LEADER 05479nam 22006615 450 001 9910899895303321 005 20260119171828.0 010 $a3-031-70051-1 024 7 $a10.1007/978-3-031-70051-4 035 $a(MiAaPQ)EBC31741711 035 $a(Au-PeEL)EBL31741711 035 $a(CKB)36403430400041 035 $a(DE-He213)978-3-031-70051-4 035 $a(EXLCZ)9936403430400041 100 $a20241025d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDigressions in Elementary Probability $eThe Unexpected in Medicine, Sports, and Society /$fby Edward Beltrami 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (118 pages) 225 1 $aQuantitative Methods in the Humanities and Social Sciences,$x2199-0964 311 08$a3-031-70050-3 320 $aIncludes bibliographical references. 327 $aSuccess Runs in Bernoulli Trials -- Chapter 2. The Remarkable Streak of Joe Di Maggio -- Chapter 3. Inherited, Not Acquired -- Chapter 4. A Subtle Bias -- Chapter 5. Addendum : Conditional Expectation -- Chapter 6. Hot Hands in Basketball -- Chapter 7. Restricted Choice -- Chapter 8. Another Conundrum : What Does Crowd Size at Wimbledon?s Tennis Match Tell us About Baseball Batting Averages?- Chapter 9. Cancer Clusters -- Chapter 10. Medical Mis-Readings -- Chapter 11. The Wrong Conclusion -- Chapter 12. Clinical Trials -- Chapter 13. Margin of Error -- Chapter 14. What Are the Odds of That?- Chapter 15. Turing?s Evidence -- Chapter 16. Bell?s Inequality -- Chapter 17. The Paradox of Random Arrivals -- Chapter 18. The Inverse Square Root Law -- Chapter 19. Runs, Again -- Chapter 20. Addendum : Tutorial on Elementary Probability. 330 $aThis book is about the interplay between chance and order, but limited to mostly binary events, such as success/failure as they occur in a diversity of interesting applications. The goal is to entertain and instruct with topics that range from unexpected encounters with chance in everyday experiences, to significant ?must know? insights regarding human health and other concerns in the social sciences. The first section provides the tools for being able to discuss random sequences with hints at what is to follow. This is followed by another surprising and, to some extent, bizarre result known as Stein?s Paradox, which is applied to baseball. The troublesome topic of disease clusters, namely to decide whether the clumping of events is due to chance or some environmental cause, is treated using both the Poisson and normal approximations to the binomial distribution and this leads naturally into a discussion of the base rate fallacy and a case study of hospital performance. Next, another medical case study this time concerning some tricky questions about the effectiveness of colonoscopy and other medical interventions. A brief discussion of the mathematics of clinical trials, follows. Then, the book examines the error in random sampling, when polling for candidate preference with specific current examples. The essential tool here is covariance of random variables. The author follows this with a treatment of the spooky quality of coincidence using appropriate mathematical tools. After this, code breaking at Bletchley Park using Baye?s theorem. It returns to Poisson events to discuss another unexpected result, followed by the use of spatial Poisson events in the delivery of emergency response services. Finally, an account of fluctuations that occur in a run of Bernoulli trials as a bookend to the very first section of the book. The probability theory involved is elementary using the binomial theorem and its extensions to Poisson and normal events in addition to conditional probability and covariance. The author provides an optional brief tutorial at the end, that covers the basic ideas in probability and statistics needed in the main text. Besides a list of references, several codes written in Matlab that were used to illustrate various topics in the text, as well as to support several figures that appear throughout, are provided. 410 0$aQuantitative Methods in the Humanities and Social Sciences,$x2199-0964 606 $aSocial sciences$xStatistical methods 606 $aStatistics 606 $aMultivariate analysis 606 $aStatistics in Social Sciences, Humanities, Law, Education, Behavorial Sciences, Public Policy 606 $aBayesian Network 606 $aProbabilitats$2thub 606 $aCičncies socials$2thub 606 $aEstadística matemŕtica$2thub 606 $aMultivariate Analysis 608 $aLlibres electrňnics$2thub 615 0$aSocial sciences$xStatistical methods. 615 0$aStatistics. 615 0$aMultivariate analysis. 615 14$aStatistics in Social Sciences, Humanities, Law, Education, Behavorial Sciences, Public Policy. 615 24$aBayesian Network. 615 7$aProbabilitats 615 7$aCičncies socials 615 7$aEstadística matemŕtica 615 24$aMultivariate Analysis. 676 $a519.2 700 $aBeltrami$b Edward$026772 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910899895303321 996 $aDigressions in Elementary Probability$94213959 997 $aUNINA