Author: Fabio Spizzichino
Publisher: CRC Press
ISBN: 1420036130
Category : Mathematics
Languages : en
Pages : 269
Book Description
Bayesian methods in reliability cannot be fully utilized and understood without full comprehension of the essential differences that exist between frequentist probability and subjective probability. Switching from the frequentist to the subjective approach requires that some fundamental concepts be rethought and suitably redefined. Subjecti
Subjective Probability Models for Lifetimes
Author: Fabio Spizzichino
Publisher: CRC Press
ISBN: 1420036130
Category : Mathematics
Languages : en
Pages : 269
Book Description
Bayesian methods in reliability cannot be fully utilized and understood without full comprehension of the essential differences that exist between frequentist probability and subjective probability. Switching from the frequentist to the subjective approach requires that some fundamental concepts be rethought and suitably redefined. Subjecti
Publisher: CRC Press
ISBN: 1420036130
Category : Mathematics
Languages : en
Pages : 269
Book Description
Bayesian methods in reliability cannot be fully utilized and understood without full comprehension of the essential differences that exist between frequentist probability and subjective probability. Switching from the frequentist to the subjective approach requires that some fundamental concepts be rethought and suitably redefined. Subjecti
Models of subjective probability
Subjective Probability
Author: George Wright
Publisher:
ISBN:
Category : Business & Economics
Languages : en
Pages : 608
Book Description
This overview of subjective probability ranges from discussion of the philosophy of axiom systems through studies in the psychological laboratory to the real world of business decision-making.
Publisher:
ISBN:
Category : Business & Economics
Languages : en
Pages : 608
Book Description
This overview of subjective probability ranges from discussion of the philosophy of axiom systems through studies in the psychological laboratory to the real world of business decision-making.
A Stochastic Model of the Calibration of Subjective Probabilities
Subjective Probability
Author: Richard Jeffrey
Publisher: Cambridge University Press
ISBN: 9780521536684
Category : Mathematics
Languages : en
Pages : 144
Book Description
Sample Text
Publisher: Cambridge University Press
ISBN: 9780521536684
Category : Mathematics
Languages : en
Pages : 144
Book Description
Sample Text
Assessing Models of Subjective Probability Judgment
Studies in Subjective Probability
Author: Henry Ely Kyburg
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 278
Book Description
Truth and probability; Foresight: its logical laws, its subjective sources; The bases of probability; Subjective probability as the measure of a non-measurable set; The elicitation of personal probabilities; Probability: beware of falsifications; Probable knowledge.
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 278
Book Description
Truth and probability; Foresight: its logical laws, its subjective sources; The bases of probability; Subjective probability as the measure of a non-measurable set; The elicitation of personal probabilities; Probability: beware of falsifications; Probable knowledge.
Probability and Bayesian Modeling
Author: Jim Albert
Publisher: CRC Press
ISBN: 1351030124
Category : Mathematics
Languages : en
Pages : 511
Book Description
Probability and Bayesian Modeling is an introduction to probability and Bayesian thinking for undergraduate students with a calculus background. The first part of the book provides a broad view of probability including foundations, conditional probability, discrete and continuous distributions, and joint distributions. Statistical inference is presented completely from a Bayesian perspective. The text introduces inference and prediction for a single proportion and a single mean from Normal sampling. After fundamentals of Markov Chain Monte Carlo algorithms are introduced, Bayesian inference is described for hierarchical and regression models including logistic regression. The book presents several case studies motivated by some historical Bayesian studies and the authors’ research. This text reflects modern Bayesian statistical practice. Simulation is introduced in all the probability chapters and extensively used in the Bayesian material to simulate from the posterior and predictive distributions. One chapter describes the basic tenets of Metropolis and Gibbs sampling algorithms; however several chapters introduce the fundamentals of Bayesian inference for conjugate priors to deepen understanding. Strategies for constructing prior distributions are described in situations when one has substantial prior information and for cases where one has weak prior knowledge. One chapter introduces hierarchical Bayesian modeling as a practical way of combining data from different groups. There is an extensive discussion of Bayesian regression models including the construction of informative priors, inference about functions of the parameters of interest, prediction, and model selection. The text uses JAGS (Just Another Gibbs Sampler) as a general-purpose computational method for simulating from posterior distributions for a variety of Bayesian models. An R package ProbBayes is available containing all of the book datasets and special functions for illustrating concepts from the book. A complete solutions manual is available for instructors who adopt the book in the Additional Resources section.
Publisher: CRC Press
ISBN: 1351030124
Category : Mathematics
Languages : en
Pages : 511
Book Description
Probability and Bayesian Modeling is an introduction to probability and Bayesian thinking for undergraduate students with a calculus background. The first part of the book provides a broad view of probability including foundations, conditional probability, discrete and continuous distributions, and joint distributions. Statistical inference is presented completely from a Bayesian perspective. The text introduces inference and prediction for a single proportion and a single mean from Normal sampling. After fundamentals of Markov Chain Monte Carlo algorithms are introduced, Bayesian inference is described for hierarchical and regression models including logistic regression. The book presents several case studies motivated by some historical Bayesian studies and the authors’ research. This text reflects modern Bayesian statistical practice. Simulation is introduced in all the probability chapters and extensively used in the Bayesian material to simulate from the posterior and predictive distributions. One chapter describes the basic tenets of Metropolis and Gibbs sampling algorithms; however several chapters introduce the fundamentals of Bayesian inference for conjugate priors to deepen understanding. Strategies for constructing prior distributions are described in situations when one has substantial prior information and for cases where one has weak prior knowledge. One chapter introduces hierarchical Bayesian modeling as a practical way of combining data from different groups. There is an extensive discussion of Bayesian regression models including the construction of informative priors, inference about functions of the parameters of interest, prediction, and model selection. The text uses JAGS (Just Another Gibbs Sampler) as a general-purpose computational method for simulating from posterior distributions for a variety of Bayesian models. An R package ProbBayes is available containing all of the book datasets and special functions for illustrating concepts from the book. A complete solutions manual is available for instructors who adopt the book in the Additional Resources section.
Subjective Probability: the Only Kind Possible
Author: Paolo Manca
Publisher: goWare
ISBN: 8867978349
Category : Mathematics
Languages : en
Pages : 106
Book Description
In the context of a non-deterministic view of the world, probability is a number which reflects the degree of confidence someone has that a given statement or event is true, based on the information they have. Probability and probability calculus, on the other hand, are essential tools for those who wish to recognise uncertainty and manage it responsibly. This presentation of subjective probability (the only one possible) will enable even those who are not experts to acquire the correct knowledge of an instrument which is essential and necessary for dealing with the world around us. The text takes only one hour to read, but it will help you to avoid many mistakes and enable you to understand the origin of those you might have made in the past. The reader will also be able to appreciate many funny examples and paradoxes such as this one: statistics tell us that 20% of motorway car accidents are caused by drivers with high blood alcohol levels. It can then be derived that 80% of accidents are caused by sober drivers. Therefore, we should supply alcohol to those who drive on motorways!
Publisher: goWare
ISBN: 8867978349
Category : Mathematics
Languages : en
Pages : 106
Book Description
In the context of a non-deterministic view of the world, probability is a number which reflects the degree of confidence someone has that a given statement or event is true, based on the information they have. Probability and probability calculus, on the other hand, are essential tools for those who wish to recognise uncertainty and manage it responsibly. This presentation of subjective probability (the only one possible) will enable even those who are not experts to acquire the correct knowledge of an instrument which is essential and necessary for dealing with the world around us. The text takes only one hour to read, but it will help you to avoid many mistakes and enable you to understand the origin of those you might have made in the past. The reader will also be able to appreciate many funny examples and paradoxes such as this one: statistics tell us that 20% of motorway car accidents are caused by drivers with high blood alcohol levels. It can then be derived that 80% of accidents are caused by sober drivers. Therefore, we should supply alcohol to those who drive on motorways!
Theories of Probability
Author: Terrence L. Fine
Publisher: Academic Press
ISBN: 1483263894
Category : Mathematics
Languages : en
Pages : 276
Book Description
Theories of Probability: An Examination of Foundations reviews the theoretical foundations of probability, with emphasis on concepts that are important for the modeling of random phenomena and the design of information processing systems. Topics covered range from axiomatic comparative and quantitative probability to the role of relative frequency in the measurement of probability. Computational complexity and random sequences are also discussed. Comprised of nine chapters, this book begins with an introduction to different types of probability theories, followed by a detailed account of axiomatic formalizations of comparative and quantitative probability and the relations between them. Subsequent chapters focus on the Kolmogorov formalization of quantitative probability; the common interpretation of probability as a limit of the relative frequency of the number of occurrences of an event in repeated, unlinked trials of a random experiment; an improved theory for repeated random experiments; and the classical theory of probability. The book also examines the origin of subjective probability as a by-product of the development of individual judgments into decisions. Finally, it suggests that none of the known theories of probability covers the whole domain of engineering and scientific practice. This monograph will appeal to students and practitioners in the fields of mathematics and statistics as well as engineering and the physical and social sciences.
Publisher: Academic Press
ISBN: 1483263894
Category : Mathematics
Languages : en
Pages : 276
Book Description
Theories of Probability: An Examination of Foundations reviews the theoretical foundations of probability, with emphasis on concepts that are important for the modeling of random phenomena and the design of information processing systems. Topics covered range from axiomatic comparative and quantitative probability to the role of relative frequency in the measurement of probability. Computational complexity and random sequences are also discussed. Comprised of nine chapters, this book begins with an introduction to different types of probability theories, followed by a detailed account of axiomatic formalizations of comparative and quantitative probability and the relations between them. Subsequent chapters focus on the Kolmogorov formalization of quantitative probability; the common interpretation of probability as a limit of the relative frequency of the number of occurrences of an event in repeated, unlinked trials of a random experiment; an improved theory for repeated random experiments; and the classical theory of probability. The book also examines the origin of subjective probability as a by-product of the development of individual judgments into decisions. Finally, it suggests that none of the known theories of probability covers the whole domain of engineering and scientific practice. This monograph will appeal to students and practitioners in the fields of mathematics and statistics as well as engineering and the physical and social sciences.