blanketglossary

Bayes estimator

Definition

In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value of a loss function. Equivalently, it maximizes the posterior expectation of a utility function. An alternative way of formulating an estimator within Bayesian statistics is maximum a posteriori estimation.

Related concepts

Accelerated failure time modelActuarial scienceAdaptive clinical trialAdmissible decision ruleAkaike information criterionAnalysis of covarianceAnalysis of varianceAnderson–Darling testAnscombe transformApproximate Bayesian computationArithmetic meanArithmetic–geometric meanAsymptotic theory (statistics)Asymptotically unbiasedAutocorrelationAutoregressive conditional heteroskedasticityAutoregressive modelAutoregressive–moving-average modelAverage absolute deviationBar chartBayes' theoremBayes factorBayesian estimatorBayesian hierarchical modelingBayesian inferenceBayesian information criterionBayesian linear regressionBayesian model averagingBayesian probabilityBayesian statisticsBernstein–von Mises theoremBeta distributionBias of an estimatorBinomial regressionBioinformaticsBiostatisticsBiplotBlocking (statistics)Bootstrapping (statistics)Box plotBox–Cox transformationBox–Jenkins methodBreusch–Godfrey testCanonical correlationCartographyCategorical variableCensusCentral limit theoremCentral tendencyChemometricsChi-squared testClinical study designClinical trialCluster analysisCluster samplingCochran–Mantel–Haenszel statisticsCoefficient of determinationCoefficient of variationCohen's kappaCoherence (philosophical gambling strategy)Cohort studyCointegrationCompleteness (statistics)Confidence intervalConfoundingConjugate priorContingency tableContinuous probability distributionContraharmonic meanControl chartConvergence of random variablesCorrelation and dependenceCorrelogramCount dataCox's theoremCredible intervalCrime statisticsCromwell's ruleCross-correlationCross-sectional studyCross-validation (statistics)Cubic meanData cleaningData collectionData preprocessingData transformation (statistics)Decision ruleDecision theoryDecomposition of time seriesDegrees of freedom (statistics)Demographic statisticsDensity estimationDescriptive statisticsDesign of experimentsDetrendingDickey–Fuller testDifferencingDimensionality reductionDiscrete setDivergence (statistics)Durbin–Watson statisticEconometricsEffect sizeEfficiency (statistics)Elliptical distributionEmpirical Bayes methodEmpirical distribution functionEncyclopedia of MathematicsEngineering statisticsEnvironmental statisticsEpidemiologyErrors and residualsEstimating equationsEstimation theoryEstimatorEuropean Mathematical SocietyEvidence lower boundExpected valueExperimentExponential familyExponential smoothingF-testFactor analysisFactorial experimentFailure rateFan chart (statistics)Feature scalingFirst-hitting-time modelFisher informationFisher transformationForest plotFourier analysisFrequency distributionFrequency domainFrequentist inferenceFriedman testG-testGamma distributionGaussian distributionGeneral linear modelGeneralized expected utilityGeneralized linear modelGeneralized meanGeographic information systemGeometric meanGeostatisticsGoodness of fitGranger causalityGraphical modelGrouped dataHarmonic meanHeatmapHeinz meanHeronian meanHistogramHodges–Lehmann estimatorHomoscedasticity and heteroscedasticityIEEEIEEE Transactions on Information TheoryIidImproper priorIndex of dispersionIntegrated nested Laplace approximationsInteraction (statistics)Internet Movie DatabaseInterquartile rangeInterval estimationIsotonic regressionJackknife resamplingJames Berger (statistician)Jarque–Bera testJohansen testJonckheere's trend testJurimetricsKaplan–Meier estimatorKendall rank correlation coefficientKolmogorov–Smirnov testKrigingKruskal–Wallis testKurtosisL-momentLaplace's approximationLaw of total expectationLaw of total varianceLeast-squares spectral analysisLehmann–Scheffé theoremLehmer meanLikelihood-ratio testLikelihood functionLikelihood intervalLikelihood principleLilliefors testLine chartLinear discriminant analysisLinear regressionList of fields of application of statisticsList of statistical testsList of statistics articlesLjung–Box testLocation parameterLocation–scale familyLog-rank testLog transformationLogistic regressionLoss functionLp spaceM-estimatorMann–Whitney U testMarginal likelihoodMarkov chain Monte CarloMaximum a posteriori estimationMaximum likelihoodMaximum likelihood estimatorMcNemar's testMeanMean square errorMean squared errorMeasure (mathematics)MedianMedian-unbiased estimatorMedical statisticsMethod of moments (statistics)Methods engineeringMinimum-variance unbiased estimatorMinimum distance estimationMinimum mean square errorMin–max normalizationMissing dataMixed modelMode (statistics)Model selectionModel specificationMoment (mathematics)Monotone likelihood ratioMultiple comparisonsMultivariate adaptive regression splinesMultivariate analysis of varianceMultivariate distributionMultivariate normal distributionMultivariate statisticsNational accountsNatural experimentNelson–Aalen estimatorNested sampling algorithmNon-informative priorNon-parametric statisticsNonlinear regressionNonparametric regressionNonparametric statisticsNormal distributionNormalization (statistics)Observational studyOfficial statisticsOne- and two-tailed testsOpinion pollOptimal decisionOptimal designOrder statisticOrdinary least squaresOutlierOutline of statisticsParametric familyParametric statisticsPareto distributionPartial autocorrelation functionPartial correlationPartition of sums of squaresPearson correlation coefficientPearson product-moment correlation coefficientPercentilePermutation testPie chartPivotal quantityPlug-in principlePoint estimationPoisson distributionPoisson regressionPopulation (statistics)Population statisticsPosterior distributionPosterior modePosterior predictive distributionPosterior probabilityPower (statistics)Power transformPrediction intervalPrincipal component analysisPrinciple of indifferencePrinciple of maximum entropyPrior distributionPrior probabilityProbabilistic designProbability distributionProportional hazards modelPsychometricsQuality controlQuantileQuasi-experimentQuestionnaireQ–Q plotRadar chartRandom assignmentRandomization testRandomized controlled trialRandomized experimentRange (statistics)Rank correlationRanking (statistics)Rao–Blackwell theoremRecursive Bayesian estimationRegression analysisRegression validationReliability engineeringReplication (statistics)Resampling (statistics)Robust regressionRobust statisticsRun chartSample medianSample size determinationSampling (statistics)Sampling distributionScale parameterScatter plotScientific controlScore testSeasonal adjustmentSemiparametric regressionShape of the distributionShape parameterShapiro–Wilk testSign testSimple linear regressionSimultaneous equations modelSkewnessSocial statisticsSpatial analysisSpearman's rank correlation coefficientSpectral density estimationStandard deviationStandard errorStandard scoreStationary processStatisticStatistical classificationStatistical dispersionStatistical distanceStatistical graphicsStatistical hypothesis testStatistical inferenceStatistical modelStatistical parameterStatistical populationStatistical powerStatistical process controlStatistical theoryStatisticsStein's phenomenonStem-and-leaf displayStochastic approximationStratified samplingStructural breakStructural equation modelingStudent's t-testSufficient statisticSurvey methodologySurvival analysisSurvival functionSystem identificationTime domainTime seriesTolerance intervalTrend estimationTruncation (statistics)U-statisticUniform distribution (continuous)Uniformly most powerful testUnit vector normalizationUp-and-Down DesignsUtilityV-statisticVan der Waerden testVarianceVariance-stabilizing transformationVariational Bayesian methodsVector autoregressionViolin plotWald testWaveletWeighted arithmetic meanWhittle likelihoodWilcoxon signed-rank testWinsorizingYeo–Johnson transformationZ-test

9 concepts already in your glossary