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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Wahrscheinlichkeitstheorie & Statistik The Principles of Probability
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The Principles of Probability
Jason Swanson (Broschiert, Englisch)
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Beschreibung
This book presents a logical system that is able to capture all aspects of modern probability as it is practiced today. The system is then used to rigorously formulate the principle of indifference. Using nine rules of inductive inference, a calculus of probability is developed that operates directly on sentences – without reference to outcomes or sample spaces. Its surprising strength is… expressed by three embedding theorems, based on an underlying many-worlds semantics in which random variables play a foundational role. The calculus allows a formal treatment of the principle of indifference. Roughly speaking, this heuristic idea, which dates back to the time of Laplace, says that we should assign the same probability to two possibilities about which we are "equally ignorant". Despite being almost self-evident, the principle has a problematic history. It is well known to produce paradoxes when used without caution. This is the first logical system to fully codify modern probability, revealing it to be a form of logic, as Leibniz and Boole envisioned. Modern science is more probabilistic today than ever before. Once shunned by the mainstream, Bayesian ideas now flourish. In such an environment, it is not enough to know how to calculate probabilities. We must understand the nature of probability itself. We must have a conceptual mindset to drive our calculations and our model building. The logical system described in this book lays bare this mindset, showing it to us with explicit clarity. 80,24 €
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Technische Daten
Erscheinungsdatum
17.04.2026
Sprache
Englisch
EAN
9783032094490
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Lecture Notes in Mathematics
Sonderedition
Nein
Autor
Jason Swanson
Seitenanzahl
288
Einbandart
Broschiert
Buch Untertitel
From Formal Logic to Measure Theory to the Principle of Indifference
Schlagwörter
principles of probability, logic and probability, probabilistic logic, inductive logic, principle of indifference, principle of insufficient reason, infinitary logic
Thema-Inhalt
PBT - Wahrscheinlichkeitsrechnung und Statistik
PBWL - Stochastik
PBCD - Mathematik: Logik
PBC - Mathematische Grundlagen
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Palgrave Macmillan, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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