A powerful investigative tool in biology is to consider not a single mathematical model but a collection of models designed to explore different working hypotheses and select the best model in that collection.In these...A powerful investigative tool in biology is to consider not a single mathematical model but a collection of models designed to explore different working hypotheses and select the best model in that collection.In these lecture notes,the usual workflow of the use of mathematical models to investigate a biological problem is described and the use of a collection of model is motivated.Models depend on parameters that must be estimated using observations;and when a collection of models is considered,the best model has then to be identified based on available observations.Hence,model calibration and selection,which are intrinsically linked,are essential steps of the workflow.Here,some procedures for model calibration and a criterion,the Akaike Information Criterion,of model selection based on experimental data are described.Rough derivation,practical technique of computation and use of this criterion are detailed.展开更多
In this paper, the estimators of the scale parameter of the exponential distribution obtained by applying four methods, using complete data, are critically examined and compared. These methods are the Maximum Likeliho...In this paper, the estimators of the scale parameter of the exponential distribution obtained by applying four methods, using complete data, are critically examined and compared. These methods are the Maximum Likelihood Estimator (MLE), the Square-Error Loss Function (BSE), the Entropy Loss Function (BEN) and the Composite LINEX Loss Function (BCL). The performance of these four methods was compared based on three criteria: the Mean Square Error (MSE), the Akaike Information Criterion (AIC), and the Bayesian Information Criterion (BIC). Using Monte Carlo simulation based on relevant samples, the comparisons in this study suggest that the Bayesian method is better than the maximum likelihood estimator with respect to the estimation of the parameter that offers the smallest values of MSE, AIC, and BIC. Confidence intervals were then assessed to test the performance of the methods by comparing the 95% CI and average lengths (AL) for all estimation methods, showing that the Bayesian methods still offer the best performance in terms of generating the smallest ALs.展开更多
初至拾取是微地震数据处理的基本步骤及重要环节,在低信噪比情况下,传统的初至拾取方法性能不佳,无法满足实际需求。为此,提出一种新算法,该算法将时域微地震数据映射到Shearlet域,利用AIC(Akaike Information Criterion)模型对Shearle...初至拾取是微地震数据处理的基本步骤及重要环节,在低信噪比情况下,传统的初至拾取方法性能不佳,无法满足实际需求。为此,提出一种新算法,该算法将时域微地震数据映射到Shearlet域,利用AIC(Akaike Information Criterion)模型对Shearlet域各尺度层的数据实现初步识别,最小AIC值作为初至时刻。通过大量实验验证Shearlet-AIC算法在低至-13 d B信噪比下自动拾取的准确性,证实该算法优于传统初至拾取算法,解决了传统初至拾取算法在低信噪比时难以有效拾取微地震初至的难题。展开更多
基金SP is supported by a Discovery Grant of the Natural Sciences and Engineering Research Council of Canada(RGOIN-2018-04967).
文摘A powerful investigative tool in biology is to consider not a single mathematical model but a collection of models designed to explore different working hypotheses and select the best model in that collection.In these lecture notes,the usual workflow of the use of mathematical models to investigate a biological problem is described and the use of a collection of model is motivated.Models depend on parameters that must be estimated using observations;and when a collection of models is considered,the best model has then to be identified based on available observations.Hence,model calibration and selection,which are intrinsically linked,are essential steps of the workflow.Here,some procedures for model calibration and a criterion,the Akaike Information Criterion,of model selection based on experimental data are described.Rough derivation,practical technique of computation and use of this criterion are detailed.
文摘In this paper, the estimators of the scale parameter of the exponential distribution obtained by applying four methods, using complete data, are critically examined and compared. These methods are the Maximum Likelihood Estimator (MLE), the Square-Error Loss Function (BSE), the Entropy Loss Function (BEN) and the Composite LINEX Loss Function (BCL). The performance of these four methods was compared based on three criteria: the Mean Square Error (MSE), the Akaike Information Criterion (AIC), and the Bayesian Information Criterion (BIC). Using Monte Carlo simulation based on relevant samples, the comparisons in this study suggest that the Bayesian method is better than the maximum likelihood estimator with respect to the estimation of the parameter that offers the smallest values of MSE, AIC, and BIC. Confidence intervals were then assessed to test the performance of the methods by comparing the 95% CI and average lengths (AL) for all estimation methods, showing that the Bayesian methods still offer the best performance in terms of generating the smallest ALs.
文摘初至拾取是微地震数据处理的基本步骤及重要环节,在低信噪比情况下,传统的初至拾取方法性能不佳,无法满足实际需求。为此,提出一种新算法,该算法将时域微地震数据映射到Shearlet域,利用AIC(Akaike Information Criterion)模型对Shearlet域各尺度层的数据实现初步识别,最小AIC值作为初至时刻。通过大量实验验证Shearlet-AIC算法在低至-13 d B信噪比下自动拾取的准确性,证实该算法优于传统初至拾取算法,解决了传统初至拾取算法在低信噪比时难以有效拾取微地震初至的难题。
