LEADER 03958nam 22006855 450 001 9910896193203321 005 20250327144746.0 010 $a9783031666193 010 $a3031666194 024 7 $a10.1007/978-3-031-66619-3 035 $a(CKB)36315294100041 035 $a(MiAaPQ)EBC31713216 035 $a(Au-PeEL)EBL31713216 035 $a(DE-He213)978-3-031-66619-3 035 $a(EXLCZ)9936315294100041 100 $a20241008d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 13$aAn Introduction to Statistical Data Science $eTheory and Models /$fby Giorgio Picci 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (437 pages) 311 08$a9783031666186 311 08$a3031666186 327 $a- 1. Introduction -- 2. Classical Statistical Inference -- 3. Linear Models -- 4. Conditioning and Regularization -- 5. Linear Hypotheses and LDA -- 6. Bayesian Statistics -- 7. Principal Component Analysis -- 8. Non Linear Inference -- 9. Time Series. 330 $aThis graduate textbook on the statistical approach to data science describes the basic ideas, scientific principles and common techniques for the extraction of mathematical models from observed data. Aimed at young scientists, and motivated by their scientific prospects, it provides first principle derivations of various algorithms and procedures, thereby supplying a solid background for their future specialization to diverse fields and applications. The beginning of the book presents the basics of statistical science, with an exposition on linear models. This is followed by an analysis of some numerical aspects and various regularization techniques, including LASSO, which are particularly important for large scale problems. Decision problems are studied both from the classical hypothesis testing perspective and, particularly, from a modern support-vector perspective, in the linear and non-linear context alike. Underlying the book is the Bayesian approach and the Bayesian interpretation of various algorithms and procedures. This is the key to principal components analysis and canonical correlation analysis, which are explained in detail. Following a chapter on nonlinear inference, including material on neural networks, the book concludes with a discussion on time series analysis and estimating their dynamic models. Featuring examples and exercises partially motivated by engineering applications, this book is intended for graduate students in applied mathematics and engineering with a general background in probability and linear algebra. 606 $aStatistics 606 $aStatistics 606 $aMachine learning 606 $aEngineering mathematics 606 $aArtificial intelligence$xData processing 606 $aStatistical Theory and Methods 606 $aBayesian Inference 606 $aStatistical Learning 606 $aStatistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences 606 $aEngineering Mathematics 606 $aData Science 615 0$aStatistics. 615 0$aStatistics. 615 0$aMachine learning. 615 0$aEngineering mathematics. 615 0$aArtificial intelligence$xData processing. 615 14$aStatistical Theory and Methods. 615 24$aBayesian Inference. 615 24$aStatistical Learning. 615 24$aStatistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences. 615 24$aEngineering Mathematics. 615 24$aData Science. 676 $a519.5 700 $aPicci$b Giorgio$0447863 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910896193203321 996 $aAn Introduction to Statistical Data Science$94215042 997 $aUNINA