A dynamical system approach to data assimilation in chaotic models

The Assimilation in the Unstable Subspace (AUS) was introduced by Trevisan and Uboldi in 2004, and developed by Trevisan, Uboldi and Carrassi, to minimize the analysis and forecast errors by exploiting the flow-dependent instabilities of the forecast-analysis cycle system, which may be thought of as a system forced by observations. In the AUS scheme the assimilation is obtained by confining the analysis increment in the unstable subspace of the forecast-analysis cycle system so that it will have the same structure of the dominant instabilities of the system. The unstable subspace is estimated by Breeding on the Data Assimilation System (BDAS). AUS- BDAS has already been tested in realistic models and observational configurations, including a Quasi-Geostrophicmodel and a high dimensional, primitive equation ocean model; the experiments include both fixed and“adaptive”observations. In these contexts, the AUS-BDAS approach greatly reduces the analysis error, with reasonable computational costs for data assimilation with respect, for example, to a prohibitive full Extended Kalman Filter. This is a follow-up study in which we revisit the AUS-BDAS approach in the more basic, highly nonlinear Lorenz 1963 convective model. We run observation system simulation experiments in a perfect model setting, and with two types of model error as well: random and systematic. In the different configurations examined, and in a perfect model setting, AUS once again shows better efficiency than other advanced data assimilation schemes. In the present study, we develop an iterative scheme that leads to a significant improvement of the overall assimilation performance with respect also to standard AUS. In particular, it boosts the efficiency of regime’s changes tracking, with a low computational cost. Other data assimilation schemes need estimates of ad hoc parameters, which have to be tuned for the specific model at hand. In Numerical Weather Prediction models, tuning of parameters — and in particular an estimate of the model error covariance matrix — may turn out to be quite difficult. Our proposed approach, instead, may be easier to implement in operational models.

Cholesky Residuals for Assessing Normal Errors in a Linear Model with Correlated Outcomes: Technical Report

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed models and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated margional residual vector by the Cholesky decomposition of the inverse of the estimated margional variance matrix. The resulting "rotated" residuals are used to construct an empirical cumulative distribution function and pointwise standard errors. The theoretical framework, including conditions and asymptotic properties, involves technical details that are motivated by Lange and Ryan (1989), Pierce (1982), and Randles (1982). Our method appears to work well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series). Our methods can produce satisfactory results even for models that do not satisfy all of the technical conditions stated in our theory.

Underestimation of Standard Errors in Multi-Site Time Series Studies

Multi-site time series studies of air pollution and mortality and morbidity have figured prominently in the literature as comprehensive approaches for estimating acute effects of air pollution on health. Hierarchical models are generally used to combine site-specific information and estimate pooled air pollution effects taking into account both within-site statistical uncertainty, and across-site heterogeneity. Within a site, characteristics of time series data of air pollution and health (small pollution effects, missing data, highly correlated predictors, non linear confounding etc.) make modelling all sources of uncertainty challenging. One potential consequence is underestimation of the statistical variance of the site-specific effects to be combined. In this paper we investigate the impact of variance underestimation on the pooled relative rate estimate. We focus on two-stage normal-normal hierarchical models and on under- estimation of the statistical variance at the first stage. By mathematical considerations and simulation studies, we found that variance underestimation does not affect the pooled estimate substantially. However, some sensitivity of the pooled estimate to variance underestimation is observed when the number of sites is small and underestimation is severe. These simulation results are applicable to any two-stage normal-normal hierarchical model for combining information of site-specific results, and they can be easily extended to more general hierarchical formulations. We also examined the impact of variance underestimation on the national average relative rate estimate from the National Morbidity Mortality Air Pollution Study and we found that variance underestimation as much as 40% has little effect on the national average.

Risk factors for patient-reported medical errors in eleven countries

OBJECTIVES The aim of this study was to identify common risk factors for patient-reported medical errors across countries. In country-level analyses, differences in risks associated with error between health care systems were investigated. The joint effects of risks on error-reporting probability were modelled for hypothetical patients with different health care utilization patterns. DESIGN Data from the Commonwealth Fund's 2010 lnternational Survey of the General Public's Views of their Health Care System's Performance in 11 Countries. SETTING Representative population samples of 11 countries were surveyed (total sample = 19,738 adults). Utilization of health care, coordination of care problems and reported errors were assessed. Regression analyses were conducted to identify risk factors for patients' reports of medical, medication and laboratory errors across countries and in country-specific models. RESULTS Error was reported by 11.2% of patients but with marked differences between countries (range: 5.4-17.0%). Poor coordination of care was reported by 27.3%. The risk of patient-reported error was determined mainly by health care utilization: Emergency care (OR = 1.7, P < 0.001), hospitalization (OR = 1.6, P < 0.001) and the number of providers involved (OR three doctors = 2.0, P < 0.001) are important predictors. Poor care coordination is the single most important risk factor for reporting error (OR = 3.9, P < 0.001). Country-specific models yielded common and country-specific predictors for self-reported error. For high utilizers of care, the probability that errors are reported rises up to P = 0.68. CONCLUSIONS Safety remains a global challenge affecting many patients throughout the world. Large variability exists in the frequency of patient-reported error across countries. To learn from others' errors is not only essential within countries but may also prove a promising strategy internationally.

Effect sizes and standardization in neighbourhood models of forest stands: potential biases and misinterpretations

Effects of conspecific neighbours on survival and growth of trees have been found to be related to species abundance. Both positive and negative relationships may explain observed abundance patterns. Surprisingly, it is rarely tested whether such relationships could be biased or even spurious due to transforming neighbourhood variables or influences of spatial aggregation, distance decay of neighbour effects and standardization of effect sizes. To investigate potential biases, communities of 20 identical species were simulated with log-series abundances but without species-specific interactions. No relationship of conspecific neighbour effects on survival or growth with species abundance was expected. Survival and growth of individuals was simulated in random and aggregated spatial patterns using no, linear, or squared distance decay of neighbour effects. Regression coefficients of statistical neighbourhood models were unbiased and unrelated to species abundance. However, variation in the number of conspecific neighbours was positively or negatively related to species abundance depending on transformations of neighbourhood variables, spatial pattern and distance decay. Consequently, effect sizes and standardized regression coefficients, often used in model fitting across large numbers of species, were also positively or negatively related to species abundance depending on transformation of neighbourhood variables, spatial pattern and distance decay. Tests using randomized tree positions and identities provide the best benchmarks by which to critically evaluate relationships of effect sizes or standardized regression coefficients with tree species abundance. This will better guard against potential misinterpretations.

Estimating parameters in Markov models for longitudinal studies with missing data or surrogate outcomes

The discrete-time Markov chain is commonly used in describing changes of health states for chronic diseases in a longitudinal study. Statistical inferences on comparing treatment effects or on finding determinants of disease progression usually require estimation of transition probabilities. In many situations when the outcome data have some missing observations or the variable of interest (called a latent variable) can not be measured directly, the estimation of transition probabilities becomes more complicated. In the latter case, a surrogate variable that is easier to access and can gauge the characteristics of the latent one is usually used for data analysis. ^ This dissertation research proposes methods to analyze longitudinal data (1) that have categorical outcome with missing observations or (2) that use complete or incomplete surrogate observations to analyze the categorical latent outcome. For (1), different missing mechanisms were considered for empirical studies using methods that include EM algorithm, Monte Carlo EM and a procedure that is not a data augmentation method. For (2), the hidden Markov model with the forward-backward procedure was applied for parameter estimation. This method was also extended to cover the computation of standard errors. The proposed methods were demonstrated by the Schizophrenia example. The relevance of public health, the strength and limitations, and possible future research were also discussed. ^

Interactions between roughness and topography in hydraulic models

Analysis of river flow using hydraulic modelling and its implications in derived environ-mental applications are inextricably connected with the way in which the river boundary shape is represented. This relationship is scale-dependent upon the modelling resolution which in turn determines the importance of a subscale performance of the model and the way subscale (surface and flow) processes are parameterised. Commonly, the subscale behaviour of the model relies upon a roughness parameterisation whose meaning depends on the dimensionality of the hydraulic model and the resolution of the topographic represen¬tation scale. This latter is, in turn, dependent on the resolution of the computational mesh as well as on the detail of measured topographic data. Flow results are affected by this interactions between scale and subscale parameterisation according to the dimensionality approach. The aim of this dissertation is the evaluation of these interactions upon hy¬draulic modelling results. Current high resolution topographic source availability induce this research which is tackled using a suitable roughness approach according to each di¬mensionality with the purpose of the interaction assessment. A 1D HEC-RAS model, a 2D raster-based diffusion-wave model with a scale-dependent distributed roughness parame-terisation and a 3D finite volume scheme with a porosity algorithm approach to incorporate complex topography have been used. Different topographic sources are assessed using a 1D scheme. LiDAR data are used to isolate the mesh resolution from the topographic content of the DEM effects upon 2D and 3D flow results. A distributed roughness parameterisation, using a roughness height approach dependent upon both mesh resolution and topographic content is developed and evaluated for the 2D scheme. Grain-size data and fractal methods are used for the reconstruction of topography with microscale information, required for some applications but not easily available. Sensitivity of hydraulic parameters to this topographic parameterisation is evaluated in a 3D scheme at different mesh resolu¬tions. Finally, the structural variability of simulated flow is analysed and related to scale interactions. Model simulations demonstrate (i) the importance of the topographic source in a 1D models; (ii) the mesh resolution approach is dominant in 2D and 3D simulations whereas in a 1D model the topographic source and even the roughness parameterisation impacts are more critical; (iii) the increment of the sensitivity to roughness parameterisa-tion in 1D and 2D schemes with detailed topographic sources and finer mesh resolutions; and (iv) the topographic content and microtopography impact throughout the vertical profile of computed 3D velocity in a depth-dependent way, whereas 2D results are not affected by topographic content variations. Finally, the spatial analysis shows that the mesh resolution controls high resolution model scale results, roughness parameterisation control 2D simulation results for a constant mesh resolution; and topographic content and micro-topography variations impacts upon the organisation of flow results depth-dependently in a 3D scheme. Resumen La topografía juega un papel fundamental en la distribución del agua y la energía en los paisajes naturales (Beven and Kirkby 1979; Wood et al. 1997). La simulación hidráulica combinada con métodos de medición del terreno por teledetección constituyen una poderosa herramienta de investigación en la comprensión del comportamiento de los flujos de agua debido a la variabilidad de la superficie sobre la que fluye. La representación e incorporación de la topografía en el esquema hidráulico tiene una importancia crucial en los resultados y determinan el desarrollo de sus aplicaciones al campo medioambiental. Cualquier simulación es una simplificación de un proceso del mundo real, y por tanto el grado de simplificación determinará el significado de los resultados simulados. Este razonamiento es particularmente difícil de trasladar a la simulación hidráulica donde aspectos de la escala tan diferentes como la escala de los procesos de flujo y de representación del contorno son considerados conjuntamente incluso en fases de parametrización (e.g. parametrización de la rugosidad). Por una parte, esto es debido a que las decisiones de escala vienen condicionadas entre ellas (e.g. la dimensionalidad del modelo condiciona la escala de representación del contorno) y por tanto interaccionan en sus resultados estrechamente. Y por otra parte, debido a los altos requerimientos numéricos y computacionales de una representación explícita de alta resolución de los procesos de flujo y discretización de la malla. Además, previo a la modelización hidráulica, la superficie del terreno sobre la que el agua fluye debe ser modelizada y por tanto presenta su propia escala de representación, que a su vez dependerá de la escala de los datos topográficos medidos con que se elabora el modelo. En última instancia, esta topografía es la que determina el comportamiento espacial del flujo. Por tanto, la escala de la topografía en sus fases de medición y modelización (resolución de los datos y representación topográfica) previas a su incorporación en el modelo hidráulico producirá a su vez un impacto que se acumulará al impacto global resultante debido a la escala computacional del modelo hidráulico y su dimensión. La comprensión de las interacciones entre las complejas geometrías del contorno y la estructura del flujo utilizando la modelización hidráulica depende de las escalas consideradas en la simplificación de los procesos hidráulicos y del terreno (dimensión del modelo, tamaño de escala computacional y escala de los datos topográficos). La naturaleza de la aplicación del modelo hidráulico (e.g. habitat físico, análisis de riesgo de inundaciones, transporte de sedimentos) determina en primer lugar la escala del estudio y por tanto el detalle de los procesos a simular en el modelo (i.e. la dimensionalidad) y, en consecuencia, la escala computacional a la que se realizarán los cálculos (i.e. resolución computacional). Esta última a su vez determina, el detalle geográfico con que deberá representarse el contorno acorde con la resolución de la malla computacional. La parametrización persigue incorporar en el modelo hidráulico la cuantificación de los procesos y condiciones físicas del sistema natural y por tanto debe incluir no solo aquellos procesos que tienen lugar a la escala de modelización, sino también aquellos que tienen lugar a un nivel subescalar y que deben ser definidos mediante relaciones de escalado con las variables modeladas explícitamente. Dicha parametrización se implementa en la práctica mediante la provisión de datos al modelo, por tanto la escala de los datos geográficos utilizados para parametrizar el modelo no sólo influirá en los resultados, sino también determinará la importancia del comportamiento subescalar del modelo y el modo en que estos procesos deban ser parametrizados (e.g. la variabilidad natural del terreno dentro de la celda de discretización o el flujo en las direcciones laterales y verticales en un modelo unidimensional). En esta tesis, se han utilizado el modelo unidimensional HEC-RAS, (HEC 1998b), un modelo ráster bidimensional de propagación de onda, (Yu 2005) y un esquema tridimensional de volúmenes finitos con un algoritmo de porosidad para incorporar la topografía, (Lane et al. 2004; Hardy et al. 2005). La geometría del contorno viene definida por la escala de representación topográfica (resolución de malla y contenido topográfico), la cual a su vez depende de la escala de la fuente cartográfica. Todos estos factores de escala interaccionan en la respuesta del modelo hidráulico a la topografía. En los últimos años, métodos como el análisis fractal y las técnicas geoestadísticas utilizadas para representar y analizar elementos geográficos (e.g. en la caracterización de superficies (Herzfeld and Overbeck 1999; Butler et al. 2001)), están promoviendo nuevos enfoques en la cuantificación de los efectos de escala (Lam et al. 2004; Atkinson and Tate 2000; Lam et al. 2006) por medio del análisis de la estructura espacial de la variable (e.g. Bishop et al. 2006; Ju et al. 2005; Myint et al. 2004; Weng 2002; Bian and Xie 2004; Southworth et al. 2006; Pozd-nyakova et al. 2005; Kyriakidis and Goodchild 2006). Estos métodos cuantifican tanto el rango de valores de la variable presentes a diferentes escalas como la homogeneidad o heterogeneidad de la variable espacialmente distribuida (Lam et al. 2004). En esta tesis, estas técnicas se han utilizado para analizar el impacto de la topografía sobre la estructura de los resultados hidráulicos simulados. Los datos de teledetección de alta resolución y técnicas GIS también están siendo utilizados para la mejor compresión de los efectos de escala en modelos medioambientales (Marceau 1999; Skidmore 2002; Goodchild 2003) y se utilizan en esta tesis. Esta tesis como corpus de investigación aborda las interacciones de esas escalas en la modelización hidráulica desde un punto de vista global e interrelacionado. Sin embargo, la estructura y el foco principal de los experimentos están relacionados con las nociones espaciales de la escala de representación en relación con una visión global de las interacciones entre escalas. En teoría, la representación topográfica debe caracterizar la superficie sobre la que corre el agua a una adecuada (conforme a la finalidad y dimensión del modelo) escala de discretización, de modo que refleje los procesos de interés. La parametrización de la rugosidad debe de reflejar los efectos de la variabilidad de la superficie a escalas de más detalle que aquellas representadas explícitamente en la malla topográfica (i.e. escala de discretización). Claramente, ambos conceptos están físicamente relacionados por un

Factors predictive of intravenous fluid administration errors in Australian surgical care wards

Background: Intravenous (IV) fluid administration is an integral component of clinical care. Errors in administration can cause detrimental patient outcomes and increase healthcare costs, although little is known about medication administration errors associated with continuous IV infusions. Objectives: ( 1) To ascertain the prevalence of medication administration errors for continuous IV infusions and identify the variables that caused them. ( 2) To quantify the probability of errors by fitting a logistic regression model to the data. Methods: A prospective study was conducted on three surgical wards at a teaching hospital in Australia. All study participants received continuous infusions of IV fluids. Parenteral nutrition and non-electrolyte containing intermittent drug infusions ( such as antibiotics) were excluded. Medication administration errors and contributing variables were documented using a direct observational approach. Results: Six hundred and eighty seven observations were made, with 124 (18.0%) having at least one medication administration error. The most common error observed was wrong administration rate. The median deviation from the prescribed rate was 247 ml/h (interquartile range 275 to + 33.8 ml/ h). Errors were more likely to occur if an IV infusion control device was not used and as the duration of the infusion increased. Conclusions: Administration errors involving continuous IV infusions occur frequently. They could be reduced by more common use of IV infusion control devices and regular checking of administration rates.

Effects of syllabic complexity in predicting accuracy of repetition and direction of errors in patients with articulatory and phonological difficulties

The purpose of this paper is to demonstrate the existence of a strong and significant effect of complexity in aphasia independent from other variables including length. Complexity was found to be a strong and significant predictor of accurate repetition in a group of 13 Italian aphasic patients when it was entered in a regression equation either simultaneously or after a large number of other variables. Significant effects were found both when complexity was measured in terms of number of complex onsets (as in a recent paper by Nickels & Howard, 2004) and when it was measured in a more comprehensive way. Significant complexity effects were also found with matched lists contrasting simple and complex words and in analyses of errors. Effects of complexity, however, were restricted to patients with articulatory difficulties. Reasons for this association and for the lack of significant results in Nickels and Howard (2004) are discussed. © 2005 Psychology Press Ltd.

Multiresponse Robust Engineering: Case with Errors in Factor Levels

2000 Mathematics Subject Classification: 62J05, 62J10, 62F35, 62H12, 62P30.

Chebanov law and Vakar formula in mathematical models of complex systems

Ecological models written in a mathematical language L(M) or model language, with a given style or methodology can be considered as a text. It is possible to apply statistical linguistic laws and the experimental results demonstrate that the behaviour of a mathematical model is the same of any literary text of any natural language. A text has the following characteristics: (a) the variables, its transformed functions and parameters are the lexic units or LUN of ecological models; (b) the syllables are constituted by a LUN, or a chain of them, separated by operating or ordering LUNs; (c) the flow equations are words; and (d) the distribution of words (LUM and CLUN) according to their lengths is based on a Poisson distribution, the Chebanov's law. It is founded on Vakar's formula, that is calculated likewise the linguistic entropy for L(M). We will apply these ideas over practical examples using MARIOLA model. In this paper it will be studied the problem of the lengths of the simple lexic units composed lexic units and words of text models, expressing these lengths in number of the primitive symbols, and syllables. The use of these linguistic laws renders it possible to indicate the degree of information given by an ecological model.

A retrospective study examining the nature, contributory factors and predictors of dispensing errors in community pharmacy

Introduction: Since 2005, the workload of community pharmacists in England has increased with a concomitant increase in stress and work pressure. However, it is unclear how these factors are impacting on the ability of community pharmacists to ensure accuracy during the dispensing process. This research seeks to extend our understanding of the nature, outcome, and predictors of dispensing errors. Methodology: A retrospective analysis of a purposive sample of incident report forms (IRFs) from the database of a pharmacist indemnity insurance provider was conducted. Data collected included; type of error, degree of harm caused, pharmacy and pharmacist demographics, and possible contributory factors. Results: In total, 339 files from UK community pharmacies were retrieved from the database. The files dated from June 2006 to November 2011. Incorrect item (45.1%, n = 153/339) followed by incorrect strength (24.5%, n = 83/339) were the most common forms of error. Almost half (41.6%, n = 147/339) of the patients suffered some form of harm ranging from minor harm (26.7%, n = 87/339) to death (0.3%, n = 1/339). Insufficient staff (51.6%, n = 175/339), similar packaging (40.7%, n = 138/339) and the pharmacy being busier than normal (39.5%, n = 134/339) were identified as key contributory factors. Cross-tabular analysis against the final accuracy check variable revealed significant association between the pharmacy location (P < 0.024), dispensary layout (P < 0.025), insufficient staff (P < 0.019), and busier than normal (P < 0.005) variables. Conclusion: The results provide an overview of some of the individual, organisational and technical factors at play at the time of a dispensing error and highlight the need to examine further the relationships between these factors and dispensing error occurrence.

Comparative study of dental arch width in plaster models, photocopies and digitized images

The aim of this study was to comparatively assess dental arch width, in the canine and molar regions, by means of direct measurements from plaster models, photocopies and digitized images of the models. The sample consisted of 130 pairs of plaster models, photocopies and digitized images of the models of white patients (n = 65), both genders, with Class I and Class II Division 1 malocclusions, treated by standard Edgewise mechanics and extraction of the four first premolars. Maxillary and mandibular intercanine and intermolar widths were measured by a calibrated examiner, prior to and after orthodontic treatment, using the three modes of reproduction of the dental arches. Dispersion of the data relative to pre- and posttreatment intra-arch linear measurements (mm) was represented as box plots. The three measuring methods were compared by one-way ANOVA for repeated measurements (α = 0.05). Initial / final mean values varied as follows: 33.94 to 34.29 mm / 34.49 to 34.66 mm (maxillary intercanine width); 26.23 to 26.26 mm / 26.77 to 26.84 mm (mandibular intercanine width); 49.55 to 49.66 mm / 47.28 to 47.45 mm (maxillary intermolar width) and 43.28 to 43.41 mm / 40.29 to 40.46 mm (mandibular intermolar width). There were no statistically significant differences between mean dental arch widths estimated by the three studied methods, prior to and after orthodontic treatment. It may be concluded that photocopies and digitized images of the plaster models provided reliable reproductions of the dental arches for obtaining transversal intra-arch measurements.

Women's satisfaction with childbirth's experience in different models of care: a descriptive study

Com o objetivo de comparar a satisfação das mulheres com a experiência do parto em três modelos assistenciais, foi realizada pesquisa descritiva, com abordagem quantitativa, em dois hospitais públicos de São Paulo, um promovendo o modelo "Típico" e o outro com um centro de parto intra-hospitalar (modelo "CPNIH") e um peri-hospitalar (modelo "CPNPH"). A amostra foi constituída por 90 puérperas, 30 de cada modelo. A comparação entre os resultados referentes à satisfação das mulheres com o atendimento prestado pelos profissionais de saúde, com a qualidade da assistência e os motivos de satisfação e insatisfação, com a indicação ou recomendação dos serviços recebidos, com a sensação de segurança no processo e com as sugestões de melhorias, mostrou que o modelo CPHPH foi o melhor avaliado, vindo em seguida o CPNIH e por último o Típico. Conclui-se que o modelo peri-hospitalar de assistência ao parto deveria receber maior apoio do SUS, por se constituir em serviço em que as mulheres se mostram satisfeitas com a atenção recebida