Journal ArticleDOI
Ellipsoidally symmetric extensions of the general location model for mixed categorical and continuous data
Chuanhai Liu,Donald B. Rubin +1 more
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TLDR
In this article, two extensions of the general location model are obtained, one replacing the common covariance matrix with different but proportional covariance matrices, where the proportionality constants are to be estimated.Abstract:
SUMMARY The general location model (Olkin & Tate, 1961; Krzanowski, 1980, 1982; Little & Schluchter, 1985) has categorical variables marginally distributed as a multinomial and continuous variables conditionally normally distributed with different means across cells defined by the categorical variables but a common covariance matrix across cells Two extensions of the general location model are obtained The first replaces the common covariance matrix with different but proportional covariance matrices, where the proportionality constants are to be estimated The second replaces the multivariate normal distributions of the first extension with multivariate t distributions, where the degrees of freedom can also vary across cells and are to be estimated The t distribution is just one example of more general ellipsoidally symmetric distributions that can be used in place of the normal These extensions can provide more accurate fits to real data and can be viewed as tools for robust inference Moreover, the models can be very useful for multiple imputation of ignorable missing values Maximum likelihood estimation using the AECM algorithm (Meng & van Dyk, 1997) is presented, as is a monotone-data Gibbs sampling scheme for drawing parameters and missing values from their posterior distributions To illustrate the techniques, a numerical example is presentedread more
Citations
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Applications of multiple imputation in medical studies: from AIDS to NHANES
John Barnard,Xiao-Li Meng +1 more
TL;DR: This paper reviews three applications of Rubin's method about estimating the reporting delay in acquired immune deficiency syndrome (AIDS) surveillance systems for the purpose of estimating survival time after AIDS diagnosis and handling nonresponse in United States National Health and Nutrition Examination Surveys (NHANES).
References
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Journal ArticleDOI
Maximum likelihood from incomplete data via the EM algorithm
Journal ArticleDOI
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
Stuart Geman,Donald Geman +1 more
TL;DR: The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.
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Statistical Analysis with Missing Data
TL;DR: This work states that maximum Likelihood for General Patterns of Missing Data: Introduction and Theory with Ignorable Nonresponse and large-Sample Inference Based on Maximum Likelihood Estimates is likely to be high.
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Bayesian Data Analysis
TL;DR: Detailed notes on Bayesian Computation Basics of Markov Chain Simulation, Regression Models, and Asymptotic Theorems are provided.
Journal ArticleDOI
Inference from Iterative Simulation Using Multiple Sequences
Andrew Gelman,Donald B. Rubin +1 more
TL;DR: The focus is on applied inference for Bayesian posterior distributions in real problems, which often tend toward normal- ity after transformations and marginalization, and the results are derived as normal-theory approximations to exact Bayesian inference, conditional on the observed simulations.