Search results for: Glenn Shafer

Items from 1 to 20 out of 32 results

article

Testing by betting: A strategy for statistical and scientific communication

Glenn Shafer

Journal of the Royal Statistical Society: Series A (Statistics in Society) > 184 > 2 > 407 - 431

The most widely used concept of statistical inference—the p‐value—is too complicated for effective communication to a wide audience. This paper introduces a simpler way of reporting statistical evidence: report the outcome of a bet against the null hypothesis. This leads to a new role for likelihood, to alternatives to power and confidence, and to a framework for meta‐analysis that accommodates both...

article

Author's reply to the Discussion of ‘Testing by betting: A strategy for statistical and scientific communication’ by Glenn Shafer

Glenn Shafer

Journal of the Royal Statistical Society: Series A (Statistics in Society) > 184 > 2 > 466 - 478

article

Constructive decision theory

Glenn Shafer

International Journal of Approximate Reasoning > 2016 > 79 > C > 45-62

We sketch a theory of decision that allows us to construct both goals and degrees of belief. Before choosing an action, we create and weight goals. We represent our beliefs about the consequences of each action by constructing a belief function on the set of possible consequences. Then we combine the beliefs and goals to see the value that will be secured and the value that will be excluded by each...

article

A Mathematical Theory of Evidence turns 40

Glenn Shafer

International Journal of Approximate Reasoning > 2016 > 79 > C > 7-25

The book that launched the Dempster–Shafer theory of belief functions appeared 40 years ago. This intellectual autobiography looks back on how I came to write the book and how its ideas played out in my later work.

article

Dempster's rule of combination

Glenn Shafer

International Journal of Approximate Reasoning > 2016 > 79 > C > 26-40

The theory of belief functions is a generalization of probability theory; a belief function is a set function more general than a probability measure but whose values can still be interpreted as degrees of belief. Dempster's rule of combination is a rule for combining two or more belief functions; when the belief functions combined are based on distinct or “independent” sources of evidence, the rule...

article

The problem of dependent evidence

Glenn Shafer

International Journal of Approximate Reasoning > 2016 > 79 > C > 41-44

It is appropriate to use Dempster's rule for combining belief functions only if the belief functions combined are based on independent items of evidence. What can be done in the case of dependent evidence? Often the answer is to reframe the problem. Three examples are given: one from everyday experience, one from probabilistic relaxation, and one from expert systems.

chapter

Non-Additive Probabilities in the Work of Bernoulli and Lambert

Glenn Shafer

Studies in Fuzziness and Soft Computing > Classic Works of the Dempster-Shafer Theory of Belief Functions > 117-182

chapter

Axioms for Probability and Belief-Function Propagation

Prakash P. Shenoy, Glenn Shafer

Studies in Fuzziness and Soft Computing > Classic Works of the Dempster-Shafer Theory of Belief Functions > 499-528

In this paper, we describe an abstract framework and axioms under which exact local computation of marginals is possible. The primitive objects of the framework are variables and valuations. The primitive operators of the framework are combination and marginalization. These operate on valuations. We state three axioms for these operators and we derive the possibility of local computation from the...

chapter

Languages and Designs for Probability Judgment

Glenn Shafer, Amos Tversky

Studies in Fuzziness and Soft Computing > Classic Works of the Dempster-Shafer Theory of Belief Functions > 345-374

Theories of subjective probability are viewed as formal languages for analyzing evidence and expressing degrees of belief. This article focuses on two probability language, the Bayesian language and the language of belief functions [199]. We describe and compare the semantics (i.e., the meaning of the scale) and the syntax (i.e., the formal calculus) of these languages. We also investigate some of...

chapter

Implementing Dempster’s Rule for Hierarchical Evidence

Glenn Shafer, Roger Logan

Studies in Fuzziness and Soft Computing > Classic Works of the Dempster-Shafer Theory of Belief Functions > 449-476

This article gives an algorithm for the exact implementation of Dempster’s rule in the case of hierarchical evidence. This algorithm is computationally efficient, and it makes the approximation suggested by Gordon and Shortliffe unnecessary. The algorithm itself is simple, but its derivation depends on a detailed understanding of the interaction of hierarchical evidence.

chapter

Allocations of Probability

Glenn Shafer

Studies in Fuzziness and Soft Computing > Classic Works of the Dempster-Shafer Theory of Belief Functions > 183-196

This paper studies belief functions, set functions which are normalized and monotone of order 8. The concepts of continuity and condensability are defined for belief functions, and it is shown how to extend continuous or condensable belief functions from an algebra of subsets to the corresponding power set. The main tool used in this extension is the theorem that every belief function can be represented...

chapter

Belief Functions and Parametric Models

Glenn Shafer

Studies in Fuzziness and Soft Computing > Classic Works of the Dempster-Shafer Theory of Belief Functions > 265-290

The theory of belief functions assesses evidence by fitting it to a scale of canonical examples in which the meaning of a message depends on chance. In order to analyse parametric statistical problems within the framework of this theory, we must specify the evidence on which the parametric model is based. This article gives several examples to show how the nature of this evidence affects the analysis...

chapter

Constructive Probability

Glenn Shafer

Studies in Fuzziness and Soft Computing > Classic Works of the Dempster-Shafer Theory of Belief Functions > 217-264

book

Algorithmic Learning in a Random World

Vladimir Vovk, Alexander Gammerman, Glenn Shafer, Springer US

Conformal prediction is a valuable new method of machine learning. Conformal predictors are among the most accurate methods of machine learning, and unlike other state-of-the-art methods, they provide information about their own accuracy and reliability. This new monograph integrates mathematical theory and revealing experimental work. It demonstrates mathematically the validity of the reliability...

chapter

Causal relevance

Glenn Shafer

Lecture Notes in Computer Science > Reasoning with Uncertainty in Robotics > 187-208

Concepts of causal relevance and irrelevance are readily formulated in the context of Bayes nets, but these formulations have significant shortcomings. Most importantly, they do not allow for the great variety that can be observed in the temporal configuration of causally related entities. For example, they deal awkwardly with progressive causation, where continued action of a cause continues to enhance...

chapter

Qualitative Markov networks

Khaled Mellouli, Glenn Shafer, Prakash P. Shenoy

Lecture Notes in Computer Science > Uncertainty in Knowledge-Based Systems > 67-74

chapter

Philosophical foundations for causal networks

Glenn Shafer

Lecture Notes in Computer Science > Advances in Intelligent Computing — IPMU '94 > 1-12

Bayes nets are seeing increasing use in expert systems [2, 6], and structural equations models continue to be popular in many branches of the social sciences [1]. Both types of models involve directed acyclic graphs with variables as nodes, and in both cases there is much mysterious talk about causal interpretation. This paper uses probability trees to give precise conditions under which Bayes nets...

chapter

Causality and Responsibility

Glenn Shafer

Studies in Fuzziness and Soft Computing > The Dynamics of Judicial Proof > Causality > 457-478

Attribution of responsibility, whether as blame or praise, always rests on a claim about causation. In order to be responsible for an event, a person must take an action that causes the event. This creates a philosophical puzzle. As philosophers, we tend to be skeptical about claims of causal knowledge. No matter how thoroughly we have studied a phenomenon, we say, we may not have gotten to the bottom...

chapter

Predicting Bond Yields Using Defensive Forecasting

Glenn Shafer, Samuel Ring

Handbook of Quantitative Finance and Risk Management > Theory, Methodology, and Applications > 1257-1272

This chapter introduces a new method of forecasting, defensive forecasting, and illustrates its potential by showing how it can be used to predict the yields of corporate bonds in real time.Defensive forecasting identifies a betting strategy that succeeds if forecasts are inaccurate and then makes forecasts that will defeat this strategy. The theory of defensive forecasting is based on the game-theoretic...

article

Belief functions and uncertainty management in networks and telecommunication

Abdelhamid Mellouk, Latifa Oukhellou, Lei Shu, Glenn Shafer

Annals of Telecommunications > 2014 > 69 > 3-4 > 131-133

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GAME-THEORETIC PROBABILITY (5)
BELIEF FUNCTION (2)
BELIEF FUNCTIONS (2)
CAUSALITY (2)
DEMPSTER'S RULE (2)
DEMPSTER–SHAFER THEORY (2)
UPPER AND LOWER PROBABILITIES (2)
ALLOCATION OF PROBABILITY (1)
ANYTIME DEDUCTION (1)
ASSET PERFORMANCE (1)
ASSET PRICING (1)
BAYES NET (1)
BAYESIAN STATISTICS (1)
BEHAVIORAL SEMANTICS (1)
BETTING SCORE (1)
CAPACITY (1)
CAPM (1)
COGNITIVE INDEPENDENCE (1)
CONDENSABILITY (1)
CONDITIONING (1)
CONSTRUCTIVE PROBABILITY (1)
CONTINUITY (1)
DEFENSIVE FORECASTING (1)
DEMPSTER’S RULE (1)
DEPENDENT EVIDENCE (1)
DOOB’S MARTINGALE CONVERGENCE THEOREM (1)
ERGODICITY OF BERNOULLI SHIFTS (1)
EVIDENCE (1)
EVIDENTIAL INDEPENDENCE (1)
EXCHANGEABILITY (1)
FIDUCIAL INFERENCE (1)
FREQUENTISM (1)
GAMBLES (1)
GAME‐THEORETIC PROBABILITY (1)
IMPRECISE PROBABILITIES (1)
INTERPRETATION OF PROBABILITY (1)
INVARIANT EVENT (1)
KOLMOGOROV’S ZERO–ONE LAW (1)
LIKELIHOOD (1)
LIKELIHOOD RATIO (1)
LOWER PROBABILITIES (1)
LÉVY’S MARTINGALE CONVERGENCE THEOREM (1)
MARTINGALE (1)
MARTINGALES (1)
MATHEMATICAL FINANCE (1)
MEASURE–THEORETIC (1)
MULTIVALENCE (1)
ON-LINE PREDICTION (1)
PARAMETRIC MODELS (1)
PERMUTABLE EVENT (1)
PREDICTING BOND YIELDS (1)
PROBABILISTIC LOGIC (1)
PROBABILITY TREE (1)
P‐VALUE (1)
REFINEMENT (1)
RELEVANCE (1)
SIGN (1)
SIMPLIFICATION (1)
STATISTICAL COMMUNICATION (1)
SUBJECTIVISM (1)
SUPPORT VECTOR MACHINES (1)
TAIL EVENT (1)
TRACKING (1)
UPPER PROBABILITIES (1)
UPPER PROBABILITY (1)
WARRANTY (1)
[JEL CLASSIFICATION CODES] C40 (1)
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INFONA - science communication portal

Search results for: Glenn Shafer

Testing by betting: A strategy for statistical and scientific communication

Author's reply to the Discussion of ‘Testing by betting: A strategy for statistical and scientific communication’ by Glenn Shafer

Constructive decision theory

A Mathematical Theory of Evidence turns 40

Dempster's rule of combination

The problem of dependent evidence

Non-Additive Probabilities in the Work of Bernoulli and Lambert

Axioms for Probability and Belief-Function Propagation

Languages and Designs for Probability Judgment

Implementing Dempster’s Rule for Hierarchical Evidence

Allocations of Probability

Belief Functions and Parametric Models

Constructive Probability

Algorithmic Learning in a Random World

Causal relevance

Qualitative Markov networks

Philosophical foundations for causal networks

Causality and Responsibility

Predicting Bond Yields Using Defensive Forecasting

Belief functions and uncertainty management in networks and telecommunication

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