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Kadane J.B. (ed.) — Robustness of Bayesian Analyses
Kadane J.B. (ed.) — Robustness of Bayesian Analyses

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Название: Robustness of Bayesian Analyses

Автор: Kadane J.B. (ed.)

Аннотация:

This paper presents algorithms for robustness analysis of Bayesian networks with global neighborhoods. Robust Bayesian inference is the calculation of bounds on posterior values
given perturbations in a probabilistic model. We present algorithms for robust inference (including expected utility, expected value and variance bounds) with global perturbations that can be modeled by ffl-contaminated, constant density ratio, constant density bounded and total variation classes of distributions.


Язык: en

Рубрика: Экономика и финансы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 314

Добавлена в каталог: 08.12.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Gamma$-minimax      81
$\Gamma$-minimax regret      81 96
$\varepsilon$-contamination class      139
$\varepsilon$-optimal decision      167
Absolute error      170 224
Admissibility      88 99
Admissible      142
Alternative hypothesis      37
Analysis of variance      50
Ancillary statistic      59
Approach, decision-theoretic      66 130
Approximate prior      72
Assumption I      130
Bayes, estimates      266
Bayes, risk      95
Bayes, risk, frequented      85 139 141
Bayesian distribution theory      20
Bayesian methodologically      129
Bayesian procedure      137
Bayes’ Theorem      3 7
Berkeley tradition      138
Bernoulli process      21
Beta distribution      21
Betting paradigms      130
Bound, upper variance      243
Bounded continuous loss      154
Bounded growth loss      156
Bounded uniformly      186 187 190 194 197 200 202 203 206 209 216 217 218 219 220 221
Bounds, symmetrically restricted      257
C-minimax      128
Cauchy distribution      137
Chi-square distribution      49
Classes of prior distribution      73
Classical statistics      3
Coefficient load curve model      278
Coherence      70
Concave function      224
Conditional inference      70
conditional probabilities      7
Confidence levels      5
Confidence procedures      87
Consistency      6 92
Continuous in $\theta$ uniformly in D      154 169 177 186 187
Convergent uniformly      168 174 177 181
Convex function      225
Credible intervals      25
Critical likelihood ratios      33
Curve, ridge      235
DATA      8
Data analysis      83
Decision procedure      137
Decision-maker      137
Decision-theoretic approach      66 130
Degrees of freedom      138
Density function      8
Density, normal      46
Design of experiments      102
Dichotomy, simple      32
Diffuseness      19
Distance function      168 170 172
Distributed lag, seasonal      292
Distribution, Bayes distribution theory      20
Distribution, Beta      21
Distribution, Cauchy      137
Distribution, chi-square      49
Distribution, classes of prior      73
Distribution, conjugate      21 98
Distribution, joint      24
Distribution, theory      4
Distributions      11
Entropy, maximum      99
Errors      5
Errors, absolute      170 224
Estimate modal      259
Estimate point      25
Estimation, interval      3 25
Estimation, interval, problem      25 102 170 185 199
Euclidean geometry      138
Exchangeability      138 294
Exchangeability between seasons      297
Exchangeability within seasons      300
Expected utility, maximization of      137
Experiments, design of      102
experts      9
extra-sensory perception (ESP)      29
Extreme bounds      253
Feasible ellipsoid      236
Fiducial probabilities      5
Finitely additive priors      110
Foundations of probability      4
Frequencies, relative      5
Frequency, long-run      138
Frequency, measures      85 139 141
Frequented Bayes risk      80
Frequentist      93 126 128
Frequentist risk      86 97
Function, concave      224
Function, convex      225
Function, distance      168 170 172
Global sensitivity      94
Groups, regression in m      255
Helly — Bray theorem      180 189
Hierarchical extreme bounds      256
Hierarchical load curve models      261
Hierarchical model      137
Hierarchical priors      100 140
Hierarchical regression models      246
Hierarchical sensitivity analysis      247
Hyperparameter      246 263 268
Hypotheses, testing      3
Hypothesis, alternative      37
Hypothesis, catchall      10
Hypothesis, composite      151
Hypothesis, null      36
Hypothesis, null testing      34
Hypothesis, simple      153
Hypothesis, test      26
Hypothesis, testing a 'fuzzy' point null hypothesis      95
Ignoring data      103
Indifference curves      34
Inference      2 137
Inference, conditional      70
Inference, probabilities      7
Information contract curve      234 265 282 303
Interocular traumatic test      30
interval      25
Interval, credible      25
Interval, estimation      3 25
Intuition      9
Inversion lemmas      245
Joint distribution      24
judgment      9
Kolmogorov      126
Least-squares      138
Least-squares, restricted      238
Levels, confidence      5
Likelihood      57 137
Likelihood, critical ratios      33
Likelihood, function      107
Likelihood, principle      37 70
Likelihood, ratios      32
Linear estimators      94 98
Local sensitivity      94
Log-odds      138
Long-run, frequency      138
Long-run, performance frequentist      132
Loss, bounded continuous      154
Loss, squared error      153 170 223
Lower variance bound      241
Marginal density      95
Marginal distribution      24 143
Markov chains      59
Matrix weighted average      234 264 281
Maximization of expected utility      137
Maximum entropy and reference priors      99
Mean      137
Measurability      109
Measurement, stable      92 96
Mechanics, Newtonian      138
Metaprior      81 101 143
Methodologically Bayesian      129
Mill, J.S.      127
minimax      87 127 128 137
Mixed regression      239
Modal estimate      259
Model robustness      85 107
Model, public      9
Multivariate regression systems      231
Newtonian mechanics      138
Non-Bayesian      130
Noninformative priors      73 98
Nonparametric statistics      24
normal      21 137
Normal density      46
Null hypothesis      36
Null hypothesis, testing      34
Objectivity      106
Observations      20
Odds      31
Opinion      2
Paradigms, betting      130
PARAMETER      8 24
Partition      10
Performance frequentist, long run      132
Personal probability      3
Personalistic      138
Point estimate      25
Population      9
Posterior      137
Posterior, robustness      78 92 101 129 137 141
PRECISION      22
Prediction problem      170 185 199
Preference, quasitransitive      71
Principle of stable estimation      10
Prior      137
Prior, approximate      72
Prior, distributions, uniform      11
Prior, finitely additive      110
Prior, hierarchical      100 140
Prior, noninformative      73 98
Prior, probability      8 137
Probabilities, fiducial      5
Probabilities, upper and lower      93 111
Probability theory      4
Procedure, Bayesian      137
Procedure, decision      137
Procedure, robustness      79 95
Procedure, sampling theory      137
Process, Bernoulli      21
Public model      9
Quality control      138
Quasitransitive preference      71
Random sampling      9
Random variable      8
Randomization      83
Rationality, type II      103
Ratios, critical likelihood      25
Reference priors      99
Regression in m groups      255
Regression, mixed      239
Regression, models, hierarchical      246
Regression, systems, multivariate      231
Relative frequencies      5
Restricted least squares      238
Restricted risk, Bayes      89 97
Revision of such opinion      2
Ridge curve      235
Risk functions      128
Risk, Bayes      95
Risk, Bayes, restricted      89 97
Robust $\alpha$-trimmed mean and variance      128
Robustness      137
Robustness, model      85 107
Robustness, posterior      78 92 101 129 137 141
Robustness, procedure      79 95
Sampling plan      138
Sampling random      9
Sampling theory procedures      137
Seasonal distributed lag      292
Seasonal smoothness model      295 303
Sensitivity, analysis, hierarchical      246
Sensitivity, theory      93
Sequential analysis      93 102
Significance levels      5
Simple dichotomy      32
Simple hypothesis      153
Smoothness model, seasonal      295 303
Snedecor’s F      49
Squared error loss      153 170 223
Stabilizing decision      148 149 150 168 169 171 177 178 181 182 204
Stable measurement      92 96
Stable strongly      146 148 149 150 168 169 171 177 178 181 182 187 190 193 194 195 197 198 199 202 206 209 213 216 217 218 221 222 226
Stable weakly      148 149 150 168 169 171 177 178 181 182 187 190 199 203 209
Standard deviation      16 17
Statistic, ancillary      59
Statistic, classical      3
Statistic, nonparametric      24
Statistic, sufficient      57
Statistical decision theory      3
Statistical inference      4
Stein effect      88 131
Stochastic processes      59
Stopping rules      58
Strongly stable      146 148 149 150 168 169 171 177 178 181 182 187 190 193 194 195 197 198 199 202 206 209 213 216 217 218 221 222 226
Student’s t      24 138
Sufficient statistic      57
Symmetric function      224
Symmetrically restricted bounds      257
Test, interocular traumatic      30
Test, two-tailed classical      45
Testing      102
Testing a 'fuzzy' point null hypothesis      95
Testing hypotheses      3
Theorem, Bayes’      3 7
Theory, sensitivity      93
Trimmed mean and variance      128
Two-tailed classical test      45
Two-tiered prior distributions      132
Type II rationality      103
Unbiasedness      59
Uncertainty      5
Uniform prior distributions      11
Uniformly bounded      186 187 190 194 197 200 202 203 206 209 216 217 218 219 220 221
Uniformly convergent      168 174 177 181
Uniformly in D, continuous in $\theta$      154 169 177 186 187
Unstable      148 149 150 168 169 171 177 178 181 182 196 202 204 209 210 213 216 217 219 220 222
Updating      75 140
Upper and lower probabilities      93 111
Upper variance bound      243
Utilitarianism      127
Utility      3 137
Vagueness      18
Variable, random      8
Variance      137
Variance, analysis of      50
Weakly stable      148 149 150 168 169 171 177 178 181 182 187 190 199 203 209
Weber fraction      42
Weber’s law      15
Weighted average, matrix      264 281
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