slides - John L. Pollock

... can make about probabilities, and a very rich mathematical theory grounding them. • It is these defeasible inferences that enable us to make practical use of probabilities without being able to deduce everything we need via the probability calculus. • I will argue that, on a certain conception of pr ...

... can make about probabilities, and a very rich mathematical theory grounding them. • It is these defeasible inferences that enable us to make practical use of probabilities without being able to deduce everything we need via the probability calculus. • I will argue that, on a certain conception of pr ...

Reducing belief simpliciter to degrees of belief

... some of them even apply qualitative and quantitative concepts of belief within one and the same theory (Isaac Levi is a classical example; cf. [27,28]).2 When we say qualitative belief here—also called ‘belief simpliciter’, ‘ﬂat-out-belief’, ‘all-or-nothing belief’, ‘binary belief’, or simply ‘belie ...

... some of them even apply qualitative and quantitative concepts of belief within one and the same theory (Isaac Levi is a classical example; cf. [27,28]).2 When we say qualitative belief here—also called ‘belief simpliciter’, ‘ﬂat-out-belief’, ‘all-or-nothing belief’, ‘binary belief’, or simply ‘belie ...

Notes on Bayesian Confirmation Theory

... “event”, for which reason bct is usually presented as a theory in which probabilities range over propositions. My formal presentation respects this custom, but the commentary uses the notion of event wherever it seems natural. ...

... “event”, for which reason bct is usually presented as a theory in which probabilities range over propositions. My formal presentation respects this custom, but the commentary uses the notion of event wherever it seems natural. ...

Logical Foundations of Induction

... the human species; John, Peter and Smith eat; therefore every man eats. It may here be said that the conclusion asserts a causal relation between humanity and eating, (ii) Aristotle may not insist on regarding the conclusion as asserting a causal relation, but show the fact that men eat, by complete ...

... the human species; John, Peter and Smith eat; therefore every man eats. It may here be said that the conclusion asserts a causal relation between humanity and eating, (ii) Aristotle may not insist on regarding the conclusion as asserting a causal relation, but show the fact that men eat, by complete ...

Probabilistic Logics and Probabilistic Networks - blogs

... Part I of this paper is devoted to showing that the fundamental question outlined above is indeed very general, providing a framework into which several common inferential procedures fit. Since the fundamental question of probabilistic logic differs from that of non-probabilistic logic, different te ...

... Part I of this paper is devoted to showing that the fundamental question outlined above is indeed very general, providing a framework into which several common inferential procedures fit. Since the fundamental question of probabilistic logic differs from that of non-probabilistic logic, different te ...

doc - John L. Pollock

... as actual instances. Theories of this sort are sometimes called “hypothetical frequency theories”. C. S. Peirce was perhaps the first to make a suggestion of this sort. Similarly, the statistician R. A. Fisher, regarded by many as “the father of modern statistics”, identified probabilities with rat ...

... as actual instances. Theories of this sort are sometimes called “hypothetical frequency theories”. C. S. Peirce was perhaps the first to make a suggestion of this sort. Similarly, the statistician R. A. Fisher, regarded by many as “the father of modern statistics”, identified probabilities with rat ...

Chap 4 from Ross

... States 0 and N are called absorbing states since once entered they are never left. Note that the preceding is a finite state random walk with absorbing barriers (states 0 and N ). ...

... States 0 and N are called absorbing states since once entered they are never left. Note that the preceding is a finite state random walk with absorbing barriers (states 0 and N ). ...

Full Article as PDF

... connected in simple or multiple chains. Here the outcome of the current trial was dependent on that of one or more preceding ones.1 In those six years, Markov could not think of a practical illustration and empirical verification of his deductions, or was not interested in finding one.2 But then, in ...

... connected in simple or multiple chains. Here the outcome of the current trial was dependent on that of one or more preceding ones.1 In those six years, Markov could not think of a practical illustration and empirical verification of his deductions, or was not interested in finding one.2 But then, in ...

When Did Bayesian Inference Become “Bayesian”?

... subjective meanings of probability. Cournot (35), for example, sharply criticized Condorcet’s and Laplace’s approach to the probabilities of causes (see Daston (38) for a detailed discussion of what all of these authors meant by these terms). This focus on the meaning of probability quickly spread t ...

... subjective meanings of probability. Cournot (35), for example, sharply criticized Condorcet’s and Laplace’s approach to the probabilities of causes (see Daston (38) for a detailed discussion of what all of these authors meant by these terms). This focus on the meaning of probability quickly spread t ...

When Did Bayesian Inference Become “Bayesian”? Stephen E. Fienberg

... subjective meanings of probability. Cournot (35), for example, sharply criticized Condorcet’s and Laplace’s approach to the probabilities of causes (see Daston (38) for a detailed discussion of what all of these authors meant by these terms). This focus on the meaning of probability quickly spread t ...

... subjective meanings of probability. Cournot (35), for example, sharply criticized Condorcet’s and Laplace’s approach to the probabilities of causes (see Daston (38) for a detailed discussion of what all of these authors meant by these terms). This focus on the meaning of probability quickly spread t ...

Why do we change whatever amount we found in the first

... This may not occur often, but when it does, the heavy loss the player incurs means that, on average, there is no advantage in switching. This resolves all practical cases of the problem, whether or not the player looks in their envelope [12] 39. ...

... This may not occur often, but when it does, the heavy loss the player incurs means that, on average, there is no advantage in switching. This resolves all practical cases of the problem, whether or not the player looks in their envelope [12] 39. ...

Design and Implementation of Advanced Bayesian Networks with

... advances in monitoring equipment and medical laboratory tests, there would be too much information to account for before the surgeon could decide on his ...

... advances in monitoring equipment and medical laboratory tests, there would be too much information to account for before the surgeon could decide on his ...

Chapter 5 Probability Representations

... Show that no one-dimensional unfolding representation is possible. ...

... Show that no one-dimensional unfolding representation is possible. ...

De Finetti on uncertainty - Oxford Academic

... can be calculated on the basis of general principles, namely, by starting out with equal probabilities as in fair games of chance (‘a priori probability’). The second is where it is possible to identify classes of more or less homogeneous trials on the basis of which relative frequencies can be dete ...

... can be calculated on the basis of general principles, namely, by starting out with equal probabilities as in fair games of chance (‘a priori probability’). The second is where it is possible to identify classes of more or less homogeneous trials on the basis of which relative frequencies can be dete ...

On Generalized Measures of Information with

... number to (measure) any phenomena that we come across, it is natural to ask the following question. How one would measure ‘information’? The question was asked at the beginning of this age of information sciences and technology itself and a satisfactory answer was given. The theory of information wa ...

... number to (measure) any phenomena that we come across, it is natural to ask the following question. How one would measure ‘information’? The question was asked at the beginning of this age of information sciences and technology itself and a satisfactory answer was given. The theory of information wa ...

A Joint Characterization of Belief Revision Rules

... three rules, the literature has focused on a ‘distance-based’approach. This consists in showing that a given revision rule is a minimal revision rule, which generates new beliefs that deviate as little as possible from initial beliefs, subject to certain constraints (given by the learning experienc ...

... three rules, the literature has focused on a ‘distance-based’approach. This consists in showing that a given revision rule is a minimal revision rule, which generates new beliefs that deviate as little as possible from initial beliefs, subject to certain constraints (given by the learning experienc ...

Notes on stochastic processes

... called a random function, is a mathematical object usually defined as a collection of random variables. Historically, the random variables were indexed by some set of increasing numbers, usually viewed as time, giving the interpretation of a stochastic process representing numerical values of some r ...

... called a random function, is a mathematical object usually defined as a collection of random variables. Historically, the random variables were indexed by some set of increasing numbers, usually viewed as time, giving the interpretation of a stochastic process representing numerical values of some r ...

Conditionals predictions

... problems by giving up the notion that conditionals denote propositions in the usual sense. Even so, however, the random-variable approach makes counterintuitive predictions in simple cases of embedded conditionals. I propose to address this problem by enriching the model with an explicit representat ...

... problems by giving up the notion that conditionals denote propositions in the usual sense. Even so, however, the random-variable approach makes counterintuitive predictions in simple cases of embedded conditionals. I propose to address this problem by enriching the model with an explicit representat ...

Physiological time-series analysis: what does regularity

... by a single epoch of quiet sleep (- 1,000 points of HR data, with some system noise present) affect statistical analysis? and 4) What is a possible physiological basis for greater regularity (decreased complexity) under pathological conditions? Over the past three years, a new mathematical approach ...

... by a single epoch of quiet sleep (- 1,000 points of HR data, with some system noise present) affect statistical analysis? and 4) What is a possible physiological basis for greater regularity (decreased complexity) under pathological conditions? Over the past three years, a new mathematical approach ...

What is Probability? Patrick Maher August 27, 2010

... It has often been asserted that “probability” means some person’s degrees of belief. Here are a few examples: By degree of probability we really mean, or ought to mean, degree of belief. (de Morgan 1847, 172) Probability measures the confidence that a particular individual has in the truth of a part ...

... It has often been asserted that “probability” means some person’s degrees of belief. Here are a few examples: By degree of probability we really mean, or ought to mean, degree of belief. (de Morgan 1847, 172) Probability measures the confidence that a particular individual has in the truth of a part ...

The Flawed Probabilistic Foundation of Law and Economics

... penalties and rewards is to align people’s selfish interests with the interests of society. The law tries to make it privately beneficial for individuals to behave in socially desirable ways. To affect individuals’ choices among different courses of action, the law’s threats of penalties and promise ...

... penalties and rewards is to align people’s selfish interests with the interests of society. The law tries to make it privately beneficial for individuals to behave in socially desirable ways. To affect individuals’ choices among different courses of action, the law’s threats of penalties and promise ...

Entropy Demystified : The Second Law Reduced to Plain Common

... The second point was while I was reading the two books by Brian Greene.3 In discussing the entropy and the Second Law, Greene wrote4 : “Among the features of common experience that have resisted complete explanation is one that taps into the deepest unresolved mysteries in modern physics.” I could n ...

... The second point was while I was reading the two books by Brian Greene.3 In discussing the entropy and the Second Law, Greene wrote4 : “Among the features of common experience that have resisted complete explanation is one that taps into the deepest unresolved mysteries in modern physics.” I could n ...

conditional probability - ANU School of Philosophy

... some body of evidence or information, probability relativised to a specified set of outcomes, where typically this set does not exhaust all possible outcomes. Yet understood that way, it might seem that all probability is conditional probability — after all, whenever we model a situation probabilist ...

... some body of evidence or information, probability relativised to a specified set of outcomes, where typically this set does not exhaust all possible outcomes. Yet understood that way, it might seem that all probability is conditional probability — after all, whenever we model a situation probabilist ...

# 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.