Philosophy of Probability and Statistical Modelling
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The Untenability of a Priori Prior Probabilities in Objective Bayesian Conditionalization
Running Head: OBJECTIVE BAYESIAN CONDITIONALIZATION 1 The Untenability of A Priori Prior Probabilities in Objective Bayesian Conditionalization Chris Arledge A Senior Thesis submitted in partial fulfillment of the requirements for graduation in the Honors Program Liberty University Spring 2013 2 OBJECTVE BAYESIAN CONDITIONALIZATION Acceptance of Senior Honors Thesis This Senior Honors Thesis is accepted in partial fulfillment of the requirements for graduation from the Honors Program of Liberty University. ______________________________ Thomas Provenzola, Ph.D. Thesis Chair ____________________________ Edward Martin, Ph.D. Committee Member ______________________________ Evangelos Skoumbourdis, Ph.D. Committee Member ______________________________ Brenda Ayres, Ph.D. Honors Director ______________________________ Date 3 OBJECTVE BAYESIAN CONDITIONALIZATION Table of Contents Preliminary Remarks ........................................................................................................ 5 A Quinean Argument Against A Priori Prior Probabilities .......................................... 9 Epistemic Issues Concerning A Priori Probability Distributions ............................... 17 Quantitative Difficulties Concerning A Priori Probability Distributions .................. 27 Problems of the Ontological Grounding of Objective A Priori Prior Probabilities in Propositions ...................................................................................................................... 31 Concluding Remarks ...................................................................................................... -
Lecture Notes for the Introduction to Probability Course
Lecture Notes for the Introduction to Probability Course Vladislav Kargin December 5, 2020 Contents 1 Combinatorial Probability and Basic Laws of Probabilistic Inference 4 1.1 What is randomness and what is probability?. 4 1.1.1 The classical definition of probability . 4 1.1.2 Kolmogorov’s Axiomatic Probability . 9 1.1.3 More about set theory and indicator functions . 12 1.2 Discrete Probability Models. 16 1.3 Sample-point method (Combinatorial probability) . 19 1.4 Conditional Probability and Independence . 29 1.4.1 Conditional probability . 30 1.4.2 Independence . 32 1.4.3 Law of total probability . 34 1.5 Bayes’ formula . 39 2 Discrete random variables and probability distributions. 44 2.1 Pmf and cdf . 44 2.2 Expected value . 49 2.2.1 Definition . 49 2.2.2 Expected value for a function of a r.v. 51 2.2.3 Properties of the expected value . 53 2.3 Variance and standard deviation . 55 2.3.1 Definition . 55 2.3.2 Properties. 57 1 2.4 The zoo of discrete random variables . 58 2.4.1 Binomial . 59 2.4.2 Geometric. 63 2.4.3 Negative binomial . 65 2.4.4 Hypergeometric . 68 2.4.5 Poisson . 70 2.5 Moments and moment-generating function . 75 2.6 Markov’s and Chebyshev’s inequalities . 80 3 Chapter 4: Continuous random variables. 84 3.1 Cdf and pdf . 84 3.2 Expected value and variance . 89 3.3 Quantiles . 91 3.4 The Uniform random variable . 92 3.5 The normal (or Gaussian) random variable. -
Husserl's Logic of Probability
Carlos Lobo / Husserl’s logic of probability META: RESEARCH IN HERMENEUTICS, PHENOMENOLOGY, AND PRACTICAL PHILOSOPHY VOL. XI, NO. 2 / DECEMBER 2019: 501-546, ISSN 2067-3655, www.metajournal.org Husserl’s Logic of Probability: An Attempt to Introduce in Philosophy the Concept of “Intensive” Possibility* Carlos Lobo Collège international de philosophie Abstract Husserl’s insisting reflections on the question of probability and the project of a logic of probability, although persisting throughout his work, published and unpublished, from the Prolegomena to later works (the Krisis), has not received any serious attention. While exposing the main lines of his project, this article aims at listing some of the reasons explaining this paradoxical situation. 1) The logic of probability is not conceived by Husserl as an extension of formal logic and especially of an already made logic, but as a reform of logic (from the recensions of Schröder to Formal and Transcendental Logic, and beyond). 2) This entails a revised notion of proposition, enlarged to every forms of “positions” or “thesis” and, extended, following the correlation of intentionality, to the noematic side. 3) The very notion of the “possible” at the basis of any logical, algebraic, arithmetic and geometric treatments of probability is enlarged and modified accordingly. 4) As a consequence, his position is rather singular and very hard to locate in the battle field among mathematicians, logicians and philosophers around the question of “foundation of probability” and the interpretation of probability calculus (a priori probability vs a posteriori probability, subjective vs objective probability, logical vs psychological probability, etc.). Keywords: possibility, modality, range, logic, von Kries In Formal and Transcendental Logic, Husserl declares explicitly that, in the Prolegomena, he committed a double fault in his presentation of “pure logic”, the second failing being a restriction of the scope of “formal logic”, by the exclusion of “modal modifications of judgement”.