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Die Architektur der Zufallsheit: Die Konstruktion moderner Statistiken mit Maßtheorie by Busra Hkt

Die Architektur der Zufallsheit: Die Konstruktion moderner Statistiken mit Maßtheorie

by Busra Hkt
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Book cover type: Paperback
  • ISBN13: 9798250418461
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Independently Published
  • Publisher Imprint: Independently Published
  • Publication Date:
  • Pages: 282
  • Original Price: GBP 18.41
  • Language: German
  • Edition: N/A
  • Item Weight: 381 grams
  • BISAC Subject(s): Calculus

Die mathematischen Grundlagen der modernen Statistik meistern

Moderne Statistik basiert nicht nur auf Formeln - sie ist auf der strengen Architektur der Ma theorie, Wahrscheinlichkeitsr�ume und der funktionalen Analysis aufgebaut. Dieses Buch bietet eine tiefgehende, systematische und axiomatische Darstellung der mathematischen Grundlagen, die die zeitgen�ssische Wahrscheinlichkeitstheorie und statistische Modellierung pr�gen.

Von Sigma-Algebren und dem Lebesgue-Ma bis zum Satz von Radon-Nikodym, bedingter Erwartung, Martingalen und statistischer Entscheidungstheorie wird der Leser durch das strukturelle R�ckgrat der modernen stochastischen Analysis gef�hrt.

Konzipiert f�r ernsthafte Lernende, Forschende und Fachleute schl�gt dieses Werk eine Br�cke zwischen reiner Ma theorie und fortgeschrittener Wahrscheinlichkeitstheorie sowie dem theoretischen Rahmen statistischer Inferenz.


F�r wen ist dieses Buch geeignet?

  • Masterstudierende der Mathematik, Statistik oder angewandten Mathematik

  • Doktoranden im Bereich Wahrscheinlichkeitstheorie oder statistische Modellierung

  • Forschende in stochastischen Prozessen und mathematischer Statistik

  • Data Scientists mit Interesse an tiefen theoretischen Grundlagen

  • Lehrende f�r ma theoretische Wahrscheinlichkeit

  • Alle, die von klassischer Wahrscheinlichkeit zu rigoroser moderner Wahrscheinlichkeitstheorie wechseln m�chten


Welche Fragen werden in diesem Buch beantwortet?

  • Wie wird das Lebesgue-Ma aus einem �u eren Ma konstruiert?

  • Was macht eine Funktion messbar?

  • Warum ist der Satz von Radon-Nikodym grundlegend f�r moderne Wahrscheinlichkeit?

  • Wie wird der Erwartungswert ma theoretisch definiert?

  • Wie sieht die rigorose Struktur der bedingten Erwartung aus?

  • Wie f�hren Produktma e zu den S�tzen von Fubini und Tonelli?

  • Welche Rolle spielt Unabh�ngigkeit in der strukturellen Wahrscheinlichkeitstheorie?

  • Wie bildet die Ma theorie das Fundament moderner statistischer Modelle?

  • Wie werden Likelihood, Suffizienz und Fisher-Information streng definiert?

  • Was verbindet Wahrscheinlichkeitsma e mit der statistischen Entscheidungstheorie?


Zentrale Themen

Grundlagen der Ma theorie
Sigma-Algebren und messbare Funktionen
Carath�odory-Konstruktion
Lebesgue-Integral und Lp-R�ume
Produktma e und unendlich-dimensionale Konstruktionen
Kolmogorov-Axiome und Wahrscheinlichkeitsr�ume
Satz von Radon-Nikodym
Bedingte Erwartung und Martingale
Unabh�ngigkeit und Null-Eins-Gesetze
Parametrische statistische Modelle
Likelihood-Theorie und Fisher-Information
Ma theoretische Entscheidungstheorie

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