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Markov Chain Monte Carlo - Methoden

Markov Chain Monte Carlo - Methoden


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About the Book

In seiner Arbeit beschäftigt sich der Autor mit der 'Markov Chain Monte Carlo', auch abgekürzt als MCMC. Dabei handelt es sich um eine Monte Carlo Methode. Allen Monte Carlo Methoden ist gemein, dass sie von einer mehr oder minder komplizierten Verteilung zufällige Szenarien erzeugen. Diese Szenarien werden dann genutzt um Aussagen über Erwartungswerte oder andere Kennzahlen der Verteilung zu treffen. Diese Aussagen sind natürlich nur zu gebrauchen, wenn man sehr viele zufällig erzeugte Szenarien auswertet. Die Methode kommt also immer dann zum Einsatz, wenn es nicht möglich ist, aus der Verteilung der Szenarien direkt Rückschlüsse auf die statistischen Kennzahlen der Verteilung zu ziehen, weder auf analytischem Wege, noch durch numerische Integration (bei sehr vielen Dimensionen steigt der Aufwand rapide an). Markov Chain Monte Carlo ist nun eine spezielle Monte Carlo Methode unter Zuhilfenahme von Markovketten. Diese kommt immer dann zum Einsatz, wenn es nicht möglich ist, von einer Verteilung auf einfache Weise Szenarien zu erzeugen. Eine Markovkette fängt bei einem Zustand an und geht von einem bestimmten Zustand mit einer bestimmten Wahrscheinlichkeit zu einem anderen Zustand über. Diese Übergangswahrscheinlichkeiten stehen in einer Übergangsmatrix. Der Knackpunkt ist nun, dass diese Form der Zustandsgenerierung oft einfacher zu implementieren ist, als direkt auf eine Verteilung zurückzugreifen. In der Arbeit gibt es mehrere konkrete Beispiele für den Einsatz solcher Methoden. Quelltexte der Implementierungen sind beigefügt.
About the Author: Thomas Plehn ist studierter Lehrer für Mathematik und Physik mit erstem Staatsexamen 2007 an der Universität Bielefeld. Nach einem zusätzlichen Masterstudium der Optimierung und Simulation an der FH Bielefeld ist er nun in der Softwareindustrie tätig.


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Product Details
  • ISBN-13: 9783956844515
  • Publisher: Bachelor + Master Publishing
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Spine Width: 3 mm
  • Weight: 132 gr
  • ISBN-10: 3956844513
  • Publisher Date: 22 May 2014
  • Height: 210 mm
  • No of Pages: 58
  • Series Title: German
  • Sub Title: Herleitung, Beweis und Implementierung
  • Width: 148 mm


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