| Description |
1 online resource (xiv, 317 pages) |
| Series |
Atlantis studies in probability and statistics ; v. 1 |
|
Atlantis studies in probability and statistics ; v. 1.
|
| Contents |
Machine generated contents note: 1. General Questions of Bayes Theory -- 1.1. brief excursus into tire history of the Bayes approach -- 1.2. Philosophy of the Bayes Approach -- 1.3. General Principles of Bayes Methodology -- 1.3.1. Possible interpretations of probability -- 1.3.2. union of prior information and empirical data -- 1.3.3. Optimally of Bayes estimation rules -- 1.4. Subjective probabilities -- 1.5. Hierarchical Bayes Methodology -- 1.6. Use of the Bayes methodology in reliability theory -- 2. Accepted Bayes Method of Estimatio -- 2.1. components of the Bayes approach -- 2.2. Classical properties in reference to Bayes estimates -- 2.2.1. Sufficiency -- 2.2.2. Consistency -- 2.2.3. Unbiasedness -- 2.2.4. Effectiveness -- 2.3. Forms of loss functions -- 2.4. choice of a prior distribution -- 2.4.1. Conjugated prior distributions -- 2.4.2. Jeffrey's introduces prior distributions representing a "scantiness of knowledge" -- 2.4.3. Choice of a prior distribution with the help of information criteria -- 2.5. general procedure of reliability estimation and the varieties of relevant problems -- 2.5.1. Reliability estimation -- 2.5.2. Varieties of problems of Bayes estimation -- 3. Methods of Parametric Bayes Estimation Based on Censored Samples -- 3.1. General description of the accepted estimation procedure -- 3.2. Likelihood function for Bayes procedures -- 3.3. Survival probability estimates for the constant failure rate -- 3.3.1. case of uniform prior distribution -- 3.3.2. case of a prior beta-distribution -- 3.4. Reliability estimates for the linear failure rate -- 3.5. Estimation of reliability for the Weibull distribution of a trouble-free time -- 3.6. Bayes estimate of time to failure probability from accelerated life tests -- 4. Nonparametric Bayes Estimation -- 4.1. Nonparametric Bayes estimates, based on Dirichlet processes |
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Note continued: 6.1.5. Solution of the minimax problem -- 6.2. partial prior information for the Bernoulli trials -- 6.2.1. Formulation of the problem -- 6.2.2. Peculiarities of the problem solution -- 6.2.3. scheme for evaluating TTF estimates -- 6.2.4. Numerical analysis for TTF estimates -- 6.2.5. different way to calculate a lower confidence limit of TTF -- 6.2.6. Comparison with known results -- 6.3. Partial prior information for the constant failure rate -- 6.3.1. problem of estimating TTF, R(t), for an arbitrary time -- 6.3.2. problem of estimating the failure rate -- 6.3.3. Solution of problem (6.43) -- 6.3.4. Estimation of the TTF with the help of the failure rate estimates -- 6.3.5. Numerical analysis for TTF estimates -- 6.4. Bayes estimates of the time to Failures probability for the restricted increasing failure rate distributions -- 6.4.1. Setting of the problem -- 6.4.2. General solution of the problem -- 6.4.3. Estimate of the TTF for the exponential distribution of the time-to-failure -- 6.4.4. TTF estimate for the binomial distribution -- 7. Empirical Bayes Estimates of Reliability -- 7.1. Setting of the problem and the state of the theory of empirical Bayes estimation -- 7.1.1. Setting of the problem of empirical Bayes estimates -- 7.1.2. Classification of methods -- 7.1.3. Parametric methods based on approximation of the Bayes decision rule -- 7.1.4. Parametric methods, based on approximation of a prior distribution -- 7.1.5. Nonparametric empirical Bayes methods -- 7.2. Empirical Bayes estimation of the survival probability for the most extended parametric distributions -- 7.2.1. General procedure for obtaining estimates -- 7.2.2. Binomial scheme -- 7.2.3. Exponential distribution -- 7.2.4. Distribution with a linearly-increasing failure rate -- 7.2.5. Weibull distribution |
| Summary |
Bayesian methods are growing more and more popular, finding new practical applications in the fields of health sciences, engineering, environmental sciences, business and economics and social sciences, among others. This book explores the use of Bayesian analysis in the statistical estimation of the unknown phenomenon of interest. The contents demonstrate that where such methods are applicable, they offer the best possible estimate of the unknown. Beyond presenting Bayesian theory and methods of analysis, the text is illustrated with a variety of applications to real world problems |
| Analysis |
statistiek |
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statistics |
|
statistische analyse |
|
statistical analysis |
|
toegepaste wiskunde |
|
applied mathematics |
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wiskundige modellen |
|
mathematical models |
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waarschijnlijkheid |
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probability |
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computerwetenschappen |
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computer sciences |
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biostatistiek |
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biostatistics |
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wetenschap |
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science |
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Statistics (General) |
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Statistiek (algemeen) |
| Bibliography |
Includes bibliographical references |
| Notes |
English |
| Subject |
Bayesian statistical decision theory.
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Bayesian statistical decision theory
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| Form |
Electronic book
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| Author |
Tsokos, Chris P.
|
| LC no. |
2011937436 |
| ISBN |
9789491216145 |
|
9491216147 |
|
9789491216138 |
|
9491216139 |
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