest that a model averaging scheme taking into account the selection procedure could be more appropriate than model selection alone. Some properties of this model averaging estimator are investigated; in particular we show using Stein's results that it is a minimax estimator and can outperform Stein-type estimators.
Bootstrapping is a computer-intensive statistical method which treats the data set as a population and draws samples from it with replacement. This resampling method has wide application areas especially in mathematically intractable problems. In this study, it is used to obtain the empirical distributions of the parameters to determine whether they are statistically significant or not in a special case of nonparametric regression, conic multivariate adaptive regression splines (CMARS), a statistical machine learning algorithm. CMARS is the modified version of the well-known nonparametric regression model, multivariate adaptive regression splines (MARS), which uses conic quadratic optimization. CMARS is at least as complex as MARS even though it performs better with respect to several criteria. To achieve a better performance of CMARS with a less complex model, three different bootstrapping regression methods, namely, random-X, fixed-X and wild bootstrap are applied on four data sets with different size and scale. Then, the performances of the models are compared using various criteria including accuracy, precision, complexity, stability, robustness and computational efficiency. The results imply that bootstrap methods give more precise parameter estimates although they are computationally inefficient and that among all, random-X resampling produces better models, particularly for medium size and scale data sets.
This article presents an overview of existing resampling methods and their applications in parameter estimations and statistical inference. It describes the essential concepts and basic operating procedures of the most frequently used resampling methods, including the jackknife, bootstrap, permutation test, and cross-validation. This article also discusses the interconnections among these methods. Finally, it briefly reviews the currently available software for implementation of the most commonly used resampling procedures.Keywords:bootstrap;cross-validation;jackknife;permutation test;resampling
Barley, globally the fourth most important cereal, provides food and beverages for humans and feed for animal husbandry. Maximizing grain yield under varying climate conditions largely depends on the optimal timing of flowering. Therefore, regulation of flowering time is of extraordinary importance to meet future food and feed demands. We developed the first barley nested association mapping (NAM) population, HEB-25, by crossing 25 wild barleys with one elite barley cultivar, and used it to dissect the genetic architecture of flowering time.
Upon cultivation of 1,420 lines in multi-field trials and applying a genome-wide association study, eight major quantitative trait loci (QTL) were identified as main determinants to control flowering time in barley. These QTL accounted for 64% of the cross-validated proportion of explained genotypic variance (pG). The strongest single QTL effect corresponded to the known photoperiod response gene Ppd-H1. After sequencing the causative part of Ppd-H1, we differentiated twelve haplotypes in HEB-25, whereof the strongest exotic haplotype accelerated flowering time by 11 days compared to the elite barley haplotype. Applying a whole genome prediction model including main effects and epistatic interactions allowed predicting flowering time with an unmatched accuracy of 77% of cross-validated pG.
The elaborated causal models represent a fundamental step to explain flowering time in barley. In addition, our study confirms that the exotic biodiversity present in HEB-25 is a valuable toolbox to dissect the genetic architecture of important agronomic traits and to replenish the elite barley breeding pool with favorable, trait-improving exotic alleles.
Sumário: A comparação dos valores médios de duas populações é um dos problemas mais comuns e aparentemente mais simples em estatística aplicada. De facto, qualquer livro elementar de estatística apresenta soluções para esta questão. As mais vulgares são o teste t (admitindo geralmente que as duas populações têm variâncias iguais) e o teste não paramétrico de Mann-Whitney, apresentado como alternativa àquele. No entanto ambos os testes admitem algumas premissas nem sempre verificadas. Neste trabalho apresenta-se um exemplo dessa situação surgido no contexto dum estudo experimental destinado a comparar dois métodos de aprendizagem para crianças em idade escolar e pré-escolar. O número de observações disponível é reduzido e nenhum dos testes anteriores permitiu obter uma conclusão definitiva, o que pode ser justificado pelo facto de, não se verificando as premissas básicas, a sua potência ser baixa. Optou-se então por usar um procedimento "bootstrap" o qual permitiu inferir sobre a diferença entre os dois métodos de aprendizagem. Procedeu-se em seguida a um estudo de simulação destinado a comparar a potência dos três procedimentos (teste t, teste de Mann-Whitney, teste "bootstrap") sob diversas condições. Os resultados desse estudo apontam para uma maior potência do teste "bootstrap". Abstract: The comparison of the means of two populations is a common problem discussed in almost every elementary book in applied statistics. The various solutions presented for this problem include the t-test and a non-parametric alternative, the Mann-Whitney test. However both tests rely on some assumptions not always fulfilled. In this case a bootstrap procedure should be applied. In a study to compare two methods of learning applied to children in their first years of school the bootstrap showed smaller p-values than the other two tests when small independent samples of children take at different age groups were analyzed. A simulation study confirmed the conjecture that the bootstrap test has greater power than the other two tests.
South Africa As the candidate's supervisor, I have approved this dissertation for submission.
If you have ever wondered when visiting the pharmacy how the dosage of your prescription is determined this book will answer your questions. Dosing information on drug labels is based on discussion between the pharmaceutical manufacturer and the drug regulatory agency, and the label is a summary of results obtained from many scientific experiments. The book introduces the drug development process, the design and the analysis of clinical trials. Many of the discussions are based on applications of statistical methods in the design and analysis of dose response studies. Important procedural steps from a pharmaceutical industry perspective are also examined.
This book presents notions and ideas from the foundations of a statistical treatment of risks. Bayesian methods are frequently used in that area, hence a reasonable proportion of the presentation is devoted to such approaches. Modern statistical tools, namely Poisson regression, analysis of deviance, extreme-value theory and threshold methods are also used to identify and solve practical problems. The knowledge of such tools facilitates the understanding of the role of probability in risk analysis and proper use of outputs given by software packages. The book is written with a student in mind who has studied elementary undergraduate courses in engineering mathematics, perhaps including an introductory course in statistics. The text emphasizes an understanding of the theory and methods presented. Hence, comments are given verbally and an intuitive reasoning is frequent. This is not just another new textbook on elementary probability and statistics, but focuses strongly on applications within the field of risk and safety analysis.
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