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Applications to Data Analytics and Modeling
Book chapter

Applications to Data Analytics and Modeling

P. Mohana Shankar
Probability, Random Variables, and Data Analytics with Engineering Applications, pp 337-420
09 Feb 2021
DOI: https://doi.org/10.1007/978-3-030-56259-5_5

Abstract

95% confidence interval Accuracy and error rates Bayes’ decision theory Bayes’ risk Bigamma models of ROC Bins, fixed bin counts, fixed bin widths Bootstrapping Bootstrapping of AUC Chi square density and chi square test statistic Chi square tests Comparison of AUCs from two sensors through bootstrapping Cost matrix and conditional cost Degrees of freedom Disease prevalence Diversity and performance improvement of detectors Equal gain combining Error rates, outages and diversity Fading False alarm rates and miss rates Gaussian fit Generalized K-distribution Hypergeometric functions Likelihood and log-likelihood functions Likelihood ratio Lognormal density Maximal ratio combining Maximum, arithmetic mean, geometric mean Mean square error (MSE) Method of moments (MOM) and maximum likelihood estimation (MLE) Multiple hypotheses Null and alternate hypothesis Parameter estimation Performance enhancement Performance index Reduced chi square test statistic Reliability ROC curves Scattering and clustered scattering Selection and generalized selection combining Shadowing Signal processing algorithms Signal-to-noise ratio Single sided and two sided z-tests Statistical modeling of data Statistics of the area under the ROC curve (AUC) Suzuki models Theoretical ROC Trigamma function values Youden’s index
In this chapter is exclusively devoted to data analytics. The topics from previous chapters are invoked to make connections to hypothesis testing (chi-square tests), parameter estimation, ROC, and performance analysis with the aim of developing data analytic approaches. Instead of presenting hypothesis testing and parameter estimation as theoretical topics, they are offered as tools in the context of data analytics, and examples reflect this paradigm shift. ROC analysis is revisited to understand the statistics of the area under the ROC curve through the study of bootstrapping. Examples of bootstrapping are given which examine the method of comparing the areas under the ROC curves generated from data from identical subject pools. A modeling example is presented by examining the statistics of signal fluctuations in wireless channels demonstrating the genesis of several densities. Diversity is introduced as a means to mitigate signal strength fluctuations in wireless channels. All the exercises involve data analytics.

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