Sets of Probability Distributions and Independence
... The goal of this paper is to offer an updated analysis of independence concepts for sets of probability distributions. A review of the recent literature on independence concepts for sets of probability distributions is presented in Section 3, where many approaches and arguments are organized into a ...
... The goal of this paper is to offer an updated analysis of independence concepts for sets of probability distributions. A review of the recent literature on independence concepts for sets of probability distributions is presented in Section 3, where many approaches and arguments are organized into a ...
4 Combinatorics and Probability
... In the example of houses and colors, we can choose any of three colors for the first house. Whatever color we choose for the first house, there are three colors in which to paint the second house. There are thus nine different ways to paint the first two houses, corresponding to the nine different p ...
... In the example of houses and colors, we can choose any of three colors for the first house. Whatever color we choose for the first house, there are three colors in which to paint the second house. There are thus nine different ways to paint the first two houses, corresponding to the nine different p ...
The Flawed Probabilistic Foundation of Law and Economics
... probability of actually being penalized for taking an action disfavored by the law. By the same token, the effectiveness of a promised reward depends on a person’s probability of actually being rewarded for taking an action that the law favors. This dependency is crucial. Because of informational as ...
... probability of actually being penalized for taking an action disfavored by the law. By the same token, the effectiveness of a promised reward depends on a person’s probability of actually being rewarded for taking an action that the law favors. This dependency is crucial. Because of informational as ...
From imprecise probability assessments to conditional probabilities
... sense of Walley. Then, after recalling the notion of finitely additive conditional probability and for the set of conditioning events the property of quasi additivity, we construct a sequence of conditional probabilities with quasi additive classes of conditioning events. We extend the conditional ...
... sense of Walley. Then, after recalling the notion of finitely additive conditional probability and for the set of conditioning events the property of quasi additivity, we construct a sequence of conditional probabilities with quasi additive classes of conditioning events. We extend the conditional ...
doc - John L. Pollock
... 4.1 Probable Proportions Theorem Let us begin with a simple example. Suppose we have a set of 10,000,000 objects. I announce that I am going to select a subset, and ask you approximately how many members it will have. Most people will protest that there is no way to answer this question. It could ha ...
... 4.1 Probable Proportions Theorem Let us begin with a simple example. Suppose we have a set of 10,000,000 objects. I announce that I am going to select a subset, and ask you approximately how many members it will have. Most people will protest that there is no way to answer this question. It could ha ...
Bayesian Perceptual Psychology
... A prior probability p(s), which assigns higher probability to certain distal shapes than others (e.g. it may assign higher probability to convex shapes). A prior probability p(θ), which assigns higher probability to an overhead lighting direction than to alternative lighting directions. A prior like ...
... A prior probability p(s), which assigns higher probability to certain distal shapes than others (e.g. it may assign higher probability to convex shapes). A prior probability p(θ), which assigns higher probability to an overhead lighting direction than to alternative lighting directions. A prior like ...
Conditionals predictions
... that determine the truth or falsehood of the antecedent: They are not yet “manifested” in the case of (1a), and “manifested” but unknown in the case of (1c). In Funk’s words, “the meaning of the conditioning frame can be said to vary from ‘if it happens that . . . ’ to ‘if it is true that . . . ’ ” ...
... that determine the truth or falsehood of the antecedent: They are not yet “manifested” in the case of (1a), and “manifested” but unknown in the case of (1c). In Funk’s words, “the meaning of the conditioning frame can be said to vary from ‘if it happens that . . . ’ to ‘if it is true that . . . ’ ” ...
Probability and Forensic Science
... What is the probability of the observations we have What is the probability of the observations we have made (E) if the prosecution hypothesis (Hp) is correct and the suspect did leave the trace? What is the probability of the observations we have made (E) if the defense hypothesis (Hd) is correc ...
... What is the probability of the observations we have What is the probability of the observations we have made (E) if the prosecution hypothesis (Hp) is correct and the suspect did leave the trace? What is the probability of the observations we have made (E) if the defense hypothesis (Hd) is correc ...
The Fallacy of Placing Confidence in Confidence Intervals
... intervals in the literature to help bridge the gap between the theoretical definition of the confidence interval and properties that are important to analysts, such as the plausibility of specific parameter values or the precision of an estimate. In this section, we explain how the various heuristic ...
... intervals in the literature to help bridge the gap between the theoretical definition of the confidence interval and properties that are important to analysts, such as the plausibility of specific parameter values or the precision of an estimate. In this section, we explain how the various heuristic ...
7. Probability and Statistics Soviet Essays
... taking some precautions, on which I cannot dwell here, an arithmetization of infinite sets, i.e., the determination of the probabilities of all their sensible propositions, is possible without contradiction. I shall only remark that the main source of the paradoxes was that the arithmetization of in ...
... taking some precautions, on which I cannot dwell here, an arithmetization of infinite sets, i.e., the determination of the probabilities of all their sensible propositions, is possible without contradiction. I shall only remark that the main source of the paradoxes was that the arithmetization of in ...
Theory of Decision under Uncertainty
... answers we can give them. From the very early days of probability theory (mid-seventeenth century), three ways of assigning probabilities to events can be documented. The first, sometimes called the “classical” approach, suggests that equal probabilities be assigned to all outcomes. The second, the ...
... answers we can give them. From the very early days of probability theory (mid-seventeenth century), three ways of assigning probabilities to events can be documented. The first, sometimes called the “classical” approach, suggests that equal probabilities be assigned to all outcomes. The second, the ...
The Probability of Inconsistencies in Complex Collective Decisions
... Table 3 illustrates the convergence results of Proposition 3. Scenarios 2, 3, 5 and 8 satisfy the conditions of 3a, and Scenarios 4, 6 and 7 satisfy the conditions of 3b. The convergence results follow from the law of large numbers. If each individual holds the sets of judgments TT, TF, FT, FF with ...
... Table 3 illustrates the convergence results of Proposition 3. Scenarios 2, 3, 5 and 8 satisfy the conditions of 3a, and Scenarios 4, 6 and 7 satisfy the conditions of 3b. The convergence results follow from the law of large numbers. If each individual holds the sets of judgments TT, TF, FT, FF with ...
conditional probability - ANU School of Philosophy
... infinite sequence of hypothetical trials) — e.g. the probability of heads for a coin is identified with the number of heads outcomes divided by the total number of trials in some suitable sequence of trials. Recalling our third justification for the ratio formula in §2.2, this seems to be naturally ...
... infinite sequence of hypothetical trials) — e.g. the probability of heads for a coin is identified with the number of heads outcomes divided by the total number of trials in some suitable sequence of trials. Recalling our third justification for the ratio formula in §2.2, this seems to be naturally ...
Running head: SIMPLICITY IN EXPLANATION Occam`s Rattle
... and whether simplicity and probability jointly constrain inference. It could be that simplicity is only used as a basis for evaluating explanations when probability information is unknown. Alternatively, simplicity and probability may make independent contributions to the quality of an explanation, ...
... and whether simplicity and probability jointly constrain inference. It could be that simplicity is only used as a basis for evaluating explanations when probability information is unknown. Alternatively, simplicity and probability may make independent contributions to the quality of an explanation, ...
MODEL UNCERTAINTY
... DMs’ beliefs by using analogies with betting behavior (Section 3.1). The result is two layers of analysis: a first, classical layer featuring probability models on states that quantify physical uncertainty; and a second, Bayesian layer characterized by a prior probability on models that quantifies m ...
... DMs’ beliefs by using analogies with betting behavior (Section 3.1). The result is two layers of analysis: a first, classical layer featuring probability models on states that quantify physical uncertainty; and a second, Bayesian layer characterized by a prior probability on models that quantifies m ...
Mixing Methods: A Bayesian Approach
... prescriptions of methodologists who see “small-n” and “large-n” analysis as drawing on a single logic or shared standards of inference (King, Keohane, and Verba, 1994; Brady and Collier, 2004). Multi-method approaches are also encouraged in the guidelines issued by many research funding agencies (Cr ...
... prescriptions of methodologists who see “small-n” and “large-n” analysis as drawing on a single logic or shared standards of inference (King, Keohane, and Verba, 1994; Brady and Collier, 2004). Multi-method approaches are also encouraged in the guidelines issued by many research funding agencies (Cr ...
What is Probability? Patrick Maher August 27, 2010
... of h justifies a rational belief in a of degree α, we say that there is a probability-relation of degree α between a and h. So I will now consider this claim: R: The inductive probability of H given E is the degree of belief in H that would be rational for a person whose evidence is E. One problem w ...
... of h justifies a rational belief in a of degree α, we say that there is a probability-relation of degree α between a and h. So I will now consider this claim: R: The inductive probability of H given E is the degree of belief in H that would be rational for a person whose evidence is E. One problem w ...
Choosing The More Likely Hypothesis
... are partitioned between a null hypothesis and an alternative hypothesis. In essence, we are trying to distinguish between two views about the world. We then ask where the estimated coefficient (or test statistic) lies in the distribution implied by the null hypothesis. If the estimated coefficient i ...
... are partitioned between a null hypothesis and an alternative hypothesis. In essence, we are trying to distinguish between two views about the world. We then ask where the estimated coefficient (or test statistic) lies in the distribution implied by the null hypothesis. If the estimated coefficient i ...
LPS 31: Introduction to Inductive Logic Lecture 1
... Even expressed this way, the sentences are still an argument. It is often helpful to re-express such informal arguments in logical form, by identifying the premises and conclusions and listing the premises first. The first example above shows how the informal argument just given might be put into lo ...
... Even expressed this way, the sentences are still an argument. It is often helpful to re-express such informal arguments in logical form, by identifying the premises and conclusions and listing the premises first. The first example above shows how the informal argument just given might be put into lo ...
On Individual Risk
... mathematical theory of counting. Since the focus is on the specific outcome of (say) a particular deal of cards or roll of a die, this classical conception is individualist. But questions as to the interpretation of the “probabilities” computed rarely raise their heads. If they do, it would typicall ...
... mathematical theory of counting. Since the focus is on the specific outcome of (say) a particular deal of cards or roll of a die, this classical conception is individualist. But questions as to the interpretation of the “probabilities” computed rarely raise their heads. If they do, it would typicall ...
Induction, Rational Acceptance, and Minimally Inconsistent Sets
... premises of the argument and the denial of the conclusion (or any truth functional equivalent) is logically inconsistent, that is, one may deduce a contradiction from the set of statements. A valid deductive argument that is also relevant is one such that the set of statements having as members the ...
... premises of the argument and the denial of the conclusion (or any truth functional equivalent) is logically inconsistent, that is, one may deduce a contradiction from the set of statements. A valid deductive argument that is also relevant is one such that the set of statements having as members the ...
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 ...
When Did Bayesian Inference Become “Bayesian”?
... 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 ...
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.