Harold Jeffreys`s Theory of Probability Revisited
... proposes a clear processing of Bayesian testing, including the dimension-free scaling of Bayes factors. This comprehensive treatment of Bayesian inference from an objective Bayes perspective is a major innovation for the time, and it has certainly contributed to the advance of a field that was then ...
... proposes a clear processing of Bayesian testing, including the dimension-free scaling of Bayes factors. This comprehensive treatment of Bayesian inference from an objective Bayes perspective is a major innovation for the time, and it has certainly contributed to the advance of a field that was then ...
2CH10L1 - Kyrene School District
... chips, 4 pink chips, 8 white chips, and 2 blue chips in the bag. B. Would you be more likely to pull a white chip or a purple chip from the bag? Since the number of white chips equals the number of purple chips in the bag, it is just as likely that you would pull a white chip as a purple from the ba ...
... chips, 4 pink chips, 8 white chips, and 2 blue chips in the bag. B. Would you be more likely to pull a white chip or a purple chip from the bag? Since the number of white chips equals the number of purple chips in the bag, it is just as likely that you would pull a white chip as a purple from the ba ...
Why so Negative to Negative Probabilities?
... different sample space and probability measure they are both equivalent in the limit, for many time steps. For a binomial tree there is a almost an unlimited amount of sample spaces to choose from, each with their own probability measure, but all leading to the same result in the limit. For more com ...
... different sample space and probability measure they are both equivalent in the limit, for many time steps. For a binomial tree there is a almost an unlimited amount of sample spaces to choose from, each with their own probability measure, but all leading to the same result in the limit. For more com ...
Conditionals, indeterminacy, and triviality
... team, and nearly unbeatable when their star Michael Jordan suits up. As a result, though ...
... team, and nearly unbeatable when their star Michael Jordan suits up. As a result, though ...
1 1. Justification of analogical reasoning • an argument that it is
... 1) Existence of determining structures must established by informal plausibility arguments (148). So what is gained by replacing the original analogical argument with a deductive argument containing a dubious premise that, in any case, has to be supported with plausibility arguments? 2) Not generall ...
... 1) Existence of determining structures must established by informal plausibility arguments (148). So what is gained by replacing the original analogical argument with a deductive argument containing a dubious premise that, in any case, has to be supported with plausibility arguments? 2) Not generall ...
Uncertainty and probability for branching selves
... and road2, and (iii) one of road2 and road2. Clearly the answer isn’t ‘neither’; the road doesn’t disappear between x1 and x2. And option (ii) is (on the face of it) inconsistent; road2 and road2 have different properties, in particular their respective destinations, so no road can become both ...
... and road2, and (iii) one of road2 and road2. Clearly the answer isn’t ‘neither’; the road doesn’t disappear between x1 and x2. And option (ii) is (on the face of it) inconsistent; road2 and road2 have different properties, in particular their respective destinations, so no road can become both ...
Uncertainty and probability for branching selves
... and road2↓, and (iii) one of road2↑ and road2↓. Clearly the answer isn’t ‘neither’; the road doesn’t disappear between x1 and x2. And option (ii) is (on the face of it) inconsistent; road2↑ and road2↓ have different properties, in particular their respective destinations, so no road can become both ...
... and road2↓, and (iii) one of road2↑ and road2↓. Clearly the answer isn’t ‘neither’; the road doesn’t disappear between x1 and x2. And option (ii) is (on the face of it) inconsistent; road2↑ and road2↓ have different properties, in particular their respective destinations, so no road can become both ...
Slides - Rutgers Statistics
... regularity: rational assignments of zero credences, and rational credence gaps, for doxastic possibilities. • I now want to explore some of the unwelcome consequences these failures of regularity have for traditional Bayesian epistemology and decision theory. ...
... regularity: rational assignments of zero credences, and rational credence gaps, for doxastic possibilities. • I now want to explore some of the unwelcome consequences these failures of regularity have for traditional Bayesian epistemology and decision theory. ...
Probabilistic thinking and probability literacy in the context of risk
... 1 the ability to balance between psychological and formal elements (a, e)); 2 the understanding that direct criteria for success are missing (b); 3 the ability to separate between randomness and causality (c); and 4 the ability to separate reflecting on a problem and making a decision (d). In the f ...
... 1 the ability to balance between psychological and formal elements (a, e)); 2 the understanding that direct criteria for success are missing (b); 3 the ability to separate between randomness and causality (c); and 4 the ability to separate reflecting on a problem and making a decision (d). In the f ...
A Logic for Inductive Probabilistic Reasoning
... background knowledge. Our treatment of incompletely specified priors, therefore, follows the first approach of taking every possible prior (statistical distribution) into account. See section 4.1 for additional comments on this issue. The main problem we address in the present paper is how to deal w ...
... background knowledge. Our treatment of incompletely specified priors, therefore, follows the first approach of taking every possible prior (statistical distribution) into account. See section 4.1 for additional comments on this issue. The main problem we address in the present paper is how to deal w ...
The Enigma Of Probability - Center for Cognition and Neuroethics
... probability interpretations that rely upon these false solutions will quickly have to find new and fresh justifications. Or else they will die. The Finite World Argument To ban everything that contains an unlimited number of entities from the realm of the possible, as this argument does, is both too ...
... probability interpretations that rely upon these false solutions will quickly have to find new and fresh justifications. Or else they will die. The Finite World Argument To ban everything that contains an unlimited number of entities from the realm of the possible, as this argument does, is both too ...
Bruno de Finetti and Imprecision
... We review several of de Finetti’s fundamental contributions where these have played and continue to play an important role in the development of imprecise probability research. Also, we discuss de Finetti’s few, but mostly critical remarks about the prospects for a theory of imprecise probabilities, ...
... We review several of de Finetti’s fundamental contributions where these have played and continue to play an important role in the development of imprecise probability research. Also, we discuss de Finetti’s few, but mostly critical remarks about the prospects for a theory of imprecise probabilities, ...
Confidence Sets - George Mason University
... Pivot Functions A straightforward way to form a confidence interval is to use a function of the sample that also involves the parameter of interest, but that does not involve any nuisance parameters. The confidence interval is then formed by separating the parameter from the sample values. A class ...
... Pivot Functions A straightforward way to form a confidence interval is to use a function of the sample that also involves the parameter of interest, but that does not involve any nuisance parameters. The confidence interval is then formed by separating the parameter from the sample values. A class ...
Power Point Slides for Chapter 13
... Making decisions under uncertainty Suppose I believe the following: P(A25 gets me there on time | …) P(A90 gets me there on time | …) P(A120 gets me there on time | …) P(A1440 gets me there on time | …) ...
... Making decisions under uncertainty Suppose I believe the following: P(A25 gets me there on time | …) P(A90 gets me there on time | …) P(A120 gets me there on time | …) P(A1440 gets me there on time | …) ...
Test martingales, Bayes factors, and p-values
... be regarded as measures of evidence against a probabilistic hypothesis (i.e., a simple statistical hypothesis). In this article, we review the well-known relationship between Bayes factors and nonnegative martingales and the less well-known relationship between p-values and the suprema of nonnegativ ...
... be regarded as measures of evidence against a probabilistic hypothesis (i.e., a simple statistical hypothesis). In this article, we review the well-known relationship between Bayes factors and nonnegative martingales and the less well-known relationship between p-values and the suprema of nonnegativ ...
§3.2 – Conditional Probability and Independence
... information about an experiment might change the probability in a specific way. For example, if you pick a card out of a deck at random, the probability that the card is from the diamond suit is 1/4, but if you knew somehow that the card was red, then the probability would jump to 1/2. We say that t ...
... information about an experiment might change the probability in a specific way. For example, if you pick a card out of a deck at random, the probability that the card is from the diamond suit is 1/4, but if you knew somehow that the card was red, then the probability would jump to 1/2. We say that t ...
Dilation for Sets of Probabilities
... Dilation leads to some interesting questions. For example, suppose the coin is tossed and we observe the outcome. Are we entitled to retain the more precise unconditional probability instead of conditioning? See Levi (1977) and Kyburg (1977) for discussion on this. To emphasize the counterintuitive ...
... Dilation leads to some interesting questions. For example, suppose the coin is tossed and we observe the outcome. Are we entitled to retain the more precise unconditional probability instead of conditioning? See Levi (1977) and Kyburg (1977) for discussion on this. To emphasize the counterintuitive ...
Fuzzy measure and probability distributions: distorted
... However, although Sugeno and Choquet integrals are powerful operators, their practical application is more difficult due to the fact that they require a large number of parameters. In fact, fuzzy measures require 2|X| parameters (where |X| is the number of information sources or input variables) be ...
... However, although Sugeno and Choquet integrals are powerful operators, their practical application is more difficult due to the fact that they require a large number of parameters. In fact, fuzzy measures require 2|X| parameters (where |X| is the number of information sources or input variables) be ...
The Uses of Probability and the Choice of a Reference Class
... things that are B's, lies between pi and p2." For most purposes we need consider only statements of this form, since even when we are dealing with the distribution of a random quantity, such as foot size, or of an original n-tuple of random quantities, when it comes to making use of that knowledge, ...
... things that are B's, lies between pi and p2." For most purposes we need consider only statements of this form, since even when we are dealing with the distribution of a random quantity, such as foot size, or of an original n-tuple of random quantities, when it comes to making use of that knowledge, ...
COMPLEX AND UNPREDICTABLE CARDANO
... objective by viewing it as a sort of disposition, or propensity, that can be attributed to a single trial or experiment. For example, that a coin has probability of one half of showing up heads means that it has an internal tendency to show up heads in one half of the trials, and this property is at ...
... objective by viewing it as a sort of disposition, or propensity, that can be attributed to a single trial or experiment. For example, that a coin has probability of one half of showing up heads means that it has an internal tendency to show up heads in one half of the trials, and this property is at ...
Chapter 8 Discrete probability and the laws of chance
... Consider the following experiment: We flip a coin and observe any one of two possible results: “heads” (H) or “tails” (T). A fair coin is one for which these results are equally likely. Similarly, consider the experiment of rolling a dice: A six-sided dice can land on any of its six faces, so that a ...
... Consider the following experiment: We flip a coin and observe any one of two possible results: “heads” (H) or “tails” (T). A fair coin is one for which these results are equally likely. Similarly, consider the experiment of rolling a dice: A six-sided dice can land on any of its six faces, so that a ...
Lesson 1: The General Multiplication Rule
... wish to remind students that a tree diagram is one method to list all the possibilities. Tree diagrams can be useful in students’ development of probabilistic ideas. Tree diagrams were analyzed from an algebraic perspective in Algebra II, Module 1, Lesson 7. Exercise 1 is designed to introduce the f ...
... wish to remind students that a tree diagram is one method to list all the possibilities. Tree diagrams can be useful in students’ development of probabilistic ideas. Tree diagrams were analyzed from an algebraic perspective in Algebra II, Module 1, Lesson 7. Exercise 1 is designed to introduce the f ...
De Finetti and Savage on the normative relevance of imprecise
... (Ellsberg 1961, Fellner 1961) and statistics (Smith 1961). Focusing mostly on de Finetti and Savage’s assessment of Cedric Smith’s foundational paper of the statistical approach to approximate reasoning (Walley 1991), we attempted to show that the way de Finetti defended his position against Smith’ ...
... (Ellsberg 1961, Fellner 1961) and statistics (Smith 1961). Focusing mostly on de Finetti and Savage’s assessment of Cedric Smith’s foundational paper of the statistical approach to approximate reasoning (Walley 1991), we attempted to show that the way de Finetti defended his position against Smith’ ...
Recitation session Bayesian networks, HMM, Kalman Filters, DBNs
... Let us also assume that it does so every 1 minute. We also know that if the class was confused at some time t there is 90% certainty that it would be confused a minute later. Similarly, if it is not confused at time it will not be confused at time with the same probability of 90%. Initially, ...
... Let us also assume that it does so every 1 minute. We also know that if the class was confused at some time t there is 90% certainty that it would be confused a minute later. Similarly, if it is not confused at time it will not be confused at time with the same probability of 90%. Initially, ...
PLAUSIBILITY AND PROBABILITY IN SCENARIO
... In short, the two words have been confused with each other for centuries, and even although they became much more distinct in the last 300 years, today plausibility often still deploys probability to define itself. Plausibility, and its connections with the pliable notion of what can be applauded, q ...
... In short, the two words have been confused with each other for centuries, and even although they became much more distinct in the last 300 years, today plausibility often still deploys probability to define itself. Plausibility, and its connections with the pliable notion of what can be applauded, q ...
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.