A Bayesian analysis of the minimal model was proposed where both glucose and insulin were analyzed simultaneously under the insulin-modified intravenous glucose tolerance test (IVGTT). The resulting model was implemen...A Bayesian analysis of the minimal model was proposed where both glucose and insulin were analyzed simultaneously under the insulin-modified intravenous glucose tolerance test (IVGTT). The resulting model was implemented with a nonlinear mixed-effects modeling setup using ordinary differential equations (ODEs), which leads to precise estimation of population parameters by separating the inter- and intra-individual variability. The results indicated that the Bayesian method applied to the glucose-insulin minimal model provided a satisfactory solution with accurate parameter estimates which were numerically stable since the Bayesian method did not require approximation by linearization.展开更多
Bayesian Hierarchical models has been widely used in modern statistical application.To deal with the data having complex structures,we propose a generalized hierarchical normal linear(GHNL)model which accommodates arb...Bayesian Hierarchical models has been widely used in modern statistical application.To deal with the data having complex structures,we propose a generalized hierarchical normal linear(GHNL)model which accommodates arbitrarily many levels,usual design matrices and'vanilla'covari-ance matrices.Objective hyperpriors can be employed for the GHNL model to express ignorance or match frequentist properties,yet the common objective Bayesian approaches are infeasible or fraught with danger in hierarchical modelling.To tackle this issue,[Berger,J,Sun,D.&Song,C.(2020b).An objective prior for hyperparameters in normal hierarchical models.Journal of Multi-variate Analysis,178,104606.https://doi.org/10.1016/jmva.2020.104606]proposed a particular objective prior and investigated its properties comprehensively.Posterior propriety is important for the choice of priors to guarantee the convergence of MCMC samplers.James Berger conjec-tured that the resulting posterior is proper for a hierarchical normal model with arbitrarily many levels,a rigorous proof of which was not given,however.In this paper,we complete this story and provide an user friendly guidance.One main contribution of this paper is to propose a new technique for deriving an elaborate upper bound on the integrated likelihood but also one uni-fied approach to checking the posterior propriety for linear models.An eficient Gibbs sampling method is also introduced and outperforms other sampling approaches considerably.展开更多
A recent paper [Thibaudeau, Slud, and Gottschalck (2017). Modeling log-linear conditional probabilities for estimation in surveys. The Annals of Applied Statistics, 11, 680–697] proposed a ‘hybrid’method of survey ...A recent paper [Thibaudeau, Slud, and Gottschalck (2017). Modeling log-linear conditional probabilities for estimation in surveys. The Annals of Applied Statistics, 11, 680–697] proposed a ‘hybrid’method of survey estimation combining coarsely cross-classified design-based survey-weightedtotals in a population with loglinear or generalised-linear model-based conditional probabilitiesfor cells in a finer cross-classification. The models were compared in weighted and unweightedforms on data from the US Survey of Income and Program Participation (SIPP), a large nationallongitudinal survey. The hybrid method was elaborated in a book-chapter [Thibaudeau, Slud,& Cheng (2019). Small-area estimation of cross-classified gross flows using longitudinal survey data. In P. Lynn (Ed.), Methodology of longitudinal surveys II. Wiley] about estimating grossflows in (two-period) longitudinal surveys, by considering fixed versus mixed effect versionsof the conditional-probability models and allowing for 3 or more outcomes in the later-periodcategories used to define gross flows within generalised logistic regression models. The methodology provided for point and interval small-area estimation, specifically area-level two-periodlabour-status gross-flow estimation, illustrated on a US Current Population Survey (CPS) datasetof survey respondents in two successive months in 16 states. In the current paper, that data analysis is expanded in two ways: (i) by analysing the CPS dataset in greater detail, incorporatingmultiple random effects (slopes as well as intercepts), using predictive as well as likelihood metrics for model quality, and (ii) by showing how Bayesian computation (MCMC) provides insightsconcerning fixed- versus mixed-effect model predictions. The findings from fixed-effect analyseswith state effects, from corresponding models with state random effects, and fom Bayes analysisof posteriors for the fixed state-effects with other model coefficients fixed, all confirm each otherand support a model with normal random state effects, independent across states.展开更多
文摘A Bayesian analysis of the minimal model was proposed where both glucose and insulin were analyzed simultaneously under the insulin-modified intravenous glucose tolerance test (IVGTT). The resulting model was implemented with a nonlinear mixed-effects modeling setup using ordinary differential equations (ODEs), which leads to precise estimation of population parameters by separating the inter- and intra-individual variability. The results indicated that the Bayesian method applied to the glucose-insulin minimal model provided a satisfactory solution with accurate parameter estimates which were numerically stable since the Bayesian method did not require approximation by linearization.
基金The research was supported by the National Natural Science Foundation of China[grant number 11671146].
文摘Bayesian Hierarchical models has been widely used in modern statistical application.To deal with the data having complex structures,we propose a generalized hierarchical normal linear(GHNL)model which accommodates arbitrarily many levels,usual design matrices and'vanilla'covari-ance matrices.Objective hyperpriors can be employed for the GHNL model to express ignorance or match frequentist properties,yet the common objective Bayesian approaches are infeasible or fraught with danger in hierarchical modelling.To tackle this issue,[Berger,J,Sun,D.&Song,C.(2020b).An objective prior for hyperparameters in normal hierarchical models.Journal of Multi-variate Analysis,178,104606.https://doi.org/10.1016/jmva.2020.104606]proposed a particular objective prior and investigated its properties comprehensively.Posterior propriety is important for the choice of priors to guarantee the convergence of MCMC samplers.James Berger conjec-tured that the resulting posterior is proper for a hierarchical normal model with arbitrarily many levels,a rigorous proof of which was not given,however.In this paper,we complete this story and provide an user friendly guidance.One main contribution of this paper is to propose a new technique for deriving an elaborate upper bound on the integrated likelihood but also one uni-fied approach to checking the posterior propriety for linear models.An eficient Gibbs sampling method is also introduced and outperforms other sampling approaches considerably.
文摘A recent paper [Thibaudeau, Slud, and Gottschalck (2017). Modeling log-linear conditional probabilities for estimation in surveys. The Annals of Applied Statistics, 11, 680–697] proposed a ‘hybrid’method of survey estimation combining coarsely cross-classified design-based survey-weightedtotals in a population with loglinear or generalised-linear model-based conditional probabilitiesfor cells in a finer cross-classification. The models were compared in weighted and unweightedforms on data from the US Survey of Income and Program Participation (SIPP), a large nationallongitudinal survey. The hybrid method was elaborated in a book-chapter [Thibaudeau, Slud,& Cheng (2019). Small-area estimation of cross-classified gross flows using longitudinal survey data. In P. Lynn (Ed.), Methodology of longitudinal surveys II. Wiley] about estimating grossflows in (two-period) longitudinal surveys, by considering fixed versus mixed effect versionsof the conditional-probability models and allowing for 3 or more outcomes in the later-periodcategories used to define gross flows within generalised logistic regression models. The methodology provided for point and interval small-area estimation, specifically area-level two-periodlabour-status gross-flow estimation, illustrated on a US Current Population Survey (CPS) datasetof survey respondents in two successive months in 16 states. In the current paper, that data analysis is expanded in two ways: (i) by analysing the CPS dataset in greater detail, incorporatingmultiple random effects (slopes as well as intercepts), using predictive as well as likelihood metrics for model quality, and (ii) by showing how Bayesian computation (MCMC) provides insightsconcerning fixed- versus mixed-effect model predictions. The findings from fixed-effect analyseswith state effects, from corresponding models with state random effects, and fom Bayes analysisof posteriors for the fixed state-effects with other model coefficients fixed, all confirm each otherand support a model with normal random state effects, independent across states.
