A novel method for evaluating an interaction effect of correlated continuous covariates in a linear model

Interaction effect is an important scientific interest for many areas of research. Common approach for investigating the interaction effect of two continuous covariates on a response variable is through a cross-product term in multiple linear regression. In epidemiological studies, the two-way analysis of variance (ANOVA) type of method has also been utilized to examine the interaction effect by replacing the continuous covariates with their discretized levels. However, the implications of model assumptions of either approach have not been examined and the statistical validation has only focused on the general method, not specifically for the interaction effect.^ In this dissertation, we investigated the validity of both approaches based on the mathematical assumptions for non-skewed data. We showed that linear regression may not be an appropriate model when the interaction effect exists because it implies a highly skewed distribution for the response variable. We also showed that the normality and constant variance assumptions required by ANOVA are not satisfied in the model where the continuous covariates are replaced with their discretized levels. Therefore, naïve application of ANOVA method may lead to an incorrect conclusion. ^ Given the problems identified above, we proposed a novel method modifying from the traditional ANOVA approach to rigorously evaluate the interaction effect. The analytical expression of the interaction effect was derived based on the conditional distribution of the response variable given the discretized continuous covariates. A testing procedure that combines the p-values from each level of the discretized covariates was developed to test the overall significance of the interaction effect. According to the simulation study, the proposed method is more powerful then the least squares regression and the ANOVA method in detecting the interaction effect when data comes from a trivariate normal distribution. The proposed method was applied to a dataset from the National Institute of Neurological Disorders and Stroke (NINDS) tissue plasminogen activator (t-PA) stroke trial, and baseline age-by-weight interaction effect was found significant in predicting the change from baseline in NIHSS at Month-3 among patients received t-PA therapy.^

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.^

A STUDY OF INFLUENZA AND OF STATISTICAL METHODS USED TO REPORT INFLUENZA

This paper defines and compares several models for describing excess influenza pneumonia mortality in Houston. First, the methodology used by the Center for Disease Control is examined and several variations of this methodology are studied. All of the models examined emphasize the difficulty of omitting epidemic weeks.^ In an attempt to find a better method of describing expected and epidemic mortality, time series methods are examined. Grouping in four-week periods, truncating the data series to adjust epidemic periods, and seasonally-adjusting the series y(,t), by:^ (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)^ is the best method examined. This new series w(,t) is stationary and a moving average model MA(1) gives a good fit for forecasting influenza and pneumonia mortality in Houston.^ Influenza morbidity, other causes of death, sex, race, age, climate variables, environmental factors, and school absenteeism are all examined in terms of their relationship to influenza and pneumonia mortality. Both influenza morbidity and ischemic heart disease mortality show a very high relationship that remains when seasonal trends are removed from the data. However, when jointly modeling the three series it is obvious that the simple time series MA(1) model of truncated, seasonally-adjusted four-week data gives a better forecast.^

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.^

Comparison of two statistical methods for rare variant association analysis

Studies have shown that rare genetic variants have stronger effects in predisposing common diseases, and several statistical methods have been developed for association studies involving rare variants. In order to better understand how these statistical methods perform, we seek to compare two recently developed rare variant statistical methods (VT and C-alpha) on 10,000 simulated re-sequencing data sets with disease status and the corresponding 10,000 simulated null data sets. The SLC1A1 gene has been suggested to be associated with diastolic blood pressure (DBP) in previous studies. In the current study, we applied VT and C-alpha methods to the empirical re-sequencing data for the SLC1A1 gene from 300 whites and 200 blacks. We found that VT method obtains higher power and performs better than C-alpha method with the simulated data we used. The type I errors were well-controlled for both methods. In addition, both VT and C-alpha methods suggested no statistical evidence for the association between the SLC1A1 gene and DBP. Overall, our findings provided an important comparison of the two statistical methods for future reference and provided preliminary and pioneer findings on the association between the SLC1A1 gene and blood pressure.^

A hybrid method in combining treatment effects from matched and unmatched studies

In the biomedical studies, the general data structures have been the matched (paired) and unmatched designs. Recently, many researchers are interested in Meta-Analysis to obtain a better understanding from several clinical data of a medical treatment. The hybrid design, which is combined two data structures, may create the fundamental question for statistical methods and the challenges for statistical inferences. The applied methods are depending on the underlying distribution. If the outcomes are normally distributed, we would use the classic paired and two independent sample T-tests on the matched and unmatched cases. If not, we can apply Wilcoxon signed rank and rank sum test on each case. ^ To assess an overall treatment effect on a hybrid design, we can apply the inverse variance weight method used in Meta-Analysis. On the nonparametric case, we can use a test statistic which is combined on two Wilcoxon test statistics. However, these two test statistics are not in same scale. We propose the Hybrid Test Statistic based on the Hodges-Lehmann estimates of the treatment effects, which are medians in the same scale.^ To compare the proposed method, we use the classic meta-analysis T-test statistic on the combined the estimates of the treatment effects from two T-test statistics. Theoretically, the efficiency of two unbiased estimators of a parameter is the ratio of their variances. With the concept of Asymptotic Relative Efficiency (ARE) developed by Pitman, we show ARE of the hybrid test statistic relative to classic meta-analysis T-test statistic using the Hodges-Lemann estimators associated with two test statistics.^ From several simulation studies, we calculate the empirical type I error rate and power of the test statistics. The proposed statistic would provide effective tool to evaluate and understand the treatment effect in various public health studies as well as clinical trials.^

Instrumental variable method for the causal relationship between soluble receptor for advanced glycation end-products (sRAGE) and risk of pancreatic cancer

This thesis project is motivated by the potential problem of using observational data to draw inferences about a causal relationship in observational epidemiology research when controlled randomization is not applicable. Instrumental variable (IV) method is one of the statistical tools to overcome this problem. Mendelian randomization study uses genetic variants as IVs in genetic association study. In this thesis, the IV method, as well as standard logistic and linear regression models, is used to investigate the causal association between risk of pancreatic cancer and the circulating levels of soluble receptor for advanced glycation end-products (sRAGE). Higher levels of serum sRAGE were found to be associated with a lower risk of pancreatic cancer in a previous observational study (255 cases and 485 controls). However, such a novel association may be biased by unknown confounding factors. In a case-control study, we aimed to use the IV approach to confirm or refute this observation in a subset of study subjects for whom the genotyping data were available (178 cases and 177 controls). Two-stage IV method using generalized method of moments-structural mean models (GMM-SMM) was conducted and the relative risk (RR) was calculated. In the first stage analysis, we found that the single nucleotide polymorphism (SNP) rs2070600 of the receptor for advanced glycation end-products (AGER) gene meets all three general assumptions for a genetic IV in examining the causal association between sRAGE and risk of pancreatic cancer. The variant allele of SNP rs2070600 of the AGER gene was associated with lower levels of sRAGE, and it was neither associated with risk of pancreatic cancer, nor with the confounding factors. It was a potential strong IV (F statistic = 29.2). However, in the second stage analysis, the GMM-SMM model failed to converge due to non- concaveness probably because of the small sample size. Therefore, the IV analysis could not support the causality of the association between serum sRAGE levels and risk of pancreatic cancer. Nevertheless, these analyses suggest that rs2070600 was a potentially good genetic IV for testing the causality between the risk of pancreatic cancer and sRAGE levels. A larger sample size is required to conduct a credible IV analysis.^

Estimates of hospital and physician costs of epilepsy in the United States for 1995 comparing the provider -based survey method and a patient -based medical charts and billing method

This investigation compares two different methodologies for calculating the national cost of epilepsy: provider-based survey method (PBSM) and the patient-based medical charts and billing method (PBMC&BM). The PBSM uses the National Hospital Discharge Survey (NHDS), the National Hospital Ambulatory Medical Care Survey (NHAMCS) and the National Ambulatory Medical Care Survey (NAMCS) as the sources of utilization. The PBMC&BM uses patient data, charts and billings, to determine utilization rates for specific components of hospital, physician and drug prescriptions. ^ The 1995 hospital and physician cost of epilepsy is estimated to be $722 million using the PBSM and $1,058 million using the PBMC&BM. The difference of $336 million results from $136 million difference in utilization and $200 million difference in unit cost. ^ Utilization. The utilization difference of $136 million is composed of an inpatient variation of $129 million, $100 million hospital and $29 million physician, and an ambulatory variation of $7 million. The $100 million hospital variance is attributed to inclusion of febrile seizures in the PBSM, $−79 million, and the exclusion of admissions attributed to epilepsy, $179 million. The former suggests that the diagnostic codes used in the NHDS may not properly match the current definition of epilepsy as used in the PBMC&BM. The latter suggests NHDS errors in the attribution of an admission to the principal diagnosis. ^ The $29 million variance in inpatient physician utilization is the result of different per-day-of-care physician visit rates, 1.3 for the PBMC&BM versus 1.0 for the PBSM. The absence of visit frequency measures in the NHDS affects the internal validity of the PBSM estimate and requires the investigator to make conservative assumptions. ^ The remaining ambulatory resource utilization variance is $7 million. Of this amount, $22 million is the result of an underestimate of ancillaries in the NHAMCS and NAMCS extrapolations using the patient visit weight. ^ Unit cost. The resource cost variation is $200 million, inpatient is $22 million and ambulatory is $178 million. The inpatient variation of $22 million is composed of $19 million in hospital per day rates, due to a higher cost per day in the PBMC&BM, and $3 million in physician visit rates, due to a higher cost per visit in the PBMC&BM. ^ The ambulatory cost variance is $178 million, composed of higher per-physician-visit costs of $97 million and higher per-ancillary costs of $81 million. Both are attributed to the PBMC&BM's precise identification of resource utilization that permits accurate valuation. ^ Conclusion. Both methods have specific limitations. The PBSM strengths are its sample designs that lead to nationally representative estimates and permit statistical point and confidence interval estimation for the nation for certain variables under investigation. However, the findings of this investigation suggest the internal validity of the estimates derived is questionable and important additional information required to precisely estimate the cost of an illness is absent. ^ The PBMC&BM is a superior method in identifying resources utilized in the physician encounter with the patient permitting more accurate valuation. However, the PBMC&BM does not have the statistical reliability of the PBSM; it relies on synthesized national prevalence estimates to extrapolate a national cost estimate. While precision is important, the ability to generalize to the nation may be limited due to the small number of patients that are followed. ^

Assessment of oral bioaccessibility of arsenic in playground soil in Madrid (Spain): A three-method comparison and implications for risk assessment

Three methodologies to assess As bioaccessibility were evaluated using playgroundsoil collected from 16 playgrounds in Madrid, Spain: two (Simplified Bioaccessibility Extraction Test: SBET, and hydrochloric acid-extraction: HCl) assess gastric-only bioaccessibility and the third (Physiologically Based Extraction Test: PBET) evaluates mouth–gastric–intestinal bioaccessibility. Aqua regia-extractable (pseudo total) As contents, which are routinely employed in riskassessments, were used as the reference to establish the following percentages of bioaccessibility: SBET – 63.1; HCl – 51.8; PBET – 41.6, the highest values associated with the gastric-only extractions. For Madridplaygroundsoils – characterised by a very uniform, weakly alkaline pH, and low Fe oxide and organic matter contents – the statistical analysis of the results indicates that, in contrast with other studies, the highest percentage of As in the samples was bound to carbonates and/or present as calcium arsenate. As opposed to the As bound to Fe oxides, this As is readily released in the gastric environment as the carbonate matrix is decomposed and calcium arsenate is dissolved, but some of it is subsequently sequestered in unavailable forms as the pH is raised to 5.5 to mimic intestinal conditions. The HCl extraction can be used as a simple and reliable (i.e. low residual standard error) proxy for the more expensive, time consuming, and error-prone PBET methodology. The HCl method would essentially halve the estimate of carcinogenic risk for children playing in Madridplaygroundsoils, providing a more representative value of associated risk than the pseudo-total concentrations used at present

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.

Alarm tree analysis using statistical techniques

This work presents a systematic method for the generation and treatment of the alarms' graphs, being its final object to find the Alarm Root Cause of the Massive Alarms that are produced in the dispatching centers. Although many works about this matter have been already developed, the problem about the alarm management in the industry is still completely unsolved. In this paper, a simple statistic analysis of the historical data base is conducted. The results obtained by the acquisition alarm systems, are used to generate a directed graph from which the more significant alarms are extracted, previously analyzing any possible case in which a great quantity of alarms are produced.

A Variational Stereo Method for the Three-Dimensional Reconstruction of Ocean Waves

We develop a novel remote sensing technique for the observation of waves on the ocean surface. Our method infers the 3-D waveform and radiance of oceanic sea states via a variational stereo imagery formulation. In this setting, the shape and radiance of the wave surface are given by minimizers of a composite energy functional that combines a photometric matching term along with regularization terms involving the smoothness of the unknowns. The desired ocean surface shape and radiance are the solution of a system of coupled partial differential equations derived from the optimality conditions of the energy functional. The proposed method is naturally extended to study the spatiotemporal dynamics of ocean waves and applied to three sets of stereo video data. Statistical and spectral analysis are carried out. Our results provide evidence that the observed omnidirectional wavenumber spectrum S(k) decays as k-2.5 is in agreement with Zakharov's theory (1999). Furthermore, the 3-D spectrum of the reconstructed wave surface is exploited to estimate wave dispersion and currents.

Statistical Calculation of the Main Reliability Functions of GaAs Concentrator III-V Solar Cells

This paper presents some of the results of a method to determine the main reliability functions of concentrator solar cells. High concentrator GaAs single junction solar cells have been tested in an Accelerated Life Test. The method can be directly applied to multi-junction solar cells. The main conclusions of this test carried out show that these solar cells are robust devices with a very low probability of failure caused by degradation during their operation life (more than 30 years). The evaluation of the probability operation function (i.e. the reliability function R(t)) is obtained for two nominal operation conditions of these cells, namely simulated concentration ratios of 700 and 1050 suns. Preliminary determination of the Mean Time to Failure indicates a value much higher than the intended operation life time of the concentrator cells.

Shadow Analysis of Soil Surface Roughness Compared to the Chain Set Method and Direct Measurement of Micro-relief.

Erosion potential and the effects of tillage can be evaluated from quantitative descriptions of soil surface roughness. The present study therefore aimed to fill the need for a reliable, low-cost and convenient method to measure that parameter. Based on the interpretation of micro-topographic shadows, this new procedure is primarily designed for use in the field after tillage. The principle underlying shadow analysis is the direct relationship between soil surface roughness and the shadows cast by soil structures under fixed sunlight conditions. The results obtained with this method were compared to the statistical indexes used to interpret field readings recorded by a pin meter. The tests were conducted on 4-m2 sandy loam and sandy clay loam plots divided into 1-m2 subplots tilled with three different tools: chisel, tiller and roller. The highly significant correlation between the statistical indexes and shadow analysis results obtained in the laboratory as well as in the field for all the soil?tool combinations proved that both variability (CV) and dispersion (SD) are accommodated by the new method. This procedure simplifies the interpretation of soil surface roughness and shortens the time involved in field operations by a factor ranging from 12 to 20.

A stochastic model updating method for parameter variability quantification based on response surface models and Monte Carlo simulation

Stochastic model updating must be considered for quantifying uncertainties inherently existing in real-world engineering structures. By this means the statistical properties,instead of deterministic values, of structural parameters can be sought indicating the parameter variability. However, the implementation of stochastic model updating is much more complicated than that of deterministic methods particularly in the aspects of theoretical complexity and low computational efficiency. This study attempts to propose a simple and cost-efficient method by decomposing a stochastic updating process into a series of deterministic ones with the aid of response surface models and Monte Carlo simulation. The response surface models are used as surrogates for original FE models in the interest of programming simplification, fast response computation and easy inverse optimization. Monte Carlo simulation is adopted for generating samples from the assumed or measured probability distributions of responses. Each sample corresponds to an individual deterministic inverse process predicting the deterministic values of parameters. Then the parameter means and variances can be statistically estimated based on all the parameter predictions by running all the samples. Meanwhile, the analysis of variance approach is employed for the evaluation of parameter variability significance. The proposed method has been demonstrated firstly on a numerical beam and then a set of nominally identical steel plates tested in the laboratory. It is found that compared with the existing stochastic model updating methods, the proposed method presents similar accuracy while its primary merits consist in its simple implementation and cost efficiency in response computation and inverse optimization.