A primer on model selection using the Akaike Information Criterion

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.

On-line Modeling of Non-stationary Network Traffic with Schwarz Information Criterion

Modeling of network traffic is a fundamental building block of computer science. Measurements of network traffic demonstrate that self-similarity is one of the basic properties of the network traffic possess at large time-scale. This paper investigates the change of non-stationary self-similarity of network traffic over time,and proposes a method of combining the discrete wavelet transform (DWT) and Schwarz information criterion (SIC) to detect change points of self-similarity in network traffic. The traffic is segmented into pieces around changing points with homogenous characteristics for the Hurst parameter,named local Hurst parameter,and then each piece of network traffic is modeled using fractional Gaussian noise (FGN) model with the local Hurst parameter. The presented experimental performance on data set from the Internet Traffic Archive (ITA) demonstrates that the method is more accurate in describing the non-stationary self-similarity of network traffic.

A Comparison of Four Methods of Estimating the Scale Parameter for the Exponential Distribution

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.

Comparison of six statistical approaches in the selection of appropriate fish growth models

The performance of six statistical approaches,which can be used for selection of the best model to describe the growth of individual fish,was analyzed using simulated and real length-at-age data.The six approaches include coefficient of determination(R2),adjusted coefficient of determination(adj.-R2),root mean squared error(RMSE),Akaike's information criterion(AIC),bias correction of AIC(AICc) and Bayesian information criterion(BIC).The simulation data were generated by five growth models with different numbers of parameters.Four sets of real data were taken from the literature.The parameters in each of the five growth models were estimated using the maximum likelihood method under the assumption of the additive error structure for the data.The best supported model by the data was identified using each of the six approaches.The results show that R2 and RMSE have the same properties and perform worst.The sample size has an effect on the performance of adj.-R2,AIC,AICc and BIC.Adj.-R2 does better in small samples than in large samples.AIC is not suitable to use in small samples and tends to select more complex model when the sample size becomes large.AICc and BIC have best performance in small and large sample cases,respectively.Use of AICc or BIC is recommended for selection of fish growth model according to the size of the length-at-age data.

Current status of small yellow croaker resources in the southern Yellow Sea and the East China Sea

We used data from bottom trawl surveys to study the factors influencing the abundance of small yellow croaker, Larimichthys polyactis, in the southern Yellow Sea （SYS） and the East China Sea （ECS）. The resource density index （RD1） was generally higher in summer and autumn than in spring and winter. RDIs were also significantly greater in the SYS than in the ECS in summer and autumn. The bottom water salinity and depth of spatial distribution of small yellow croaker was similar between the two areas in summer, but different in other seasons. Regression analysis suggested that environmental factors such as bottom water temperature, salinity, and depth influenced the RDIs in summer in these areas. Growth condition factor （GCF） in the two areas varied monthly and the croaker in the SYS grew more slowly than those in the ECS. This was likely due to the low bottom temperature of the Yellow Sea Cold Water Mass in summer and autumn or to higher human fishing pressure in the ECS. To ensure sustainable utilization of the croaker stocks in these regions, we recommend reducing the fishing intensity, increasing the cod-end mesh size, and improving the protection of juveniles.

An improved joint method for onset picking of acoustic emission signals with noise

The onset times of acoustic signals with spikes,heavy bodies and unclear takeoffs are difficult to be picked accurately by the automatic method at present.To deal with this problem,an improved joint method based on the discrete wavelet transform(DWT),modified energy ratio(MER)and Akaike information criterion(AIC)pickers,has been proposed in this study.First,the DWT is used to decompose the signal into various components.Then,the joint application of MER and AIC pickers is carried out to pick the initial onset times of all selected components,where the minimum AIC position ahead of MER onset time is regarded as the initial onset time.Last,the average for initial onset times of all selected components is calculated as the final onset time of this signal.This improved joint method is tested and validated by the acoustic signals with different signal to noise ratios(SNRs)and waveforms.The results show that the improved joint method is not affected by the variations of SNR,and the onset times picked by this method are always accurate in different SNRs.Moreover,the onset times of all acoustic signals with spikes,heavy bodies and unclear takeoffs can be accurately picked by the improved joint method.Compared to some other methods including MER,AIC,DWT-MER and DWT-AIC,the improved joint method has better SNR stabilities and waveform adaptabilities.

一项优化AJCC/UICC pTNM胃癌分期预后预测效能的多中心研究

背景与目的美国癌症联合会与国际抗癌联盟(AmericanJointCommitteeonCancer/UnionforInternationalCancerControl,A JCC/UICC)联合发布的第8版TNM病理分期(pathological tumor?node?metastasis,p TNM)较前进行了重要修改,以提高胃癌患者预后预测准确性。然而,该分期不同亚组间患者的预后仍存在一定的同质性。本研究旨在对比第8版和第7版AJCC/UICC pTNM分期对胃癌预后的预测效能,并纳入外部验证对现有分期进行优化。方法共纳入分析7911例就诊于中国3家大型医疗中心和10,208例美国流行病监测与最终治疗结果(Surveillance Epidemiology and End Results,SEER)数据库的患者临床资料。采用log-rank检验、线性趋势检验、似然比检验和赤池信息量准则(akaike information criterion,AIC)梯度评估第7、8版AJCC/UICC pTNM分期系统的同质性、辨别力和单调性,在此基础上优化分期并以SEER数据集作为外部验证。结果第7、8版分期系统在两组数据集中均存在明显分期偏移,且集中在III期患者。IIIA、IIIB和IIIC期各亚组内患者的生存率有显著差异,表明两个系统分期分层的同质性较差。我们根据中国患者数据构建一个新的改良版p TNM分期,上述分层同质性问题得到明显改善,进一步以SEER数据作为验证集同样得到了良好的结果。相较第7、8版分期系统,改良版p TNM分期在两组数据集中均有较高的log-rank、线性趋势、似然比卡方值和较低的AIC值,显示出更优的辨别力、同质性、单调性和预后预测效能。结论第8版AJCC/UICC pTNM分期系统优于第7版,但预后预测的同质性均较差。我们构建的改良版p TNM分期在两组大样本胃癌数据集中均显示出理想的分期分层和预后预测效能。

On the volatility of daily stock returns of Total Nigeria Plc: evidence from GARCH models, value-at-risk and backtesting

This study investigates the volatility in daily stock returns for Total Nigeria Plc using nine variants of GARCH models:sGARCH,girGARCH,eGARCH,iGARCH,aGARCH,TGARCH,NGARCH,NAGARCH,and AVGARCH along with value at risk estimation and backtesting.We use daily data for Total Nigeria Plc returns for the period January 2,2001 to May 8,2017,and conclude that eGARCH and sGARCH perform better for normal innovations while NGARCH performs better for student t innovations.This investigation of the volatility,VaR,and backtesting of the daily stock price of Total Nigeria Plc is important as most previous studies covering the Nigerian stock market have not paid much attention to the application of backtesting as a primary approach.We found from the results of the estimations that the persistence of the GARCH models are stable except for few cases for which iGARCH and eGARCH were unstable.Additionally,for student t innovation,the sGARCH and girGARCH models failed to converge;the mean reverting number of days for returns differed from model to model.From the analysis of VaR and its backtesting,this study recommends shareholders and investors continue their business with Total Nigeria Plc because possible losses may be overcome in the future by improvements in stock prices.Furthermore,risk was reflected by significant up and down movement in the stock price at a 99%confidence level,suggesting that high risk brings a high return.

An ICPSO-RBFNN nonlinear inversion for electrical resistivity imaging

To improve the global search ability and imaging quality of electrical resistivity imaging(ERI) inversion, a two-stage learning ICPSO algorithm of radial basis function neural network(RBFNN) based on information criterion(IC) and particle swarm optimization(PSO) is presented. In the proposed method, IC is applied to obtain the hidden layer structure by calculating the optimal IC value automatically and PSO algorithm is used to optimize the centers and widths of the radial basis functions in the hidden layer. Meanwhile, impacts of different information criteria to the inversion results are compared, and an implementation of the proposed ICPSO algorithm is given. The optimized neural network has one hidden layer with 261 nodes selected by AKAIKE's information criterion(AIC) and it is trained on 32 data sets and tested on another 8 synthetic data sets. Two complex synthetic examples are used to verify the feasibility and effectiveness of the proposed method with two learning stages. The results show that the proposed method has better performance and higher imaging quality than three-layer and four-layer back propagation neural networks(BPNNs) and traditional least square(LS) inversion.

An unsupervised clustering method for nuclear magnetic resonance transverse relaxation spectrums based on the Gaussian mixture model and its application

To make the quantitative results of nuclear magnetic resonance(NMR) transverse relaxation(T;) spectrums reflect the type and pore structure of reservoir more directly, an unsupervised clustering method was developed to obtain the quantitative pore structure information from the NMR T;spectrums based on the Gaussian mixture model(GMM). Firstly, We conducted the principal component analysis on T;spectrums in order to reduce the dimension data and the dependence of the original variables. Secondly, the dimension-reduced data was fitted using the GMM probability density function, and the model parameters and optimal clustering numbers were obtained according to the expectation-maximization algorithm and the change of the Akaike information criterion. Finally, the T;spectrum features and pore structure types of different clustering groups were analyzed and compared with T;geometric mean and T;arithmetic mean. The effectiveness of the algorithm has been verified by numerical simulation and field NMR logging data. The research shows that the clustering results based on GMM method have good correlations with the shape and distribution of the T;spectrum, pore structure, and petroleum productivity, providing a new means for quantitative identification of pore structure, reservoir grading, and oil and gas productivity evaluation.

The improved local linear prediction of chaotic time series

Based on the Bayesian information criterion, this paper proposes the improved local linear prediction method to predict chaotic time series. This method uses spatial correlation and temporal correlation simultaneously. Simulation results show that the improved local linear prediction method can effectively make multi-step and one-step prediction of chaotic time series and the multi-step prediction performance and one-step prediction accuracy of the improved local linear prediction method are superior to those of the traditional local linear prediction method.

Time-series analysis of monthly rainfall data for the Mahanadi River Basin, India

Time series analysis has two goals, modeling random mechanisms and predicting future series using historical data. In the present work, a uni-variate time series autoregressive integrated moving average （ARIMA） model has been developed for （a） simulating and forecasting mean rainfall, obtained using Theissen weights; over the Mahanadi River Basin in India, and （b） simula^ag and forecasting mean rainfall at 38 rain-gauge stations in district towns across the basin. For the analysis, monthly rainfall data of each district town for the years 1901-2002 （102 years） were used. Theissen weights were obtained over the basin and mean monthly rainfall was estimated. The trend and seasonality observed in ACF and PACF plots of rainfall data were removed using power transformation （a=0.5） and first order seasonal differencing prior to the development of the ARIMA model. Interestingly, the AR1MA model （1,0,0）（0,1,1）12 developed here was found to be most suitable for simulating and forecasting mean rainfall over the Mahanadi River Basin and for all 38 district town rain-gauge stations, separately. The Akaike Information Criterion （AIC）, good- ness of fit （Chi-square）, R2 （coefficient of determination）, MSE （mean square error） and MAE （mea absolute error） were used to test the validity and applicability of the developed ARIMA model at different stages. This model is considered appropriate to forecast the monthly rainfall for the upcoming 12 years in each district town to assist decision makers and policy makers establish priorities for water demand, storage, distribution, and disaster management.

基于新纲目的卫勤训练理论考核系统的设计与实现

为了实践卫勤新纲目,提高基于新纲目的卫勤训练理论考核的信息化程度。按照卫勤新纲目的标准设计了训练、考核等功能模块,实现了系统训练及考核评估功能。结果表明该系统对于提高基于新纲目的卫勤理论考核信息化程度、检验训练效果、提高考核效率等具有现实意义。

Spatial Modeling and Mapping of Tuberculosis Using Bayesian Hierarchical Approaches

Global spread of infectious disease threatens the well-being of human, domestic, and wildlife health. A proper understanding of global distribution of these diseases is an important part of disease management and policy making. However, data are subject to complexities by heterogeneity across host classes. The use of frequentist methods in biostatistics and epidemiology is common and is therefore extensively utilized in answering varied research questions. In this paper, we applied the hierarchical Bayesian approach to study the spatial distribution of tuberculosis in Kenya. The focus was to identify best fitting model for modeling TB relative risk in Kenya. The Markov Chain Monte Carlo (MCMC) method via WinBUGS and R packages was used for simulations. The Deviance Information Criterion (DIC) proposed by [1] was used for models comparison and selection. Among the models considered, unstructured heterogeneity model perfumes better in terms of modeling and mapping TB RR in Kenya. Variation in TB risk is observed among Kenya counties and clustering among counties with high TB Relative Risk (RR). HIV prevalence is identified as the dominant determinant of TB. We find clustering and heterogeneity of risk among high rate counties. Although the approaches are less than ideal, we hope that our formulations provide a useful stepping stone in the development of spatial methodology for the statistical analysis of risk from TB in Kenya.

Spatio-temporal epidemic type aftershock sequence model for Tangshan aftershock sequence

Shallow earthquakes usually show obvious spatio-temporal clustering patterns. In this study, several spatio-temporal point process models are applied to investigate the clustering characteristics of the well-known Tangshan sequence based on classical empirical laws and a few assumptions. The relative fit of competing models is compared by Akalke Information Criterion. The spatial clustering pattern is well characterized by the model which gives the best fit to the data. A simulated aftershock sequence is generated by thinning algorithm and compared with the real seismicity.

A New Generalized Weibull Model:Classical and Bayesian Estimation

Statistical distributions play a prominent role in applied sciences,particularly in biomedical sciences.The medical data sets are generally skewed to the right,and skewed distributions can be used quite effectively to model such kind of data sets.In the present study,therefore,we propose a new family of distributions suitable for modeling right-skewed medical data sets.The proposed family may be called a new generalized-X family.A special sub-model of the proposed family called a new generalized-Weibull distribution is discussed in detail.The maximum likelihood estimators of the model parameters are obtained.A brief Monte Carlo simulation study is conducted to evaluate the performance of these estimators.Finally,the proposed model is applied to the remission times of the stomach cancer patient’s data.The comparison of the goodness of fit results of the proposed model is made with the other competing models such as Weibull,Kumaraswamy Weibull,and exponentiated Weibull distributions.Certain analytical measures such as Akaike information criterion,Bayesian information criterion,Anderson Darling statistic,and Kolmogorov-Smirnov test statistic are considered to show which distribution provides the best fit to data.Based on these measures,it is showed that the proposed distribution is a reasonable candidate for modeling data in medical sciences and other related fields.

Characteristic Analysis and Harmonic Feature Identification of Micro-Vibration on Flywheels

To avoid the negative effects of disturbances on satellites,the characteristics of micro-vibration on flywheels are studied.Considering rotor imbalance,bearing imperfections and structural elasticity,the extended model of micro-vibration is established.In the feature extraction of micro-vibration,singular value decomposition combined with the improved Akaike Information Criterion(AIC-SVD)is applied to denoise.More robust and self-adaptable than the peak threshold denoising,AIC-SVD can effectively remove the noise components.Subsequently,the effective harmonic coefficients are extracted by the binning algorithm.The results show that the harmonic coefficients have great identification in frequency domain.Except for the fundamental frequency caused by rotor imbalance,the harmonics are also caused by the coupling of imperfections on bearing components.

Clustering of the Values of a Response Variable and Simultaneous Covariate Selection Using a Stepwise Algorithm

In supervised learning the number of values of a response variable can be very high. Grouping these values in a few clusters can be useful to perform accurate supervised classification analyses. On the other hand selecting relevant covariates is a crucial step to build robust and efficient prediction models. We propose in this paper an algorithm that simultaneously groups the values of a response variable into a limited number of clusters and selects stepwise the best covariates that discriminate this clustering. These objectives are achieved by alternate optimization of a user-defined model selection criterion. This process extends a former version of the algorithm to a more general framework. Moreover possible further developments are discussed in detail.

Selecting the Quantity of Models in Mixture Regression

Mixture regression is a regression problem with mixed data. Specifically, in the observations, some data are from one model, while others from other models. Only after assuming the quantity of the model is given, EM or other algorithms can be used to solve this problem. We propose an information criterion for mixture regression model in this paper. Compared to ordinary information citizen by data simulations, results show our citizen has better performance on choosing the correct quantity of models.

Multimodel inference based on smoothed information criteria

The multimodel inference makes statistical inferences from a set of plausible models rather than from a single model.In this paper,we focus on the multimodel inference based on smoothed information criteria proposed by seminal monographs(see Buckland et al.(1997)and Burnham and Anderson(2003)),which are termed as smoothed Akaike information criterion(SAIC)and smoothed Bayesian information criterion(SBIC)methods.Due to their simplicity and applicability,these methods are very widely used in many fields.By using an illustrative example and deriving limiting properties for the weights in the linear regression,we find that the existing variance estimation for SAIC is not applicable because of a restrictive condition,but for SBIC it is applicable.Especially,we propose a simulation-based inference for SAIC based on the limiting properties.Both the simulation study and the real data example show the promising performance of the proposed simulationbased inference.