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Bayesian Inference with Inequality Constraints
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 Title & Authors
Bayesian Inference with Inequality Constraints
Oh, Man-Suk;
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This paper reviews Bayesian inference with inequality constraints. It focuses on ⅰ) comparison of models with various inequality/equality constraints on parameters, ⅱ) multiple tests on equalities of parameters when parameters are under inequality constraints, ⅲ) multiple test on equalities of score parameters in models for contingency tables with ordinal categorical variables.
Order restricted;multiple test;Markov chain Monte Carlo;Savage-Dickey density ratio;Bayes factor;
 Cited by
Akaike, H. (1987). Factor analysis and AIC, Psychometrika, 52, 317-332. crossref(new window)

Agresti, A., Chuang, C. and Kezouh, A. (1987). Order-restricted score parameters in association models for contingency tables, Journal of the American Statistical Association, 82, 619-623. crossref(new window)

Agresti, A. and Coull, B. A. (2002). The analysis of contingency tables under inequality constraints, Journal of Statistical Planning and Inference, 107, 45-73. crossref(new window)

Albert. J. and Chib, S. (1991). Bayesian Analysis of binary and polychotomous response Data, Journal of the American Statistical Association, 88, 669-679

Anraku, K. (1999). An information criterion for parameters under a simple order restriction, Biometrika, 86, 141-152 crossref(new window)

Bacchetti, P. (1989). Addictive isotonic models, Journal of the American Statistical Association, 84, 289-294.

Barlow, R. E., Bartholomew, D. J., Bremner, J. M. and Brunk, H. D. (1972). Statistical Inference Under Order Restrictions, New York, NY: Wiley.

Dickey, J. (1971). The weighted likelihood ration, linear hypotheses on normal location parameters, The Annals of Statistics, 42, 204-223. crossref(new window)

Dickey, J. (1976). Approximate posterior distributions, Journal of the American Statistical Association, 71, 680-689. crossref(new window)

Dickey, J. and Lientz, B. P. (1970). The weighted likelihood ration, sharp hypotheses about chances, the order of a Markov Chain, Annals of Mathematical Statistics, 41, 214-226. crossref(new window)

Dunson, D. B. and Neelon, B. (2003). Bayesian inference on order-constrained parameters in generalized linear models, Biometrics, 59, 286-295. crossref(new window)

Dykstra, R. L., Robertson, T. and Silvapulle, M. J. (2002). Statistical inference under inequality constraints, Special issue, Journal of Statistical Planning and Inference, 107, 1-2. crossref(new window)

Galindo-Garre, F. G.and Vermunt, J. K. (2004). The order restricted association model : Two estimation algorithms and issues in testing, Psychometrika, 68, 614-654.

Galindo-Garre, F. G. and Vermunt, J. K. (2005). Testing log-linear models with inequality constraints: A comparison of asymptotic, bootstrap and posterior predictive p-values, Statistical Netherlandica, 59, 82-94. crossref(new window)

Goodman, L. A., (1979). Simple models for the analysis of association in cross-classifications having ordered categories, Journal of the American Statistical Association, 74, 537-552. crossref(new window)

Hayter, A. J. (1990). A one-sided studentized range test for testing against a simple ordered alternative, Journal of the American Statistical Association, 85, 778-785.

Hoijtink, H. (2013). Objective Bayes factors for inequality constrained hypotheses, International Statistical Review, 81, 207-229 crossref(new window)

Hoijtink, H., Klugkist, I. and Boelen, P. A. (2008). Bayesian Evaluation of Informative Hypotheses, Springer, New York.

Iliopoulos, G., Kateri, M. and Ntzoufras, I. (2007). Bayesian estimation of unrestricted and order-restricted association models for two-way contingency table, Computational Statistics and Data Analysis, 51, 4643-4655. crossref(new window)

Iliopoulos, G., Kateri, M. and Ntzoufras, I. (2009). Bayesian model comparison for the order-restricted RC association model, Psychometrika, 74, 561-587. crossref(new window)

Johnson, N. L. and Kotz, S. (1972). Distributions in Statistics, John & Wiley, New York.

Klugkist, I., Kata, B. and Hoijtink, H. (2005). Bayesian model selection using encompassing priors, Statistica Neerlandica, 59, 57-59. crossref(new window)

Klugkist, I., Laudy, O. and Hoijtink, H. (2005). Inequality constrained analysis of variance: A Bayesian approach, Psychological Methods, 10, 477-493. crossref(new window)

Klugkist, I. and Hoijtink, H. (2007). The Bayes factor for inequality and about equality constrained models, Computational Statistics and Data Analysis, 51, 6367-6379. crossref(new window)

Kuiper, R. M., Hoijtink, H.J.A. and Silvapulle, M. J. (2011). An Akaike-type information criterion for model selection under inequality constraints, Biometrika, 98, 495-501. crossref(new window)

Kuiper, R. M., Hoijtink, H. J. A. and Silvapulle, M. J., (2012). Generalization of the order-restricted information criterion for multivariate normal linear models, Journal of Statistical Planning and Inference, 142, 2454-2463. crossref(new window)

Laudy, O. and Hoijtink, H. (2007). Bayesian methods for the analysis of inequality and equality constrained contingency tables, Statistical Methods in Medical Research, 16, 123-138. crossref(new window)

Lindley, D. V. (1957). A statistical paradox, Biometrika, 44, 187-192. crossref(new window)

Liu, L., Lee, C. C. and Peng, J. (2002). Max-min multiple comparison procedure for isotonic does-response curves, Journal of Statistical Planning and Inference, 107, 133-141. crossref(new window)

Liu, L. (2001). Simultaneous statistical inference for monotone dose-response means, Doctoral dissertation, Memorial University of Newfoundland, St, John's, Canada.

Marden, J. H. and Allen, L. R. (2002). Molecules, muscles, and machines: Universal performance characteristics of motors, The National Academy of Sciences USA, 99, 4161-4166. crossref(new window)

Marden, J. I. and Gao. Y. H.(2002). Rank-based procedures for structural hypotheses of the covariance matrix, Sankhya, 64, 653-677

Marcus, R. and Peritz, E. (1976). Some simultaneous confidence bounds in normal models with restricted alternatives, Journal of the Royal Statistical Society, 38, 157-165.

Marcus, R. (1982). Some results on simultaneous confidence intervals for monotone contrasts in one-way ANOVA model, Communications in Statistics A, 11, 615-622. crossref(new window)

Maxwell, I. E. (1961). Maxwell, E. A. Recent trends in factor analysis, Journal of the Royal Statistical Society, 124, 49-59. crossref(new window)

Moreno, E. (2005). Objective Bayesian methods for one-sided testing, Journal of the American Statistical Association, 14, 181-198.

Monton-Jones, T., Diggle, P., Parker, L., Dickinson, H. O. and Binks, K. (2000). Addictive isotonic regression models in epidemiology, Statistics in Medicine, 19, 849-859. crossref(new window)

Mulder, J. (2014a). Prior adjusted default Bayes factors for testing (in) equality constrained hypotheses, Computational Statistics and Data Analysis, 71, 448-463. crossref(new window)

Mulder, J. (2014b). Bayes factors for testing inequality constrained hypotheses: Issues with prior specification, British Journal of Mathematical and Statistical Psychology, 67, 153-171. crossref(new window)

Mulder, J., Hoijtink, H. and Klugkist, I. (2010). Equality and inequality constrained multivariate linear models: Objective model selection using constrained posterior priors, Journal of Statistical Planning and Inference, 140, 887-906. crossref(new window)

Nashimoto, K. and Wright, F. T. (2005). A note on multiple comparison procedures for detecting difference in simply ordered means, Statistics and Probability Letters, 73, 393-401. crossref(new window)

Oh, M. S. (1999). Estimation of posterior density functions from a posterior sample, Computational Statistics and Data Analysis, 29, 411-427. crossref(new window)

Oh, M. S. and Shin, D. W. (2011). A unified Bayesian inference on treatment means with order constraints, Computational Statistics and Data Analysis, 55, 924-934. crossref(new window)

Oh, M. S. (2013). Bayesian multiple comparison of models for binary data with inequality constraints, Statistics and Computing, 23, 481-490. crossref(new window)

Oh, M. S. (2014a). Bayesian test one quality of score parameters in the order restricted RC association model, Computational Statistics and Data Analysis, 72, 147-157. crossref(new window)

Oh, M. S. (2014b). Bayesian comparison of model swith inequality and equality constraints, Statistics and Probability Letters, 84, 176-182. crossref(new window)

Ritov, Y. and Gilula, Z. (1993). The order restricted RC model for ordered contingency tables: estimation and testing for fit, Annals of Statistics, 19, 2090-2101.

Robertson, T., Wright, F. T. and Dykstra, R. L. (1988). Order Restricted Statistical Inference, John Wiley and Sons, New York.

Schwarz, G. (1978). Estimating the dimension of a model, Annals of Statistics, 6, 461-464. crossref(new window)

Shang, J., Cavanaugh, J. E. and Wright, F. T. (2008). A Bayesian multiple comparison procedure for orderrestricted mixed models, International Statistical Review, 76, 268-284. crossref(new window)

Shayamall, D. P. and Dunson, D. B. (2005). Estimation of order-restricted means from correlated data, Biometrika, 92, 703-715. crossref(new window)

Silvapulle, M. J. and Sen, P. K. (2004). Constrained Statistical Inference, Wiley, New York.

Tarantola, C., Consonni, G. and Dellaportas, P. (2008). Bayesian clustering of row effects models, Journal of Statistical Planning and Inference, 138, 2223-2235. crossref(new window)

Taylor, J. M. G., Wang, L. and Li, Z. (2007). Analysis on binary responses with ordered covariates and missing data, Statistics in Medicine, 26, 3443-3458. crossref(new window)

Van Wesel, F., Hoijtink, H. and Klugkist, I. (2011). Choosing priors for constrained analysis of variance: Methods based on training data, Scandinavian Journal of Statistics, 38, 666-690. crossref(new window)

Verdinelli, I. and Wasserman, L. (1995). Computing Bayes factors using a generalization of the Savage-Dickey density ratio, Journal of the American Statistical Association, 90, 613-618.

Wetzels, R., Vandekerckhove, J., Tuerlinckx, F. and Wagenmakers, E. (2010). Bayesian parameter estimation in the expectancy valence model of the Iowa gambling task, Journal of Mathematical Psychology, 54, 14-27. crossref(new window)

Williams, D. A. (1977). Some inference procedures for monotonically ordered normal means, Biometrika, 64, 9-14. crossref(new window)