Number Of Data Variables Research Articles

Resampling for estimation of parameters uncertainty in genetic algorithm based model fitting

Resampling methods draw samples from the observed data to draw certain conclusions about the population of interest.The study is the employment of resampling to the calculation of parameters uncertainty in hard model fitting of chemical and spectrochemical data, assisted by genetic algorithm. Four data sets are investigated including: a simulated two steps of complexometric spectrophotometric titration data, a real data from IgG purification by ion exchange chromatography, one 1H NMR spectrum from a real metabolomics data set, and a simulated metabolomics 1H NMR spectrum. In the first data, the logarithm of formation constants in the first and second steps were 4.500 and 7.200, respectively. The mean of estimated parameters and standard deviations using the proposed method were obtained as 4.504 ± 0.005 and 7.205 ± 0.017 by removing around half of the samples while for NGLM algorithm and Hessian matrix were 4.503 ± 0.005 and 7.203 ± 0.018. In the second data, desorption coefficient (kdes,0), equilibrium coefficient (Keq,0), and a constant parameter that describes ion exchange characteristics (β) were well estimated with root mean square error (RMSE) of 0.031 mg mL−1. In the third and last data sets, parameters including chemical shifts and intensity of each metabolite were well calculated with low relative error of 4.23 × 10−4. The estimated uncertainty of parameters were different. In some cases, the means of estimated parameters were dependent of the number of eliminated samples in resampling. Effect of number of variables in data and model deficiency on the results from resampling was investigated. Due to the complexity of the mentioned datasets, use of resampling and GA is useful and important strategy for acquiring parameter mean and uncertainty, when we are not able to determine the Hessian matrix.

A Facility Location Model for Air Pollution Detection

We describe mathematical models and practical algorithms for a problem concerned with monitoring the air pollution in a large city. We have worked on this problem within a project for assessing the air quality in the city of Rome by placing a certain number of sensors on some of the city buses. We cast the problem as a facility location model. By reducing the large number of data variables and constraints, we were able to solve to optimality the resulting MILP model within minutes. Furthermore, we designed a genetic algorithm whose solutions were on average very close to the optimal ones. In our computational experiments we studied the placement of sensors on 187 candidate bus routes. We considered the coverage provided by 10 up to 60 sensors.

SOFTWARE TESTING DEFECT PREDICTION MODEL - A PRACTICAL APPROACH

Software defects prediction aims to reduce software testing efforts by guiding the testers through the defect classification of software systems. Defect predictors are widely used in many organizations to predict software defects in order to save time, improve quality, testing and for better planning of the resources to meet the timelines. The application of statistical software testing defect prediction model in a real life setting is extremely difficult because it requires more number of data variables and metrics and also historical defect data to predict the next releases or new similar type of projects. This paper explains our statistical model, how it will accurately predict the defects for upcoming software releases or projects. We have used 20 past release data points of software project, 5 parameters and build a model by applying descriptive statistics, correlation and multiple linear regression models with 95% confidence intervals (CI). In this appropriate multiple linear regression model the R-square value was 0.91 and its Standard Error is 5.90%. The Software testing defect prediction model is now being used to predict defects at various testing projects and operational releases. We have found 90.76% precision between actual and predicted defects.

Variable reduction on electronic tongue data

Reduction of the number of variables in data from a so-called electronic tongue contributes to simpler model calculations and less storage requirements. In this study, we have developed a model for this purpose. This model describes the response from the electrodes in the electronic tongue with two exponential functions plus a constant term, i(t)=k+k f e −tα+k c e −tβ , where t is the time. From the model, five parameters which describe the signal are extracted. These parameters can be used as inputs instead of the original signal to any multivariate algorithm. The results show that the variables obtained are at least as good as the original data to separate between different classes, even though the number of parameters has been reduced between 80 and 199 times.

Determination of the spatial distribution of a physical parameter from the distribution of another physical variable— a differential inverse problem

We propose a new type of inverse problem, in which the spatial distribution of the relative value of a physical parameter can be determined only from the distribution of another physical variable in the region of interest if there is no source in that region. The inverse problem proposed here has two features different from conventional remote probing type problems. One is that the physical variable data are given throughout the region of interest although the number of data variables is insufficient to determine directly the physical parameter of interest, while only remote data are given in a conventional problem. The other is the mathematical structure of the inverse problem: this new inverse problem yields a spatial differential equation on the target parameter, while the conventional problem becomes an integral equation on the target parameter. To show the nature of the problem, we formulated an illustrative inverse problem on the steady-state electric current field, in which the spatial distribution of the relative conductivity can be determined from the distribution of either the potential or the current density. We give examples of computational results obtained when using the simulated potential data and the current density data. This proposed formalism for a new type of inverse problem could provide a new approach and open up new measurement schemes in many fields of science and engineering.

Computerized Construction in Fortran of a Discriminant Function for Categorical Data

SUMMARY A non-parametric discriminant function for categorical or discrete-valued data belonging to at least two a priori classes is constructed by a computer program from the base sample data. There is no limit to the number of data variables measured oh members of the base sample, but each variable can have no more than 10 possible values. The program prints out the discriminant function in the form of a branching key for use by hand; also in the form of a Fortran function which can be punched out on cards by the computer. A simple program to read the same variables for each individual, and then call the function, will classify a prospective series from the same population. The key itself may have a descriptive use, especially when the number of variables is enormous. In this case it may be used as a preliminary analysis which may suggest testable hypotheses about the interactions between some of the variables. The algorithm itself is presented in the algorithms section of this issue of Applied Statistics (Sturt, 1980).