Extensions of a Conflict Measure of Inconsistencies in Bayesian Hierarchical Models Export

@article{citeulike:6048240, abstract = {.\&\#8194; In a recent paper we extended and refined some tools introduced by O'Hagan for criticism of Bayesian hierarchical models. Especially, avoiding double use of data by a data-splitting approach was a main concern. Such tools can be applied at each node of the model, with a view to diagnosing problems of model fit at any point in the model structure. As O'Hagan, we investigated a Gaussian model of one-way analysis of variance. Through extensive Markov chain Monte Carlo simulations it was shown that our method detects model misspecification about as well as the one of O'Hagan, when this is properly calibrated, while retaining the desired false warning probability for data generated from the assumed model. In the present paper, we suggest some new measures of conflict based on tail probabilities of the so-called integrated posterior distributions introduced in our recent paper. These new measures are equivalent to the measure applied in the latter paper in simple Gaussian models, but seem more appropriately adjusted to deviations from normality and to conflicts not concerning location parameters. A general linear normal model with known covariance matrices is considered in detail.}, author = {Gasemyr, Jorund and Natvig, B. E. N. T.}, citeulike-article-id = {6048240}, citeulike-linkout-0 = {http://dx.doi.org/10.1111/j.1467-9469.2009.00659.x}, citeulike-linkout-1 = {http://www.ingentaconnect.com/content/bpl/sjos/2009/00000036/00000004/art00014}, doi = {10.1111/j.1467-9469.2009.00659.x}, issn = {0303-6898}, journal = {Scandinavian Journal of Statistics}, keywords = {anova, bayesian, detection, error, gaussian, hierarchical, model, statistics}, month = {December}, number = {4}, pages = {822--838}, posted-at = {2009-11-13 17:46:06}, priority = {2}, publisher = {Blackwell Publishing}, title = {Extensions of a Conflict Measure of Inconsistencies in Bayesian Hierarchical Models}, url = {http://dx.doi.org/10.1111/j.1467-9469.2009.00659.x}, volume = {36}, year = {2009} }

TY - JOUR ID - citeulike:6048240 L3 - citeulike-article-id:6048240 N2 - .  In a recent paper we extended and refined some tools introduced by O'Hagan for criticism of Bayesian hierarchical models. Especially, avoiding double use of data by a data-splitting approach was a main concern. Such tools can be applied at each node of the model, with a view to diagnosing problems of model fit at any point in the model structure. As O'Hagan, we investigated a Gaussian model of one-way analysis of variance. Through extensive Markov chain Monte Carlo simulations it was shown that our method detects model misspecification about as well as the one of O'Hagan, when this is properly calibrated, while retaining the desired false warning probability for data generated from the assumed model. In the present paper, we suggest some new measures of conflict based on tail probabilities of the so-called integrated posterior distributions introduced in our recent paper. These new measures are equivalent to the measure applied in the latter paper in simple Gaussian models, but seem more appropriately adjusted to deviations from normality and to conflicts not concerning location parameters. A general linear normal model with known covariance matrices is considered in detail. IS - 4 JF - Scandinavian Journal of Statistics SN - 0303-6898 EP - 838 TI - Extensions of a Conflict Measure of Inconsistencies in Bayesian Hierarchical Models PB - Blackwell Publishing VL - 36 SP - 822 KW - anova KW - bayesian KW - detection KW - error KW - gaussian KW - hierarchical KW - model KW - statistics AU - Gasemyr, Jorund AU - Natvig, BENT PY - 2009/12// UR - http://dx.doi.org/10.1111/j.1467-9469.2009.00659.x ER -