Probability and Statistics
... individuals originating from identical ova, become very different from each other. In addition, the environment influences the conditions of selection; it thus changes the type both directly and obliquely. As long as such changes are reversible, their study is guided by the principles described abov ...
... individuals originating from identical ova, become very different from each other. In addition, the environment influences the conditions of selection; it thus changes the type both directly and obliquely. As long as such changes are reversible, their study is guided by the principles described abov ...
Dissertations on Probability in Paris in the 1930s
... some basic information, referring the reader to their work.32 However a few words on the careers of Doeblin and Fortet will provide some context for their doctoral research.33 In 1938, five years after arriving in Paris, Doeblin published a paper, “Sur les propriétés asymptotiques de mouvements re ...
... some basic information, referring the reader to their work.32 However a few words on the careers of Doeblin and Fortet will provide some context for their doctoral research.33 In 1938, five years after arriving in Paris, Doeblin published a paper, “Sur les propriétés asymptotiques de mouvements re ...
The origins and legacy of Kolmogorov`s Grundbegriffe
... equally likely cases, held sway for two hundred years. Its elements were put in place by Jacob Bernoulli and Abraham De Moivre early in the eighteenth century, and they remained in place in the early twentieth century. Even today the classical foundation is used in teaching probability. Although twe ...
... equally likely cases, held sway for two hundred years. Its elements were put in place by Jacob Bernoulli and Abraham De Moivre early in the eighteenth century, and they remained in place in the early twentieth century. Even today the classical foundation is used in teaching probability. Although twe ...
4 Combinatorics and Probability
... nine squares of a tic-tac-toe board (a 3×3 matrix) in any combination (i.e., unlike ordinary tic-tac-toe, it is not necessary that X’s and O’s be placed alternately, so, for example, all the squares could wind up with X’s). Squares may also be blank, i.e., not containing either an X or and O. How ma ...
... nine squares of a tic-tac-toe board (a 3×3 matrix) in any combination (i.e., unlike ordinary tic-tac-toe, it is not necessary that X’s and O’s be placed alternately, so, for example, all the squares could wind up with X’s). Squares may also be blank, i.e., not containing either an X or and O. How ma ...
Physics and chance
... quantitative evidence of the interconvertibility of heat and overt mechanical energy with the conservation of their sum, and on the large body of evidence for the atomic constitution of matter coming from other areas of science (chemistry, electro-chemistry, and so on). 2. Maxwell In I860, J. Maxwel ...
... quantitative evidence of the interconvertibility of heat and overt mechanical energy with the conservation of their sum, and on the large body of evidence for the atomic constitution of matter coming from other areas of science (chemistry, electro-chemistry, and so on). 2. Maxwell In I860, J. Maxwel ...
From imprecise probability assessments to conditional probabilities
... The values p◦ , p◦ can be determined by exploiting a suitable algorithm given in Biazzo and Gilio [2000]. By the same algorithm, starting with a g-coherent assessment AJn on FJn , we can make the ”least-committal” correction (see Pelessoni and Vicig [1998]) of AJn . In this way, we obtain the cohere ...
... The values p◦ , p◦ can be determined by exploiting a suitable algorithm given in Biazzo and Gilio [2000]. By the same algorithm, starting with a g-coherent assessment AJn on FJn , we can make the ”least-committal” correction (see Pelessoni and Vicig [1998]) of AJn . In this way, we obtain the cohere ...
On Worst-Case to Average-Case Reductions for NP Problems
... neither of them uses the fact that the reduction that transforms the adversary into an algorithm for L is correct even if the adversary only performs its task well on average. In fact, the arguments merely assume that the reduction behaves correctly when given oracle access to an adversary that vio ...
... neither of them uses the fact that the reduction that transforms the adversary into an algorithm for L is correct even if the adversary only performs its task well on average. In fact, the arguments merely assume that the reduction behaves correctly when given oracle access to an adversary that vio ...
De Finetti and Savage on the normative relevance of imprecise
... SMITH (1965, 478) illustrated his viewpoint as follows: «if I am willing to bet 2 to 1 on sun against rain, and 1 to 4 on rain against sun, this means that I regard sun as between 2 and 4 times as probable as rain; and I do not need to be more precise than this». As a result the elicitation of proba ...
... SMITH (1965, 478) illustrated his viewpoint as follows: «if I am willing to bet 2 to 1 on sun against rain, and 1 to 4 on rain against sun, this means that I regard sun as between 2 and 4 times as probable as rain; and I do not need to be more precise than this». As a result the elicitation of proba ...
Conditionals, indeterminacy, and triviality
... If (1-a) is Ramseyan, then the likelihood of (1-a) goes by the conditional likelihood that the Bulls won given that Jordan played last night—and the latter value is high since the Bulls almost always win when Jordan plays, so we predict that (1-a) is very likely. Furthermore, we predict if (1-b) is ...
... If (1-a) is Ramseyan, then the likelihood of (1-a) goes by the conditional likelihood that the Bulls won given that Jordan played last night—and the latter value is high since the Bulls almost always win when Jordan plays, so we predict that (1-a) is very likely. Furthermore, we predict if (1-b) is ...
- Philsci
... addressing the mainly methodological question how causality can be inferred from statistical data. By contrast, this article is about causal probability, i.e. the conceptual question how probability can be integrated into a general framework of induction and causation. In recent discussions on the f ...
... addressing the mainly methodological question how causality can be inferred from statistical data. By contrast, this article is about causal probability, i.e. the conceptual question how probability can be integrated into a general framework of induction and causation. In recent discussions on the f ...
Thesis - Connected Mathematics: Building Concrete Relationships
... This research develops an approach to learning mathematics called "connected mathematics" which emphasizes learners’ negotiation of mathematical meaning. I have employed this approach by conducting in-depth mathematical interviews with adult learners. Through these interviews, I also infer the impac ...
... This research develops an approach to learning mathematics called "connected mathematics" which emphasizes learners’ negotiation of mathematical meaning. I have employed this approach by conducting in-depth mathematical interviews with adult learners. Through these interviews, I also infer the impac ...
Symmetry and Probability - Academic Commons
... outcomes. . . Thousands of soldiers during the medieval times could attest to the dierences in the. . . relative frequencies. . . of dierent events related to the outcomes in [a game in which two dice are cast]. . .. While waiting to attack a certain town, the soldiers had thousands of hours with ...
... outcomes. . . Thousands of soldiers during the medieval times could attest to the dierences in the. . . relative frequencies. . . of dierent events related to the outcomes in [a game in which two dice are cast]. . .. While waiting to attack a certain town, the soldiers had thousands of hours with ...
Conditioning using conditional expectations: The Borel
... insufficiency in naïve conditioning that can be avoided within the measure theoretic framework by formulating the problem of conditioning properly and carefully. Once this is done, the BorelKolmogorov Paradox is resolved. Kolmogorov himself took this latter position [16][p. 50-51]. Billingsley [2][p ...
... insufficiency in naïve conditioning that can be avoided within the measure theoretic framework by formulating the problem of conditioning properly and carefully. Once this is done, the BorelKolmogorov Paradox is resolved. Kolmogorov himself took this latter position [16][p. 50-51]. Billingsley [2][p ...
Full Version
... the next day is sunny with 80% probability and rainy with 20% probability). Forecasting is also used by many firms, investors, and governments to make decisions based on the forecasts of variables such as demand, stock prices, unemployment rates, and energy consumption. Entire industries, such as ma ...
... the next day is sunny with 80% probability and rainy with 20% probability). Forecasting is also used by many firms, investors, and governments to make decisions based on the forecasts of variables such as demand, stock prices, unemployment rates, and energy consumption. Entire industries, such as ma ...
Probability and Forensic Science
... Given the use to which our assessment is being Given the use to which our assessment is being put, it is desirable that our assessment is not wholly based on intuition wholly based on intuition Is there a way in which we can do this? ...
... Given the use to which our assessment is being Given the use to which our assessment is being put, it is desirable that our assessment is not wholly based on intuition wholly based on intuition Is there a way in which we can do this? ...
arXiv:math/0006233v3 [math.ST] 9 Oct 2001
... a “typical” member. Following Shen [17] (see also [21], [18], [20]), this can be generalized to computable probability mass functions for which the data is “typical.” Related aspects of “randomness deficiency” (formally defined later in (IV.1)) were formulated in [12], [13] and studied in [17], [21] ...
... a “typical” member. Following Shen [17] (see also [21], [18], [20]), this can be generalized to computable probability mass functions for which the data is “typical.” Related aspects of “randomness deficiency” (formally defined later in (IV.1)) were formulated in [12], [13] and studied in [17], [21] ...
7. Probability and Statistics Soviet Essays
... empirical checking of its deductions leads to the conclusion that the theory of probability is far from being able to consider all abstract sets. However, under appropriate restrictions and taking some precautions, on which I cannot dwell here, an arithmetization of infinite sets, i.e., the determin ...
... empirical checking of its deductions leads to the conclusion that the theory of probability is far from being able to consider all abstract sets. However, under appropriate restrictions and taking some precautions, on which I cannot dwell here, an arithmetization of infinite sets, i.e., the determin ...
Probability and Chance
... a subjective probability to a proposition is sometimes called a partial belief. In its second form, associated most often with the term logical probability, epistemic probability measures the impact of a piece or pieces of evidence on a proposition. As such, it may not have the structure of a probab ...
... a subjective probability to a proposition is sometimes called a partial belief. In its second form, associated most often with the term logical probability, epistemic probability measures the impact of a piece or pieces of evidence on a proposition. As such, it may not have the structure of a probab ...
The Curious Case of Noninteractive Commitments
... {0, 1}n which f (x) is accepted by the circuit. It is easy to see that a random oracle is a hitting oneway function with overwhelming probability (see Lemma 5.2). Furthermore, we show that there exists a non-black-box construction of non-interactive commitments from hitting one-way functions as foll ...
... {0, 1}n which f (x) is accepted by the circuit. It is easy to see that a random oracle is a hitting oneway function with overwhelming probability (see Lemma 5.2). Furthermore, we show that there exists a non-black-box construction of non-interactive commitments from hitting one-way functions as foll ...
Bruno de Finetti and Imprecision
... countably additive probability, both regarding unconditional and conditional probability. Criticism from the prevailing measure theoretic approach to probability often dubbed finitely additive subjective probability as arbitrary. It might have been too hard to spread the even more innovative concepts ...
... countably additive probability, both regarding unconditional and conditional probability. Criticism from the prevailing measure theoretic approach to probability often dubbed finitely additive subjective probability as arbitrary. It might have been too hard to spread the even more innovative concepts ...
Probability
... 4. Katie is trick or treating. The man answering the door holds out two bags. In one bag, there are 3 bars of dark chocolate and 1 bar of white chocolate. In the other bag, there are 3 pieces of strawberry licorice, 1 piece of cherry licorice, and 1 piece of orange licorice. If Katie gets to randoml ...
... 4. Katie is trick or treating. The man answering the door holds out two bags. In one bag, there are 3 bars of dark chocolate and 1 bar of white chocolate. In the other bag, there are 3 pieces of strawberry licorice, 1 piece of cherry licorice, and 1 piece of orange licorice. If Katie gets to randoml ...
65. Gnedenko, Khinchin. Elementary probability
... Thirty five years have passed since the appearance of the first edition of this book written on the suggestion of the late Khinchin. After his death I have inserted various changes and additions. The book did not lose readers and I am pleased that some of them have accordingly been led to deep thoug ...
... Thirty five years have passed since the appearance of the first edition of this book written on the suggestion of the late Khinchin. After his death I have inserted various changes and additions. The book did not lose readers and I am pleased that some of them have accordingly been led to deep thoug ...
A Probabilistic Boolean Logic and its Meaning
... studied the power of axiomatic systems and mathematical proof of a probabilistic nature [9]). Historically, probabilistic behavior was realized by adding an external source of randomness to conventional logic based constructs, such as gates and automata, to induce randomness and hence probabilistic ...
... studied the power of axiomatic systems and mathematical proof of a probabilistic nature [9]). Historically, probabilistic behavior was realized by adding an external source of randomness to conventional logic based constructs, such as gates and automata, to induce randomness and hence probabilistic ...
Probability - OnlineStatBook
... Inferential statistics is built on the foundation of probability theory, and has been remarkably successful in guiding opinion about the conclusions to be drawn from data. Yet (paradoxically) the very idea of probability has been plagued by controversy from the beginning of the subject to the presen ...
... Inferential statistics is built on the foundation of probability theory, and has been remarkably successful in guiding opinion about the conclusions to be drawn from data. Yet (paradoxically) the very idea of probability has been plagued by controversy from the beginning of the subject to the presen ...
Algorithmic Statistics - Computer Science
... data is a “typical” member. Following Shen [16] (see also [20], [17], [19]), this can be generalized to computable probability mass functions for which the data is “typical.” Related aspects of “randomness deficiency” (formally defined later in (IV.1)) were formulated in [11], [12] and studied in [1 ...
... data is a “typical” member. Following Shen [16] (see also [20], [17], [19]), this can be generalized to computable probability mass functions for which the data is “typical.” Related aspects of “randomness deficiency” (formally defined later in (IV.1)) were formulated in [11], [12] and studied in [1 ...
History of randomness
In ancient history, the concepts of chance and randomness were intertwined with that of fate. Many ancient peoples threw dice to determine fate, and this later evolved into games of chance. At the same time, most ancient cultures used various methods of divination to attempt to circumvent randomness and fate.The Chinese were perhaps the earliest people to formalize odds and chance 3,000 years ago. The Greek philosophers discussed randomness at length, but only in non-quantitative forms. It was only in the sixteenth century that Italian mathematicians began to formalize the odds associated with various games of chance. The invention of modern calculus had a positive impact on the formal study of randomness. In the 19th century the concept of entropy was introduced in physics.The early part of the twentieth century saw a rapid growth in the formal analysis of randomness, and mathematical foundations for probability were introduced, leading to its axiomatization in 1933. At the same time, the advent of quantum mechanics changed the scientific perspective on determinacy. In the mid to late 20th-century, ideas of algorithmic information theory introduced new dimensions to the field via the concept of algorithmic randomness.Although randomness had often been viewed as an obstacle and a nuisance for many centuries, in the twentieth century computer scientists began to realize that the deliberate introduction of randomness into computations can be an effective tool for designing better algorithms. In some cases, such randomized algorithms are able to outperform the best deterministic methods.