Bayesian Analysis of Constrained Parameter and Truncated Data Problems

By Alan E. Gelfand, Adrian F. M. Smith, Tai-Ming Lee. 1991

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Citations in the corpus

Fair Inference on Outcomes (2017, background): “A well known result (Gelfand, Smith, and Lee 1992) states that a Gibbs sampler will generate samples from a constrained posterior directly if it rejects all draws that violate the constraint.”
Approximate Bayesian inference for quantiles (2005, background): “Hanson and Johnson (2002) generalized this approach to smooth out the partitioning effect by using a mixture of Polya trees. Kottas and Gelfand (2001) and Gelfand and Kottas (2003) proposed alternative approaches for modeling of median 0 residuals distributions using mixtures.”
Data analytic methods for latent partially ordered classification models (2002, methodology): “Markov chain Monte Carlo estimation methods as described in Gelfand et al. (1992) were implemented to obtain item parameter estimates under order constraints pu.ei/ > pl.ei/; ei ∈ E .”
Sequential classification on partially ordered sets (2003, methodology): “Markov chainMonte Carlo parameter estimation techniques incorporating order constraints have been employed, as described in Gelfand et al. (1992).”
Simulation of truncated normal variables (2009, unknown): “This method is quite reasonable when µ− < µ but is of no use when µ− is several standard deviations to the right of µ. Similarly, Gelfand et al. (1992) and Chen and Deely (1992) suggest to use the classical c.d.f. inversion technique, namely to simulate u ∼ U[0,1] and to take z = µ + Φ−1 ( Φ ( µ− −…”
Efficient sampling methods for truncated multivariate normal and student-t distributions subject to linear inequality constraints (2015, methodology): “Several other applications are illustrated by Gelfand et al. (1992), Liechty and Lu (2010) and Yu and Tian (2011), including the truncated multivariate probit models in market research, and modeling co-skewness of the skew-normal distributions, shape-restricted nonparametric regressions, and so on.”
Markov chain estimation for test theory without an answer key (2003, unknown): “As in Gelfand, Smith, and Lee (1992) , such a complicated prior is routinely accommodated for GCM-ORD posterior estimation by modifying Step 2 of the MCMC algorithm to sample each of the Oi one-by-one.”