The Weighted Likelihood Ratio, Linear Hypotheses on Normal Location Parameters

1971/02/01 by James M. Dickey, James Dickey · 47 citations
Mathematics · Decision Sciences · #Statistical Distribution Estimation and Applications #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring

paper · doi:10.1214/aoms/1177693507

Abstract

Raiffa and Schlaifer's theory of conjugate prior distributions is here applied to Jeffrey's theory of tests for a sharp hypothesis, for simple normal sampling, for model I analysis of variance, and for univariate and multivariate Behrens-Fisher probelms. Leonard J. Savage's Bayesianization of Jeffrey's theory is given with new generalizations. A new conjugate prior family for normal sampling which allows prior independence of unknown mena and variance is given.

Cited by

• Searching for Exotrojans in Pulsar Systems
• The MeerKAT Pulsar Timing Array: the first search for gravitational waves with the MeerKAT radio telescope
• Solar Hegemony: M-Dwarfs Are Unlikely to Host Observers Such as Ourselves
• Neutrino physics with the PTOLEMY project: active neutrino properties and the light sterile case
• The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background
• Invited Discussion of "Model Uncertainty and Missing Data: An Objective Bayesian Perspective" by Gonzalo García-Donato , María Eugenia Castellanos , Stefano Cabras Alicia Quirós , and Anabel Forte
• Bayes Factor Hypothesis Testing in Meta-Analyses: Practical Advantages and Methodological Considerations
• A Generalized Savage-Dickey Ratio
• The NANOGrav 15 yr Dataset: Customized Chromatic Noise Models
• Bayes Factors
• Is There a Free Lunch in Inference?
• On the robustness of Bayesian inference of gene flow to intragenic recombination and natural selection
• A tutorial on bridge sampling
• Default Bayesian Model Selection of Constrained Multivariate Normal Linear Models
• Isolation in Motion: How Riverscapes Shape the Evolution of Plants in Fast‐Flowing River Archipelagos
• Contribution from Nonlinear Quasi-normal Modes in GW250114
• CHIME-o-Grav: Wideband Timing of Four Millisecond Pulsars from the NANOGrav 15-yr dataset
• Bayes Factor Tests for Group Differences in Ordinal and Binary Graphical Models
• Expectations for the first supermassive black-hole binary resolved by PTAs I: Model efficacy
• Black Hole Spectroscopy and Tests of General Relativity with GW250114
• Inferring Mbh-Mbulge Evolution from the Gravitational Wave Background
• Targeted search for an individual SMBHB in NANOGrav 15-year and EPTA DR2 data sets
• To Vary or Not To Vary: A Flexible Empirical Bayes Factor for Testing Variance Components
• Testing Inflationary Cosmology
• Semi-parametric estimation of the EASI model: Welfare implications of\n taxes identifying clusters due to unobserved preference heterogeneity
• A Multivariate Multilevel Approach to the Modeling of Accuracy and Speed of Test Takers. [europepmc]
• A Bayesian Outbreak Detection Method for Influenza-Like Illness. [europepmc]
• Detection of Motor Changes in Huntington's Disease Using Dynamic Causal Modeling. [europepmc]
• Level-weighted averaging in elevation to synchronous amplitude-modulated sounds. [europepmc]
• Working Memory-Related Effective Connectivity in Huntington's Disease Patients. [europepmc]
• Linking structural and effective brain connectivity: structurally informed Parametric Empirical Bayes (si-PEB). [europepmc]
• Simple Bayesian testing of scientific expectations in linear regression models. [europepmc]
• Comparing Gaussian graphical models with the posterior predictive distribution and Bayesian model selection. [europepmc]
• Perceptual Coupling Based on Depth and Motion Cues in Stereovision-Impaired Subjects. [europepmc]
• UV radiation affects antipredatory defense traits in Daphnia pulex . [europepmc]
• New Estimators of the Bayes Factor for Models with High-Dimensional Parameter and/or Latent Variable Spaces. [europepmc]
• Bayesian Multivariate Mixed-Effects Location Scale Modeling of Longitudinal Relations Among Affective Traits, States, and Physical Activity. [europepmc]
• A Review of Bayesian Hypothesis Testing and Its Practical Implementations. [europepmc]
• Bayesian Noise Modelling for State Estimation of the Spread of COVID-19 in Saudi Arabia with Extended Kalman Filters. [europepmc]
• A Bayesian Reanalysis of the Overall and Sex-Disaggregated Results of the Neonatal Oxygenation Prospective Meta-Analysis (NeOProM). [europepmc]
• History and nature of the Jeffreys-Lindley paradox. [europepmc]
• The probabilistic and dynamic nature of perception in human generalization behavior. [europepmc]
• A tutorial on Bayesian hypothesis testing of correlation coefficients using the BFpack-module in JASP. [europepmc]
• Bayes Factor Tests for Group Differences in Ordinal and Binary Graphical Models. [europepmc]
• More than one species of the naked mole-rat, a new biomedical model. [europepmc]
• On the robustness of Bayesian inference of gene flow to intragenic recombination and natural selection. [europepmc]
• Reliability, bias, and computational cost of estimating the Bayes factor using bridge sampling and the Savage-Dickey density ratio. [europepmc]

Related

• Enriched standard conjugate priors and the right invariant prior for Wishart distributions
• Statistical models, likelihood, penalized likelihood and hierarchical likelihood
• Bayesian Linear Models: A compact general set of results
• On Consistent and Calibrated Inference about the Parameters of Sampling Distributions
• Generalizations related to hypothesis testing with the Posterior distribution of the Likelihood Ratio