000			05639nam a2200565Ii 4500
001			9781315370576
003			FlBoTFG
005			20220711212604.0
006			m o d
007			cr
008			190122t20182016fluab ob 001 0 eng d
020			_a9781315370576 (e-book : PDF)
035			_a(OCoLC)958800457
040			_aFlBoTFG _cFlBoTFG _erda
041	1		_aeng
050		4	_aQA273
072		7	_aMAT _x029000 _2bisacsh
072		7	_aMAT _x029010 _2bisacsh
072		7	_aPBT _2bicscc
082	0	4	_a519.201
100	1		_aProschan, Michael A., _eauthor. _917899
245	1	0	_aEssentials of Probability Theory for Statisticians / _cby Michael A. Proschan and Pamela A. Shaw.
250			_aFirst edition.
264		1	_aBoca Raton, FL : _bChapman and Hall/CRC, _c[2018].
264		4	_c©2016.
300			_a1 online resource (344 pages) : _b69 illustrations, text file, PDF.
336			_atext _2rdacontent
337			_acomputer _2rdamedia
338			_aonline resource _2rdacarrier
490	1		_aChapman & Hall/CRC Texts in Statistical Science
505	0	0	_tIntroduction Why More Rigor Is Needed -- Size Matters Cardinality Summary -- The Elements of Probability Theory Introduction Sigma-Fields The Event That An Occurs Infinitely Often Measures/Probability Measures Why Restriction of Sets Is Needed When We Cannot Sample Uniformly The Meaninglessness of Post-Facto Probability Calculations Summary -- Random Variables and Vectors Random Variables Random Vectors The Distribution Function of a Random Variable The Distribution Function of a Random Vector Introduction to Independence Take (, F, P) = ((0, 1), B(0,1), L), Please! Summary -- Integration and Expectation Heuristics of Two Different Types of Integrals LebesgueStieltjes Integration Properties of Integration Important Inequalities Iterated Integrals and More on Independence Densities Keep It Simple Summary -- Modes of Convergence Convergence of Random Variables Connections between Modes of Convergence Convergence of Random Vectors Summary -- Laws of Large Numbers Basic Laws and Applications Proofs and Extensions Random Walks Summary -- Central Limit Theorems CLT for iid Random Variables and Applications CLT for Non iid Random Variables Harmonic Regression Characteristic Functions Proof of Standard CLT Multivariate Ch.f.s and CLT Summary -- More on Convergence in Distribution Uniform Convergence of Distribution Functions The Delta Method Convergence of Moments: Uniform Integrability Normalizing Sequences Review of Equivalent Conditions for Weak Convergence Summary -- Conditional Probability and Expectation When There Is a Density or Mass FunctionMore General Definition of Conditional Expectation Regular Conditional Distribution Functions Conditional Expectation as a Projection Conditioning and Independence Sufficiency Expect the Unexpected from Conditional Expectation Conditional Distribution Functions as Derivatives Appendix: RadonNikodym Theorem Summary -- Applications F(X) ~ U[0, 1] and Asymptotics Asymptotic Power and Local Alternatives Insufficient Rate of Convergence in Distribution Failure to Condition on All Information Failure to Account for the Design Validity of Permutation Tests: I Validity of Permutation Tests: II Validity of Permutation Tests III A Brief Introduction to Path Diagrams Estimating the Effect Size Asymptotics of an Outlier Test An Estimator Associated with the Logrank Statistic -- Appendix A: Whirlwind Tour of Prerequisites Appendix B: Common Probability Distributions Appendix C: References Appendix D: Mathematical Symbols and Abbreviations -- Index.
520	3		_aEssentials of Probability Theory for Statisticians provides graduate students with a rigorous treatment of probability theory, with an emphasis on results central to theoretical statistics. It presents classical probability theory motivated with illustrative examples in biostatistics, such as outlier tests, monitoring clinical trials, and using adaptive methods to make design changes based on accumulating data. The authors explain different methods of proofs and show how they are useful for establishing classic probability results. After building a foundation in probability, the text intersperses examples that make seemingly esoteric mathematical constructs more intuitive. These examples elucidate essential elements in definitions and conditions in theorems. In addition, counterexamples further clarify nuances in meaning and expose common fallacies in logic. This text encourages students in statistics and biostatistics to think carefully about probability. It gives them the rigorous foundation necessary to provide valid proofs and avoid paradoxes and nonsensical conclusions.
530			_aAlso available in print format.
650		0	_aMathematical statistics. _99597
650		0	_aProbabilities. _94604
650		7	_aMATHEMATICS / Probability & Statistics / Bayesian Analysis. _2bisacsh _910717
650		7	_abiostatistics examples. _2bisacsh _917900
650		7	_aclassic probability results. _2bisacsh _917901
650		7	_adesign of clinical trials. _2bisacsh _917902
650		7	_ameasure theory. _2bisacsh _917335
650		7	_aprobability theory textbook. _2bisacsh _917903
650		7	_atheoretical statistics. _2bisacsh _917904
655		0	_aElectronic books. _93294
700	1		_aShaw, Pamela A., _eauthor. _917905
710	2		_aTaylor and Francis. _910719
776	0	8	_iPrint version: _z9781498704199
830		0	_aChapman & Hall/CRC Texts in Statistical Science. _917906
856	4	0	_uhttps://www.taylorfrancis.com/books/9781315370576 _zClick here to view.
942			_cEBK
999			_c71668 _d71668