A Simple Statistical Test of Violation of the Weak Axiom of Cost Minimization

A problem with a practical application of Varian.s Weak Axiom of Cost Minimization is that an observed violation may be due to random variation in the output quantities produced by firms rather than due to inefficiency on the part of the firm. In this paper, unlike in Varian (1985), the output rather than the input quantities are treated as random and an alternative statistical test of the violation of WACM is proposed. We assume that there is no technical inefficiency and provide a test of the hypothesis that an observed violation of WACM is merely due to random variations in the output levels of the firms being compared.. We suggest an intuitive approach for specifying a value of the variance of the noise term that is needed for the test. The paper includes an illustrative example utilizing a data set relating to a number of U.S. airlines.

Toxics Release Inventory facilities and childhood cancer: Geographic information systems based approach

Purpose. To examine the association between living in proximity to Toxics Release Inventory (TRI) facilities and the incidence of childhood cancer in the State of Texas. ^ Design. This is a secondary data analysis utilizing the publicly available Toxics release inventory (TRI), maintained by the U.S. Environmental protection agency that lists the facilities that release any of the 650 TRI chemicals. Total childhood cancer cases and childhood cancer rate (age 0-14 years) by county, for the years 1995-2003 were used from the Texas cancer registry, available at the Texas department of State Health Services website. Setting: This study was limited to the children population of the State of Texas. ^ Method. Analysis was done using Stata version 9 and SPSS version 15.0. Satscan was used for geographical spatial clustering of childhood cancer cases based on county centroids using the Poisson clustering algorithm which adjusts for population density. Pictorial maps were created using MapInfo professional version 8.0. ^ Results. One hundred and twenty five counties had no TRI facilities in their region, while 129 facilities had at least one TRI facility. An increasing trend for number of facilities and total disposal was observed except for the highest category based on cancer rate quartiles. Linear regression analysis using log transformation for number of facilities and total disposal in predicting cancer rates was computed, however both these variables were not found to be significant predictors. Seven significant geographical spatial clusters of counties for high childhood cancer rates (p<0.05) were indicated. Binomial logistic regression by categorizing the cancer rate in to two groups (<=150 and >150) indicated an odds ratio of 1.58 (CI 1.127, 2.222) for the natural log of number of facilities. ^ Conclusion. We have used a unique methodology by combining GIS and spatial clustering techniques with existing statistical approaches in examining the association between living in proximity to TRI facilities and the incidence of childhood cancer in the State of Texas. Although a concrete association was not indicated, further studies are required examining specific TRI chemicals. Use of this information can enable the researchers and public to identify potential concerns, gain a better understanding of potential risks, and work with industry and government to reduce toxic chemical use, disposal or other releases and the risks associated with them. TRI data, in conjunction with other information, can be used as a starting point in evaluating exposures and risks. ^

Statistical Methods for Differential Expressions of Genes Detected in Multiple-Condition Experiment of Microarray

Most studies of differential gene-expressions have been conducted between two given conditions. The two-condition experimental (TCE) approach is simple in that all genes detected display a common differential expression pattern responsive to a common two-condition difference. Therefore, the genes that are differentially expressed under the other conditions other than the given two conditions are undetectable with the TCE approach. In order to address the problem, we propose a new approach called multiple-condition experiment (MCE) without replication and develop corresponding statistical methods including inference of pairs of conditions for genes, new t-statistics, and a generalized multiple-testing method for any multiple-testing procedure via a control parameter C. We applied these statistical methods to analyze our real MCE data from breast cancer cell lines and found that 85 percent of gene-expression variations were caused by genotypic effects and genotype-ANAX1 overexpression interactions, which agrees well with our expected results. We also applied our methods to the adenoma dataset of Notterman et al. and identified 93 differentially expressed genes that could not be found in TCE. The MCE approach is a conceptual breakthrough in many aspects: (a) many conditions of interests can be conducted simultaneously; (b) study of association between differential expressions of genes and conditions becomes easy; (c) it can provide more precise information for molecular classification and diagnosis of tumors; (d) it can save lot of experimental resources and time for investigators.^

Quantitative comparison of late effects following photon versus proton external-beam radiation therapies: Toward an evidence-based approach to selecting a treatment modality

Radiation therapy has been used as an effective treatment for malignancies in pediatric patients. However, in many cases, the side effects of radiation diminish these patients’ quality of life. In order to develop strategies to minimize radiogenic complications, one must first quantitatively estimate pediatric patients’ relative risk for radiogenic late effects, which has not become feasible till recently because of the calculational complexity. The goals of this work were to calculate the dose delivered to tissues and organs in pediatric patients during contemporary photon and proton radiotherapies; to estimate the corresponding risk of radiogenic second cancer and cardiac toxicity based on the calculated doses and on dose-risk models from the literature; to test for the statistical significance of the difference between predicted risks after photon versus proton radiotherapies; and to provide a prototype of an evidence-based approach to selecting treatment modalities for pediatric patients, taking second cancer and cardiac toxicity into account. The results showed that proton therapy confers a lower predicted risk of radiogenic second cancer, and lower risks of radiogenic cardiac toxicities, compared to photon therapy. An uncertainty analysis revealed that the qualitative findings of this study are insensitive to changes in a wide variety of host and treatment related factors.

Distribution of quality adjusted life expectancy: A systems approach

Statistical methods are developed which assess survival data for two attributes; (1) prolongation of life, (2) quality of life. Health state transition probabilities correspond to prolongation of life and are modeled as a discrete-time semi-Markov process. Imbedded within the sojourn time of a particular health state are the quality of life transitions. They reflect events which differentiate perceptions of pain and suffering over a fixed time period. Quality of life transition probabilities are derived from the assumptions of a simple Markov process. These probabilities depend on the health state currently occupied and the next health state to which a transition is made. Utilizing the two forms of attributes the model has the capability to estimate the distribution of expected quality adjusted life years (in addition to the distribution of expected survival times). The expected quality of life can also be estimated within the health state sojourn time making more flexible the assessment of utility preferences. The methods are demonstrated on a subset of follow-up data from the Beta Blocker Heart Attack Trial (BHAT). This model contains the structure necessary to make inferences when assessing a general survival problem with a two dimensional outcome. ^

The application of principal component analysis on human development indicators: Temporal approach from 1999 to 2010

Background and Objective. Ever since the human development index was published in 1990 by the United Nations Development Programme (UNDP), many researchers started searching and corporative studying for more effective methods to measure the human development. Published in 1999, Lai’s “Temporal analysis of human development indicators: principal component approach” provided a valuable statistical way on human developmental analysis. This study presented in the thesis is the extension of Lai’s 1999 research. ^ Methods. I used the weighted principal component method on the human development indicators to measure and analyze the progress of human development in about 180 countries around the world from the year 1999 to 2010. The association of the main principal component obtained from the study and the human development index reported by the UNDP was estimated by the Spearman’s rank correlation coefficient. The main principal component was then further applied to quantify the temporal changes of the human development of selected countries by the proposed Z-test. ^ Results. The weighted means of all three human development indicators, health, knowledge, and standard of living, were increased from 1999 to 2010. The weighted standard deviation for GDP per capita was also increased across years indicated the rising inequality of standard of living among countries. The ranking of low development countries by the main principal component (MPC) is very similar to that by the human development index (HDI). Considerable discrepancy between MPC and HDI ranking was found among high development countries with high GDP per capita shifted to higher ranks. The Spearman’s rank correlation coefficient between the main principal component and the human development index were all around 0.99. All the above results were very close to outcomes in Lai’s 1999 report. The Z test result on temporal analysis of main principal components from 1999 to 2010 on Qatar was statistically significant, but not on other selected countries, such as Brazil, Russia, India, China, and U.S.A.^ Conclusion. To synthesize the multi-dimensional measurement of human development into a single index, the weighted principal component method provides a good model by using the statistical tool on a comprehensive ranking and measurement. Since the weighted main principle component index is more objective because of using population of nations as weight, more effective when the analysis is across time and space, and more flexible when the countries reported to the system has been changed year after year. Thus, in conclusion, the index generated by using weighted main principle component has some advantage over the human development index created in UNDP reports.^

Statistical issues on studies of mixed longitudinal design

Mixed longitudinal designs are important study designs for many areas of medical research. Mixed longitudinal studies have several advantages over cross-sectional or pure longitudinal studies, including shorter study completion time and ability to separate time and age effects, thus are an attractive choice. Statistical methodology used in general longitudinal studies has been rapidly developing within the last few decades. Common approaches for statistical modeling in studies with mixed longitudinal designs have been the linear mixed-effects model incorporating an age or time effect. The general linear mixed-effects model is considered an appropriate choice to analyze repeated measurements data in longitudinal studies. However, common use of linear mixed-effects model on mixed longitudinal studies often incorporates age as the only random-effect but fails to take into consideration the cohort effect in conducting statistical inferences on age-related trajectories of outcome measurements. We believe special attention should be paid to cohort effects when analyzing data in mixed longitudinal designs with multiple overlapping cohorts. Thus, this has become an important statistical issue to address. ^ This research aims to address statistical issues related to mixed longitudinal studies. The proposed study examined the existing statistical analysis methods for the mixed longitudinal designs and developed an alternative analytic method to incorporate effects from multiple overlapping cohorts as well as from different aged subjects. The proposed study used simulation to evaluate the performance of the proposed analytic method by comparing it with the commonly-used model. Finally, the study applied the proposed analytic method to the data collected by an existing study Project HeartBeat!, which had been evaluated using traditional analytic techniques. Project HeartBeat! is a longitudinal study of cardiovascular disease (CVD) risk factors in childhood and adolescence using a mixed longitudinal design. The proposed model was used to evaluate four blood lipids adjusting for age, gender, race/ethnicity, and endocrine hormones. The result of this dissertation suggest the proposed analytic model could be a more flexible and reliable choice than the traditional model in terms of fitting data to provide more accurate estimates in mixed longitudinal studies. Conceptually, the proposed model described in this study has useful features, including consideration of effects from multiple overlapping cohorts, and is an attractive approach for analyzing data in mixed longitudinal design studies.^

Exploration of genetic susceptibility to pancreatic cancer: A GWAS approach

Pancreatic cancer is the 4th most common cause for cancer death in the United States, accompanied by less than 5% five-year survival rate based on current treatments, particularly because it is usually detected at a late stage. Identifying a high-risk population to launch an effective preventive strategy and intervention to control this highly lethal disease is desperately needed. The genetic etiology of pancreatic cancer has not been well profiled. We hypothesized that unidentified genetic variants by previous genome-wide association study (GWAS) for pancreatic cancer, due to stringent statistical threshold or missing interaction analysis, may be unveiled using alternative approaches. To achieve this aim, we explored genetic susceptibility to pancreatic cancer in terms of marginal associations of pathway and genes, as well as their interactions with risk factors. We conducted pathway- and gene-based analysis using GWAS data from 3141 pancreatic cancer patients and 3367 controls with European ancestry. Using the gene set ridge regression in association studies (GRASS) method, we analyzed 197 pathways from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database. Using the logistic kernel machine (LKM) test, we analyzed 17906 genes defined by University of California Santa Cruz (UCSC) database. Using the likelihood ratio test (LRT) in a logistic regression model, we analyzed 177 pathways and 17906 genes for interactions with risk factors in 2028 pancreatic cancer patients and 2109 controls with European ancestry. After adjusting for multiple comparisons, six pathways were marginally associated with risk of pancreatic cancer ( P < 0.00025): Fc epsilon RI signaling, maturity onset diabetes of the young, neuroactive ligand-receptor interaction, long-term depression (Ps < 0.0002), and the olfactory transduction and vascular smooth muscle contraction pathways (P = 0.0002; Nine genes were marginally associated with pancreatic cancer risk (P < 2.62 × 10−5), including five reported genes (ABO, HNF1A, CLPTM1L, SHH and MYC), as well as four novel genes (OR13C4, OR 13C3, KCNA6 and HNF4 G); three pathways significantly interacted with risk factors on modifying the risk of pancreatic cancer (P < 2.82 × 10−4): chemokine signaling pathway with obesity ( P < 1.43 × 10−4), calcium signaling pathway (P < 2.27 × 10−4) and MAPK signaling pathway with diabetes (P < 2.77 × 10−4). However, none of the 17906 genes tested for interactions survived the multiple comparisons corrections. In summary, our current GWAS study unveiled unidentified genetic susceptibility to pancreatic cancer using alternative methods. These novel findings provide new perspectives on genetic susceptibility to and molecular mechanisms of pancreatic cancer, once confirmed, will shed promising light on the prevention and treatment of this disease. ^

BAYESIAN STATISTICAL METHODS IN GENE-ENVIRONMENT AND GENE-GENE INTERACTION STUDIES

Complex diseases such as cancer result from multiple genetic changes and environmental exposures. Due to the rapid development of genotyping and sequencing technologies, we are now able to more accurately assess causal effects of many genetic and environmental factors. Genome-wide association studies have been able to localize many causal genetic variants predisposing to certain diseases. However, these studies only explain a small portion of variations in the heritability of diseases. More advanced statistical models are urgently needed to identify and characterize some additional genetic and environmental factors and their interactions, which will enable us to better understand the causes of complex diseases. In the past decade, thanks to the increasing computational capabilities and novel statistical developments, Bayesian methods have been widely applied in the genetics/genomics researches and demonstrating superiority over some regular approaches in certain research areas. Gene-environment and gene-gene interaction studies are among the areas where Bayesian methods may fully exert its functionalities and advantages. This dissertation focuses on developing new Bayesian statistical methods for data analysis with complex gene-environment and gene-gene interactions, as well as extending some existing methods for gene-environment interactions to other related areas. It includes three sections: (1) Deriving the Bayesian variable selection framework for the hierarchical gene-environment and gene-gene interactions; (2) Developing the Bayesian Natural and Orthogonal Interaction (NOIA) models for gene-environment interactions; and (3) extending the applications of two Bayesian statistical methods which were developed for gene-environment interaction studies, to other related types of studies such as adaptive borrowing historical data. We propose a Bayesian hierarchical mixture model framework that allows us to investigate the genetic and environmental effects, gene by gene interactions (epistasis) and gene by environment interactions in the same model. It is well known that, in many practical situations, there exists a natural hierarchical structure between the main effects and interactions in the linear model. Here we propose a model that incorporates this hierarchical structure into the Bayesian mixture model, such that the irrelevant interaction effects can be removed more efficiently, resulting in more robust, parsimonious and powerful models. We evaluate both of the 'strong hierarchical' and 'weak hierarchical' models, which specify that both or one of the main effects between interacting factors must be present for the interactions to be included in the model. The extensive simulation results show that the proposed strong and weak hierarchical mixture models control the proportion of false positive discoveries and yield a powerful approach to identify the predisposing main effects and interactions in the studies with complex gene-environment and gene-gene interactions. We also compare these two models with the 'independent' model that does not impose this hierarchical constraint and observe their superior performances in most of the considered situations. The proposed models are implemented in the real data analysis of gene and environment interactions in the cases of lung cancer and cutaneous melanoma case-control studies. The Bayesian statistical models enjoy the properties of being allowed to incorporate useful prior information in the modeling process. Moreover, the Bayesian mixture model outperforms the multivariate logistic model in terms of the performances on the parameter estimation and variable selection in most cases. Our proposed models hold the hierarchical constraints, that further improve the Bayesian mixture model by reducing the proportion of false positive findings among the identified interactions and successfully identifying the reported associations. This is practically appealing for the study of investigating the causal factors from a moderate number of candidate genetic and environmental factors along with a relatively large number of interactions. The natural and orthogonal interaction (NOIA) models of genetic effects have previously been developed to provide an analysis framework, by which the estimates of effects for a quantitative trait are statistically orthogonal regardless of the existence of Hardy-Weinberg Equilibrium (HWE) within loci. Ma et al. (2012) recently developed a NOIA model for the gene-environment interaction studies and have shown the advantages of using the model for detecting the true main effects and interactions, compared with the usual functional model. In this project, we propose a novel Bayesian statistical model that combines the Bayesian hierarchical mixture model with the NOIA statistical model and the usual functional model. The proposed Bayesian NOIA model demonstrates more power at detecting the non-null effects with higher marginal posterior probabilities. Also, we review two Bayesian statistical models (Bayesian empirical shrinkage-type estimator and Bayesian model averaging), which were developed for the gene-environment interaction studies. Inspired by these Bayesian models, we develop two novel statistical methods that are able to handle the related problems such as borrowing data from historical studies. The proposed methods are analogous to the methods for the gene-environment interactions on behalf of the success on balancing the statistical efficiency and bias in a unified model. By extensive simulation studies, we compare the operating characteristics of the proposed models with the existing models including the hierarchical meta-analysis model. The results show that the proposed approaches adaptively borrow the historical data in a data-driven way. These novel models may have a broad range of statistical applications in both of genetic/genomic and clinical studies.

Vision-based vehicle detection and tracking with a mobile camera using a statistical framework

En esta tesis se aborda la detección y el seguimiento automático de vehículos mediante técnicas de visión artificial con una cámara monocular embarcada. Este problema ha suscitado un gran interés por parte de la industria automovilística y de la comunidad científica ya que supone el primer paso en aras de la ayuda a la conducción, la prevención de accidentes y, en última instancia, la conducción automática. A pesar de que se le ha dedicado mucho esfuerzo en los últimos años, de momento no se ha encontrado ninguna solución completamente satisfactoria y por lo tanto continúa siendo un tema de investigación abierto. Los principales problemas que plantean la detección y seguimiento mediante visión artificial son la gran variabilidad entre vehículos, un fondo que cambia dinámicamente debido al movimiento de la cámara, y la necesidad de operar en tiempo real. En este contexto, esta tesis propone un marco unificado para la detección y seguimiento de vehículos que afronta los problemas descritos mediante un enfoque estadístico. El marco se compone de tres grandes bloques, i.e., generación de hipótesis, verificación de hipótesis, y seguimiento de vehículos, que se llevan a cabo de manera secuencial. No obstante, se potencia el intercambio de información entre los diferentes bloques con objeto de obtener el máximo grado posible de adaptación a cambios en el entorno y de reducir el coste computacional. Para abordar la primera tarea de generación de hipótesis, se proponen dos métodos complementarios basados respectivamente en el análisis de la apariencia y la geometría de la escena. Para ello resulta especialmente interesante el uso de un dominio transformado en el que se elimina la perspectiva de la imagen original, puesto que este dominio permite una búsqueda rápida dentro de la imagen y por tanto una generación eficiente de hipótesis de localización de los vehículos. Los candidatos finales se obtienen por medio de un marco colaborativo entre el dominio original y el dominio transformado. Para la verificación de hipótesis se adopta un método de aprendizaje supervisado. Así, se evalúan algunos de los métodos de extracción de características más populares y se proponen nuevos descriptores con arreglo al conocimiento de la apariencia de los vehículos. Para evaluar la efectividad en la tarea de clasificación de estos descriptores, y dado que no existen bases de datos públicas que se adapten al problema descrito, se ha generado una nueva base de datos sobre la que se han realizado pruebas masivas. Finalmente, se presenta una metodología para la fusión de los diferentes clasificadores y se plantea una discusión sobre las combinaciones que ofrecen los mejores resultados. El núcleo del marco propuesto está constituido por un método Bayesiano de seguimiento basado en filtros de partículas. Se plantean contribuciones en los tres elementos fundamentales de estos filtros: el algoritmo de inferencia, el modelo dinámico y el modelo de observación. En concreto, se propone el uso de un método de muestreo basado en MCMC que evita el elevado coste computacional de los filtros de partículas tradicionales y por consiguiente permite que el modelado conjunto de múltiples vehículos sea computacionalmente viable. Por otra parte, el dominio transformado mencionado anteriormente permite la definición de un modelo dinámico de velocidad constante ya que se preserva el movimiento suave de los vehículos en autopistas. Por último, se propone un modelo de observación que integra diferentes características. En particular, además de la apariencia de los vehículos, el modelo tiene en cuenta también toda la información recibida de los bloques de procesamiento previos. El método propuesto se ejecuta en tiempo real en un ordenador de propósito general y da unos resultados sobresalientes en comparación con los métodos tradicionales. ABSTRACT This thesis addresses on-road vehicle detection and tracking with a monocular vision system. This problem has attracted the attention of the automotive industry and the research community as it is the first step for driver assistance and collision avoidance systems and for eventual autonomous driving. Although many effort has been devoted to address it in recent years, no satisfactory solution has yet been devised and thus it is an active research issue. The main challenges for vision-based vehicle detection and tracking are the high variability among vehicles, the dynamically changing background due to camera motion and the real-time processing requirement. In this thesis, a unified approach using statistical methods is presented for vehicle detection and tracking that tackles these issues. The approach is divided into three primary tasks, i.e., vehicle hypothesis generation, hypothesis verification, and vehicle tracking, which are performed sequentially. Nevertheless, the exchange of information between processing blocks is fostered so that the maximum degree of adaptation to changes in the environment can be achieved and the computational cost is alleviated. Two complementary strategies are proposed to address the first task, i.e., hypothesis generation, based respectively on appearance and geometry analysis. To this end, the use of a rectified domain in which the perspective is removed from the original image is especially interesting, as it allows for fast image scanning and coarse hypothesis generation. The final vehicle candidates are produced using a collaborative framework between the original and the rectified domains. A supervised classification strategy is adopted for the verification of the hypothesized vehicle locations. In particular, state-of-the-art methods for feature extraction are evaluated and new descriptors are proposed by exploiting the knowledge on vehicle appearance. Due to the lack of appropriate public databases, a new database is generated and the classification performance of the descriptors is extensively tested on it. Finally, a methodology for the fusion of the different classifiers is presented and the best combinations are discussed. The core of the proposed approach is a Bayesian tracking framework using particle filters. Contributions are made on its three key elements: the inference algorithm, the dynamic model and the observation model. In particular, the use of a Markov chain Monte Carlo method is proposed for sampling, which circumvents the exponential complexity increase of traditional particle filters thus making joint multiple vehicle tracking affordable. On the other hand, the aforementioned rectified domain allows for the definition of a constant-velocity dynamic model since it preserves the smooth motion of vehicles in highways. Finally, a multiple-cue observation model is proposed that not only accounts for vehicle appearance but also integrates the available information from the analysis in the previous blocks. The proposed approach is proven to run near real-time in a general purpose PC and to deliver outstanding results compared to traditional methods.

Combining statistical and semantic approaches to the translation of ontologies and taxonomies

Ontologies and taxonomies are widely used to organize concepts providing the basis for activities such as indexing, and as background knowledge for NLP tasks. As such, translation of these resources would prove useful to adapt these systems to new languages. However, we show that the nature of these resources is significantly different from the "free-text" paradigm used to train most statistical machine translation systems. In particular, we see significant differences in the linguistic nature of these resources and such resources have rich additional semantics. We demonstrate that as a result of these linguistic differences, standard SMT methods, in particular evaluation metrics, can produce poor performance. We then look to the task of leveraging these semantics for translation, which we approach in three ways: by adapting the translation system to the domain of the resource; by examining if semantics can help to predict the syntactic structure used in translation; and by evaluating if we can use existing translated taxonomies to disambiguate translations. We present some early results from these experiments, which shed light on the degree of success we may have with each approach

An approach to operational modal analysis using the expectation maximization algorithm

This paper presents the Expectation Maximization algorithm (EM) applied to operational modal analysis of structures. The EM algorithm is a general-purpose method for maximum likelihood estimation (MLE) that in this work is used to estimate state space models. As it is well known, the MLE enjoys some optimal properties from a statistical point of view, which make it very attractive in practice. However, the EM algorithm has two main drawbacks: its slow convergence and the dependence of the solution on the initial values used. This paper proposes two different strategies to choose initial values for the EM algorithm when used for operational modal analysis: to begin with the parameters estimated by Stochastic Subspace Identification method (SSI) and to start using random points. The effectiveness of the proposed identification method has been evaluated through numerical simulation and measured vibration data in the context of a benchmark problem. Modal parameters (natural frequencies, damping ratios and mode shapes) of the benchmark structure have been estimated using SSI and the EM algorithm. On the whole, the results show that the application of the EM algorithm starting from the solution given by SSI is very useful to identify the vibration modes of a structure, discarding the spurious modes that appear in high order models and discovering other hidden modes. Similar results are obtained using random starting values, although this strategy allows us to analyze the solution of several starting points what overcome the dependence on the initial values used.

Looking for a more comprehensive approach

The necessity/convenience for improving accuracy in determining the flood frequency is widely accepted further than among hydrologists, and is increasingly deepened in relationship with the statement of different thresholds related to the respective management systems. And both Scientific and Management Communities fully accept the necessity of living with determined levels of flood risk. Most of the approaches for “Advancing Methods” improving concentrate on the statistical ways, even since Climate in fact is not a Stationary process. The question is here reflected since the SMARTeST research and final highlights, policy and recommendations. The paper looks at a better agreement between Hydrology and the whole Climate as the result of the Global Thermal Machine and takes mainly into account a historical approach, trying to show the necessity of a wider collection and analysis of climate data for statistical approaches.

Statistical models for short-term wind power ramp forecasting

La predicción de energía eólica ha desempeñado en la última década un papel fundamental en el aprovechamiento de este recurso renovable, ya que permite reducir el impacto que tiene la naturaleza fluctuante del viento en la actividad de diversos agentes implicados en su integración, tales como el operador del sistema o los agentes del mercado eléctrico. Los altos niveles de penetración eólica alcanzados recientemente por algunos países han puesto de manifiesto la necesidad de mejorar las predicciones durante eventos en los que se experimenta una variación importante de la potencia generada por un parque o un conjunto de ellos en un tiempo relativamente corto (del orden de unas pocas horas). Estos eventos, conocidos como rampas, no tienen una única causa, ya que pueden estar motivados por procesos meteorológicos que se dan en muy diferentes escalas espacio-temporales, desde el paso de grandes frentes en la macroescala a procesos convectivos locales como tormentas. Además, el propio proceso de conversión del viento en energía eléctrica juega un papel relevante en la ocurrencia de rampas debido, entre otros factores, a la relación no lineal que impone la curva de potencia del aerogenerador, la desalineación de la máquina con respecto al viento y la interacción aerodinámica entre aerogeneradores. En este trabajo se aborda la aplicación de modelos estadísticos a la predicción de rampas a muy corto plazo. Además, se investiga la relación de este tipo de eventos con procesos atmosféricos en la macroescala. Los modelos se emplean para generar predicciones de punto a partir del modelado estocástico de una serie temporal de potencia generada por un parque eólico. Los horizontes de predicción considerados van de una a seis horas. Como primer paso, se ha elaborado una metodología para caracterizar rampas en series temporales. La denominada función-rampa está basada en la transformada wavelet y proporciona un índice en cada paso temporal. Este índice caracteriza la intensidad de rampa en base a los gradientes de potencia experimentados en un rango determinado de escalas temporales. Se han implementado tres tipos de modelos predictivos de cara a evaluar el papel que juega la complejidad de un modelo en su desempeño: modelos lineales autorregresivos (AR), modelos de coeficientes variables (VCMs) y modelos basado en redes neuronales (ANNs). Los modelos se han entrenado en base a la minimización del error cuadrático medio y la configuración de cada uno de ellos se ha determinado mediante validación cruzada. De cara a analizar la contribución del estado macroescalar de la atmósfera en la predicción de rampas, se ha propuesto una metodología que permite extraer, a partir de las salidas de modelos meteorológicos, información relevante para explicar la ocurrencia de estos eventos. La metodología se basa en el análisis de componentes principales (PCA) para la síntesis de la datos de la atmósfera y en el uso de la información mutua (MI) para estimar la dependencia no lineal entre dos señales. Esta metodología se ha aplicado a datos de reanálisis generados con un modelo de circulación general (GCM) de cara a generar variables exógenas que posteriormente se han introducido en los modelos predictivos. Los casos de estudio considerados corresponden a dos parques eólicos ubicados en España. Los resultados muestran que el modelado de la serie de potencias permitió una mejora notable con respecto al modelo predictivo de referencia (la persistencia) y que al añadir información de la macroescala se obtuvieron mejoras adicionales del mismo orden. Estas mejoras resultaron mayores para el caso de rampas de bajada. Los resultados también indican distintos grados de conexión entre la macroescala y la ocurrencia de rampas en los dos parques considerados. Abstract One of the main drawbacks of wind energy is that it exhibits intermittent generation greatly depending on environmental conditions. Wind power forecasting has proven to be an effective tool for facilitating wind power integration from both the technical and the economical perspective. Indeed, system operators and energy traders benefit from the use of forecasting techniques, because the reduction of the inherent uncertainty of wind power allows them the adoption of optimal decisions. Wind power integration imposes new challenges as higher wind penetration levels are attained. Wind power ramp forecasting is an example of such a recent topic of interest. The term ramp makes reference to a large and rapid variation (1-4 hours) observed in the wind power output of a wind farm or portfolio. Ramp events can be motivated by a broad number of meteorological processes that occur at different time/spatial scales, from the passage of large-scale frontal systems to local processes such as thunderstorms and thermally-driven flows. Ramp events may also be conditioned by features related to the wind-to-power conversion process, such as yaw misalignment, the wind turbine shut-down and the aerodynamic interaction between wind turbines of a wind farm (wake effect). This work is devoted to wind power ramp forecasting, with special focus on the connection between the global scale and ramp events observed at the wind farm level. The framework of this study is the point-forecasting approach. Time series based models were implemented for very short-term prediction, this being characterised by prediction horizons up to six hours ahead. As a first step, a methodology to characterise ramps within a wind power time series was proposed. The so-called ramp function is based on the wavelet transform and it provides a continuous index related to the ramp intensity at each time step. The underlying idea is that ramps are characterised by high power output gradients evaluated under different time scales. A number of state-of-the-art time series based models were considered, namely linear autoregressive (AR) models, varying-coefficient models (VCMs) and artificial neural networks (ANNs). This allowed us to gain insights into how the complexity of the model contributes to the accuracy of the wind power time series modelling. The models were trained in base of a mean squared error criterion and the final set-up of each model was determined through cross-validation techniques. In order to investigate the contribution of the global scale into wind power ramp forecasting, a methodological proposal to identify features in atmospheric raw data that are relevant for explaining wind power ramp events was presented. The proposed methodology is based on two techniques: principal component analysis (PCA) for atmospheric data compression and mutual information (MI) for assessing non-linear dependence between variables. The methodology was applied to reanalysis data generated with a general circulation model (GCM). This allowed for the elaboration of explanatory variables meaningful for ramp forecasting that were utilized as exogenous variables by the forecasting models. The study covered two wind farms located in Spain. All the models outperformed the reference model (the persistence) during both ramp and non-ramp situations. Adding atmospheric information had a noticeable impact on the forecasting performance, specially during ramp-down events. Results also suggested different levels of connection between the ramp occurrence at the wind farm level and the global scale.

Looking for a more comprehensive approach

The necessity/convenience for improving accuracy in determining the flood frequency is widely accepted further than among hydrologists, and is increasingly deepened in relationship with the statement of different thresholds related to the respective management systems. And both Scientific and Management Communities fully accept the necessity of living with determined levels of flood risk. Most of the approaches for “Advancing Methods” improving concentrate on the statistical ways, even since Climate in fact is not a Stationary process. The question is here reflected since the SMARTeST research and final highlights, policy and recommendations. The paper looks at a better agreement between Hydrology and the whole Climate as the result of the Global Thermal Machine and takes mainly into account a historical approach, trying to show the necessity of a wider collection and analysis of climate data for statistical approaches.