When Did Bayesian Inference Become “Bayesian”? Stephen E. Fienberg
... of inverse probability. Why did the change occur? To whom should the term and its usage be attributed? What was the impact of the activities surrounding the adoption of the adjective “Bayesian”? Why do many statisticians now refer to themselves as Bayesian?7 These are some of the questions I plan to ...
... of inverse probability. Why did the change occur? To whom should the term and its usage be attributed? What was the impact of the activities surrounding the adoption of the adjective “Bayesian”? Why do many statisticians now refer to themselves as Bayesian?7 These are some of the questions I plan to ...
De Finetti on uncertainty - Oxford Academic
... Singell, 1987), because probability is not an objective attribute of external events, but a property of the way individuals think about them. But as we will see, it can equally be argued that Knight’s estimates do not necessarily coincide with subjective probabilities even from an epistemic viewpoin ...
... Singell, 1987), because probability is not an objective attribute of external events, but a property of the way individuals think about them. But as we will see, it can equally be argued that Knight’s estimates do not necessarily coincide with subjective probabilities even from an epistemic viewpoin ...
Probabilistic Logics and Probabilistic Networks - blogs
... concerned with the extent that a (logically complex) conclusion hypothesis is confirmed by a range of premise hypotheses and evidential statements which are themselves uncertain. In bioinformatics we are often interested in the probability that a complex molecule ψ is present, given the uncertain pr ...
... concerned with the extent that a (logically complex) conclusion hypothesis is confirmed by a range of premise hypotheses and evidential statements which are themselves uncertain. In bioinformatics we are often interested in the probability that a complex molecule ψ is present, given the uncertain pr ...
Probability - OnlineStatBook
... Probabilities can also be thought of in terms of relative frequencies. If we tossed a coin millions of times, we would expect the proportion of tosses that came up heads to be pretty close to 1/2. As the number of tosses increases, the proportion of heads approaches 1/2. Therefore, we can say that t ...
... Probabilities can also be thought of in terms of relative frequencies. If we tossed a coin millions of times, we would expect the proportion of tosses that came up heads to be pretty close to 1/2. As the number of tosses increases, the proportion of heads approaches 1/2. Therefore, we can say that t ...
Unit 6 - EduGAINS
... Home Activity or Further Classroom Consolidation Think of an experiment of your own. 1. Describe your experiment in one or two sentences 2. Conduct the experiment and record the results of ten trials. 3. Calculate the theoretical probability for your experiments. 4. Write a sentence or two discussin ...
... Home Activity or Further Classroom Consolidation Think of an experiment of your own. 1. Describe your experiment in one or two sentences 2. Conduct the experiment and record the results of ten trials. 3. Calculate the theoretical probability for your experiments. 4. Write a sentence or two discussin ...
Conditioning using conditional expectations: The Borel
... The structure of the paper is the following. Section 2 is a concise review of the notion of conditional expectation and the concept of conditional probability defined via conditional expectations. Section 3 describes the conditional expectation in the case when the set of elementary events are the p ...
... The structure of the paper is the following. Section 2 is a concise review of the notion of conditional expectation and the concept of conditional probability defined via conditional expectations. Section 3 describes the conditional expectation in the case when the set of elementary events are the p ...
Estimating the probability of negative events
... less probable, than neutral outcomes? In attempting to answer this fundamental question, it seems necessary to dispose of as many potential confounds as possible, and avoid the ambiguities that trouble the interpretation of verbal probability expressions. We therefore wanted a task in which particip ...
... less probable, than neutral outcomes? In attempting to answer this fundamental question, it seems necessary to dispose of as many potential confounds as possible, and avoid the ambiguities that trouble the interpretation of verbal probability expressions. We therefore wanted a task in which particip ...
Combinatorial Probability
... Example 2.15. Consider a die with 1 painted on three sides, 2 painted on two sides, and 3 painted on one side. If we roll this die ten times what is the probability we get five 1’s, three 2’s and two 3’s? The answer is ...
... Example 2.15. Consider a die with 1 painted on three sides, 2 painted on two sides, and 3 painted on one side. If we roll this die ten times what is the probability we get five 1’s, three 2’s and two 3’s? The answer is ...
Approximations of upper and lower probabilities by measurable
... set A ∈ A0 . In other words, we shall investigate under which conditions the equality P(Γ)(A) = [P∗ (A), P ∗ (A)] holds. This is important because, as we shall show, when these two sets are not equal the use of the upper and the lower probability could carry some serious loss of information. The stu ...
... set A ∈ A0 . In other words, we shall investigate under which conditions the equality P(Γ)(A) = [P∗ (A), P ∗ (A)] holds. This is important because, as we shall show, when these two sets are not equal the use of the upper and the lower probability could carry some serious loss of information. The stu ...
Notes on Bayesian Confirmation Theory
... There are three basic elements to bct. First, it is assumed that the scientist assigns what we will call credences or subjective probabilities to different competing hypotheses. These credences are numbers between zero and one reflecting something like the scientist’s level of expectation that a par ...
... There are three basic elements to bct. First, it is assumed that the scientist assigns what we will call credences or subjective probabilities to different competing hypotheses. These credences are numbers between zero and one reflecting something like the scientist’s level of expectation that a par ...
Probability
... in everyday life. For example, when the Bureau of Meteorology predicts that the chance of rain tomorrow is 20%, there is no clear, simple procedure involving random mixing as in the coin toss. Rather, there is a long history of conditions like those leading up to tomorrow. So the reasoning is, appro ...
... in everyday life. For example, when the Bureau of Meteorology predicts that the chance of rain tomorrow is 20%, there is no clear, simple procedure involving random mixing as in the coin toss. Rather, there is a long history of conditions like those leading up to tomorrow. So the reasoning is, appro ...
RACSAM Rev. R. Acad. Cien. Serie A. Mat. V
... Our focus here is primarily technical: to produce the specific “rule” and “law” that arise from adopting the reference prior approach to objective Bayesian analysis, as this approach has proven itself to be quite successful in a wide variety of contexts (see Bernardo, 1979, 2005 ([5, 7]); Berger and ...
... Our focus here is primarily technical: to produce the specific “rule” and “law” that arise from adopting the reference prior approach to objective Bayesian analysis, as this approach has proven itself to be quite successful in a wide variety of contexts (see Bernardo, 1979, 2005 ([5, 7]); Berger and ...
Probability Models
... Probability theory comes up very often in our daily lives. We offer a few examples here. Suppose you are considering buying a “Lotto 6/49” lottery ticket. In this lottery, you are to pick 6 distinct integers between 1 and 49. Another 6 distinct integers between 1 and 49 are then selected at random by ...
... Probability theory comes up very often in our daily lives. We offer a few examples here. Suppose you are considering buying a “Lotto 6/49” lottery ticket. In this lottery, you are to pick 6 distinct integers between 1 and 49. Another 6 distinct integers between 1 and 49 are then selected at random by ...
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 ...
A detailed interpretation of probability, and its link with quantum
... the limiting frequency version due to physicist and mathematician Richard von Mises [3,4]. However, in philosophy and the foundations of quantum mechanics other interpretations, in particular the subjective interpretation2 associating probability and „degree of belief‟, are increasingly popular (for ...
... the limiting frequency version due to physicist and mathematician Richard von Mises [3,4]. However, in philosophy and the foundations of quantum mechanics other interpretations, in particular the subjective interpretation2 associating probability and „degree of belief‟, are increasingly popular (for ...
Automatically Verified Reasoning with Both Intervals and Probability
... So far, the algorithm is essentially as described by Ingram et al. [2]. Colombo and Jaarsma’s further development [3] uses histogram bars of varying width but constant mass, as does A. S. Moore [10]. Kaplan’s variation [8] approximates the bars with their midpoints and probability masses. It is uncl ...
... So far, the algorithm is essentially as described by Ingram et al. [2]. Colombo and Jaarsma’s further development [3] uses histogram bars of varying width but constant mass, as does A. S. Moore [10]. Kaplan’s variation [8] approximates the bars with their midpoints and probability masses. It is uncl ...
Constructing Probability Boxes and Dempster
... useful for risk analysis that generalize real numbers, intervals, probability distributions, interval bounds on probability distributions (probability boxes), and finite DempsterShafer structures whose elements are closed intervals of the real line. The report will show that probability boxes and th ...
... useful for risk analysis that generalize real numbers, intervals, probability distributions, interval bounds on probability distributions (probability boxes), and finite DempsterShafer structures whose elements are closed intervals of the real line. The report will show that probability boxes and th ...
Ruin Probabilities - UNL Math - University of Nebraska–Lincoln
... We can consider a symmetric interpretation of this gambling game. Instead of a single gambler playing at a casino, trying to make a goal a before being ruined, consider two gamblers Alice and Bill playing against each other. Let Alice’s initial capital be T0 and let her play against adversary Bill ...
... We can consider a symmetric interpretation of this gambling game. Instead of a single gambler playing at a casino, trying to make a goal a before being ruined, consider two gamblers Alice and Bill playing against each other. Let Alice’s initial capital be T0 and let her play against adversary Bill ...
Reality and Probability: Introducing a New Type
... if we analyze carefully the way in which we attribute several properties at once to an entity. At first sight one could think that attributing the two properties a and b to the piece of wood has to do with performing both experiments at once, or one after the other, or . . . , well at least perform ...
... if we analyze carefully the way in which we attribute several properties at once to an entity. At first sight one could think that attributing the two properties a and b to the piece of wood has to do with performing both experiments at once, or one after the other, or . . . , well at least perform ...
Arguments for–or against–Probabilism?
... Converse Dutch Book theorem, revised: If you obey probability theory, there does not exist a set of bets, each of which you consider fair-or-favourable, which collectively guarantee your loss. Czech Book theorem, revised: If you violate probability theory, there exists a set of bets, each of which y ...
... Converse Dutch Book theorem, revised: If you obey probability theory, there does not exist a set of bets, each of which you consider fair-or-favourable, which collectively guarantee your loss. Czech Book theorem, revised: If you violate probability theory, there exists a set of bets, each of which y ...
Empirical Interpretations of Probability
... of geometry is the study of space phenomena, so probability theory deals with mass phenomena and repetitive events" (p. vii). To talk to the probability of an event, for von Mises, makes sense only if we have in mind some definite collective relative to which we have defined this probability. At fir ...
... of geometry is the study of space phenomena, so probability theory deals with mass phenomena and repetitive events" (p. vii). To talk to the probability of an event, for von Mises, makes sense only if we have in mind some definite collective relative to which we have defined this probability. At fir ...
Probabilistic Horn abduction and Bayesian networks
... Determining what is in a system from observations (diagnosis and recognition) is an important part of AI. There have been many logic-based proposals as to what is a diagnosis 17, 57, 13, 45, 12]. One problem with all of these proposals is that for any diagnostic problem of a reasonable size there a ...
... Determining what is in a system from observations (diagnosis and recognition) is an important part of AI. There have been many logic-based proposals as to what is a diagnosis 17, 57, 13, 45, 12]. One problem with all of these proposals is that for any diagnostic problem of a reasonable size there a ...
Probability and Chance
... less confusing, and quite tolerable, to take propositions as the primary bearers of both kinds of probability. Nothing important is thought to turn on the choice. The three axioms of probability, though simple, may be used to prove a wide range of interesting and strong mathematical theorems. Becaus ...
... less confusing, and quite tolerable, to take propositions as the primary bearers of both kinds of probability. Nothing important is thought to turn on the choice. The three axioms of probability, though simple, may be used to prove a wide range of interesting and strong mathematical theorems. Becaus ...
65. Gnedenko, Khinchin. Elementary probability
... This figure will certainly be sometimes larger and at times smaller, but in the mean it will be near to 16. In most batches of a thousand articles, it will also be near to 16. We certainly suppose that all the conditions of work are invariable. Such examples can obviously be indefinitely multiplied. ...
... This figure will certainly be sometimes larger and at times smaller, but in the mean it will be near to 16. In most batches of a thousand articles, it will also be near to 16. We certainly suppose that all the conditions of work are invariable. Such examples can obviously be indefinitely multiplied. ...
Dempster–Shafer theory
The theory of belief functions, also referred to as evidence theory or Dempster–Shafer theory (DST), is a general framework for reasoning with uncertainty, with understood connections to other frameworks such as probability, possibility and imprecise probability theories. First introduced by Arthur P. Dempster in the context of statistical inference, the theory was later developed by Glenn Shafer into a general framework for modeling epistemic uncertainty - a mathematical theory of evidence. The theory allows one to combine evidence from different sources and arrive at a degree of belief (represented by a mathematical object called belief function) that takes into account all the available evidence.In a narrow sense, the term Dempster–Shafer theory refers to the original conception of the theory by Dempster and Shafer. However, it is more common to use the term in the wider sense of the same general approach, as adapted to specific kinds of situations. In particular, many authors have proposed different rules for combining evidence, often with a view to handling conflicts in evidence better. The early contributions have also been the starting points of many important developments, including the Transferable Belief Model and the Theory of Hints.