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L'architettura della Casualità: La Costruzione della Statistica Moderna con la Teoria della Misura by Busra Hkt

L'architettura della Casualità: La Costruzione della Statistica Moderna con la Teoria della Misura

by Busra Hkt
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Book cover type: Paperback
  • ISBN13: 9798250419994
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Independently Published
  • Publisher Imprint: Independently Published
  • Publication Date:
  • Pages: 266
  • Original Price: GBP 18.41
  • Language: Italian
  • Edition: N/A
  • Item Weight: 359 grams
  • BISAC Subject(s): General

Padroneggia i fondamenti matematici della statistica moderna

La statistica moderna non si basa soltanto su formule - � costruita sull'architettura rigorosa della teoria della misura, degli spazi di probabilit� e dell'analisi funzionale. Questo libro offre un'esplorazione profonda, sistematica e assiomatica delle fondamenta matematiche che modellano la teoria contemporanea della probabilit� e la modellizzazione statistica.

Dalle sigma-algebre e dalla misura di Lebesgue al teorema di Radon-Nikodym, all'aspettazione condizionata, alle martingale e alla teoria della decisione statistica, il lettore viene guidato attraverso la struttura portante dell'analisi stocastica moderna.

Progettato per studenti avanzati, ricercatori e professionisti, quest'opera collega la teoria pura della misura alla probabilit� avanzata e al quadro teorico dell'inferenza statistica.


Chi dovrebbe leggere questo libro?

  • Studenti magistrali in matematica, statistica o matematica applicata

  • Dottorandi in teoria della probabilit� o modellizzazione statistica

  • Ricercatori in processi stocastici e statistica matematica

  • Data scientist che desiderano solide basi teoriche

  • Docenti di probabilit� assiomatica

  • Chiunque voglia passare dalla probabilit� classica alla probabilit� moderna rigorosa


Domande a cui questo libro risponde

  • Come viene costruita la misura di Lebesgue a partire dalla misura esterna?

  • Cosa rende una funzione misurabile?

  • Perch� il teorema di Radon-Nikodym � fondamentale nella probabilit� moderna?

  • Come viene definita l'aspettazione in termini misura-teorici?

  • Qual � la struttura rigorosa dell'aspettazione condizionata?

  • In che modo le misure prodotto conducono ai teoremi di Fubini e Tonelli?

  • Qual � il ruolo dell'indipendenza nella probabilit� strutturale?

  • Come la teoria della misura costituisce la base dei modelli statistici moderni?

  • Come vengono definite rigorosamente la verosimiglianza, la sufficienza e l'informazione di Fisher?

  • Qual � il legame tra misure di probabilit� e teoria della decisione statistica?


Argomenti principali trattati

Fondamenti di teoria della misura
Sigma-algebre e funzioni misurabili
Costruzione di Carath�odory
Integrale di Lebesgue e spazi Lp
Misure prodotto e costruzioni infinito-dimensionali
Assiomi di Kolmogorov e spazi di probabilit�
Teorema di Radon-Nikodym
Aspettazione condizionata e martingale
Indipendenza e leggi zero-uno
Modelli statistici parametrici
Teoria della verosimiglianza e informazione di Fisher
Teoria della decisione in prospettiva misura-teorica

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