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71	Observation error model selection by information criteria vs. normality testing Lehmann, Rüdiger 17 October 2016 (has links) (PDF) To extract the best possible information from geodetic and geophysical observations, it is necessary to select a model of the observation errors, mostly the family of Gaussian normal distributions. However, there are alternatives, typically chosen in the framework of robust M-estimation. We give a synopsis of well-known and less well-known models for observation errors and propose to select a model based on information criteria. In this contribution we compare the Akaike information criterion (AIC) and the Anderson Darling (AD) test and apply them to the test problem of fitting a straight line. The comparison is facilitated by a Monte Carlo approach. It turns out that the model selection by AIC has some advantages over the AD test. Maximum-Likelihood-Schätzung Robuste Schätzung Gaußsche Normalverteilung Laplace-Verteilung Verallgemeinerte Normalverteilung Kontaminierte Normalverteilung Akaike's Informationskriterium Anderson-Darling-Test Monte-Carlo-Methode maximum likelihood estimation robust estimation Gaussian normal distribution Laplace distribution generalized normal distribution contaminated normal distribution Akaike information criterion Anderson Darling test Monte Carlo method ddc:500 rvk:ZI 9070
72	Comparison of Multiple Models for Diabetes Using Model Averaging Al-Mashat, Alex January 2021 (has links) Pharmacometrics is widely used in drug development. Models are developed to describe pharmacological measurements with data gathered from a clinical trial. The information can then be applied to, for instance, safely establish dose-response relationships of a substance. Glycated hemoglobin (HbA1c) is a common biomarker used by models within antihyperglycemic drug development, as it reflects the average plasma glucose level over the previous 8-12 weeks. There are five different nonlinear mixed-effects models that describes HbA1c-formation. They use different biomarkers such as mean plasma glucose (MPG), fasting plasma glucose (FPG), fasting plasma insulin (FPI) or a combination of those. The aim of this study was to compare their performances on a population and an individual level using model averaging (MA) and to explore if reduced trial durations and different treatment could affect the outcome. Multiple weighting methods were applied to the MA workflow, such as the Akaike information criterion (AIC), cross-validation (CV) and a bootstrap model averaging method. Results show that in general, models that use MPG to describe HbA1c-formation on a population level could potentially outperform models using other biomarkers, however, models have shown similar performance on individual level. Further studies on the relationship between biomarkers and model performances must be conducted, since it could potentially lay the ground for better individual HbA1c-predictions. It can then be applied in antihyperglycemic drug development and to possibly reduce sample sizes in a clinical trial. With this project, we have illustrated how to perform MA on the aforementioned models, using different biomarkers as well as the difference between model weights on a population and individual level. pharmacometrics population pharmacokinetics pop-pk pop-PK diabetes model averaging MA cross-validation cv CV akaike information criterion Akaike aic AIC MPG mpg FPG fpg FPI fpi HbA1c hba1c farmakometri populationsfarmakokinetik diabetes model averaging MA cross-validation cv CV akaike Akaike aic AIC MPG mpg FPG fpg FPI fpi HbA1c hba1c Pharmaceutical Sciences Farmaceutiska vetenskaper
73	Transformation model selection by multiple hypotheses testing Lehmann, Rüdiger January 2014 (has links) Transformations between different geodetic reference frames are often performed such that first the transformation parameters are determined from control points. If in the first place we do not know which of the numerous transformation models is appropriate then we can set up a multiple hypotheses test. The paper extends the common method of testing transformation parameters for significance, to the case that also constraints for such parameters are tested. This provides more flexibility when setting up such a test. One can formulate a general model with a maximum number of transformation parameters and specialize it by adding constraints to those parameters, which need to be tested. The proper test statistic in a multiple test is shown to be either the extreme normalized or the extreme studentized Lagrange multiplier. They are shown to perform superior to the more intuitive test statistics derived from misclosures. It is shown how model selection by multiple hypotheses testing relates to the use of information criteria like AICc and Mallows’ Cp, which are based on an information theoretic approach. Nevertheless, whenever comparable, the results of an exemplary computation almost coincide. info:eu-repo/classification/ddc/500 ddc:500
74	Observation error model selection by information criteria vs. normality testing Lehmann, Rüdiger January 2015 (has links) To extract the best possible information from geodetic and geophysical observations, it is necessary to select a model of the observation errors, mostly the family of Gaussian normal distributions. However, there are alternatives, typically chosen in the framework of robust M-estimation. We give a synopsis of well-known and less well-known models for observation errors and propose to select a model based on information criteria. In this contribution we compare the Akaike information criterion (AIC) and the Anderson Darling (AD) test and apply them to the test problem of fitting a straight line. The comparison is facilitated by a Monte Carlo approach. It turns out that the model selection by AIC has some advantages over the AD test. info:eu-repo/classification/ddc/500 ddc:500
75	空間相關存活資料之貝氏半參數比例勝算模式 / Bayesian semiparametric proportional odds models for spatially correlated survival data 張凱嵐, Chang, Kai lan Unknown Date (has links) 近來地理資訊系統(GIS)之資料庫受到不同領域的統計學家廣泛的研究，以期建立及分析可描述空間聚集效應及變異之模型，而描述空間相關存活資料之統計模式為公共衛生及流行病學上新興的研究議題。本文擬建立多維度半參數的貝氏階層模型，並結合空間及非空間隨機效應以描述存活資料中的空間變異。此模式將利用多變量條件自回歸(MCAR)模型以檢驗在不同地理區域中是否存有空間聚集效應。而基準風險函數之生成為分析貝氏半參數階層模型的重要步驟，本研究將利用混合Polya樹之方式生成基準風險函數。美國國家癌症研究院之「流行病監測及最終結果」(Surveillance Epidemiology and End Results, SEER)資料庫為目前美國最完整的癌症病人長期追蹤資料，包含癌症病人存活狀況、多重癌症史、居住地區及其他分析所需之個人資料。本文將自此資料庫擷取美國愛荷華州之癌症病人資料為例作實證分析，並以貝氏統計分析中常用之模型比較標準如條件預測指標(CPO)、平均對數擬邊際概似函數值(ALMPL)、離差訊息準則(DIC)分別測試其可靠度。 / The databases of Geographic Information System (GIS) have gained attention among different fields of statisticians to develop and analyze models which account for spatial clustering and variation. There is an emerging interest in modeling spatially correlated survival data in public health and epidemiologic studies. In this article, we develop Bayesian multivariate semiparametric hierarchical models to incorporate both spatially correlated and uncorrelated frailties to answer the question of spatial variation in the survival patterns, and we use multivariate conditionally autoregressive (MCAR) model to detect that whether there exists the spatial cluster across different areas. The baseline hazard function will be modeled semiparametrically using mixtures of finite Polya trees. The SEER (Surveillance Epidemiology and End Results) database from the National Cancer Institute (NCI) provides comprehensive cancer data about patient’s survival time, regional information, and others demographic information. We implement our Bayesian hierarchical spatial models on Iowa cancer data extracted from SEER database. We illustrate how to compute the conditional predictive ordinate (CPO), the average log-marginal pseudo-likelihood (ALMPL), and deviance information criterion (DIC), which are Bayesian criterions for model checking and comparison among competing models. 空間聚集比例勝算模型貝氏階層模型混合Polya樹馬可夫鏈蒙地卡羅模擬多變量條件自回歸模型條件預測指標平均對數擬邊際概似函數值離差訊息準則 spatial clusters proportional odds Bayesian hierarchical model mixture of Polya trees Markov Chain Monte Carlo (MCMC) conditional predictive ordinate (CPO) deviance information criterion (DIC)

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