Joint prior distributions for variance parameters in Bayesian analysis of normal hierarchical models

Date

2015-03-01

Author

Demirhan, Haydar
Kalaylıoğlu Akyıldız, Zeynep Işıl

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

178
views

0
downloads

In random effect models, error variance (stage 1 variance) and scalar random effect variance components (stage 2 variances) are a priori modeled independently. Considering the intrinsic link between the stages 1 and 2 variance components and their interactive effect on the parameter draws in Gibbs sampling, we propose modeling the variances of the two stages a priori jointly in a multivariate fashion. We use random effects linear growth model for illustration and consider multivariate distributions to model the variance components jointly including the recently developed generalized multivariate log gamma (G-MVLG) distribution. We discuss these variance priors as well as the independent variance priors exercised in the literature in different aspects including noninformativeness and propriety of the associated posterior density. We show through an extensive simulation experiment that modeling the variance components of different stages multivariately results in better estimation properties for the response and random effect model parameters compared to independent modeling. We scrutinize the sensitivity of response model coefficient estimates to the parameters of considered noninformative variance priors and find that their full conditional expectations are insensitive to noninformative G-MVLG prior parameters. We apply independent and joint models for analysis of a real dataset and find that multivariate priors for variance components lead to better fitted hierarchical model than the univariate variance priors.

Subject Keywords

Hierarchical models, Multi-level models, Multivariate log gamma, Random coefficient, Random effect, Variance components, Hyperprior, Hyperparameter, Directional derivative, Sensitivity analysis

URI

https://hdl.handle.net/11511/49158

Journal

JOURNAL OF MULTIVARIATE ANALYSIS

DOI

https://doi.org/10.1016/j.jmva.2014.12.013

Collections

Department of Statistics, Article

Suggestions

OpenMETU
Core

On the generalized multivariate Gumbel distribution Demirhan, Haydar; Kalaylıoğlu Akyıldız, Zeynep Işıl (2015-08-01) In this article, main characteristics, marginal, joint, and conditional inferences of a generalized multivariate Gumbel model are derived, and random vector generation is described. Distribution of the sum where summands come from a bivariate generalized multivariate Gumbel distribution is derived.
Integrated nonlinear regression analysis of tracer and well test data Akın, Serhat (Elsevier BV, 2003-08-01) One frequent observation from conventional pressure transient test analysis is that field data match mathematical models derived for homogeneous systems. This observation suggests that pressure data as presently interpreted may not contain details concerning certain reservoir heterogeneities. On the other hand, tracer tests may be more sensitive to heterogeneous elements present in the reservoir because of the convective nature of the flow test. In this study, a possible improvement of conventional pressure...
Semi-Bayesian Inference of Time Series Chain Graphical Models in Biological Networks Farnoudkia, Hajar; Purutçuoğlu Gazi, Vilda (null; 2018-09-20) The construction of biological networks via time-course datasets can be performed both deterministic models such as ordinary differential equations and stochastic models such as diffusion approximation. Between these two branches, the former has wider application since more data can be available. In this study, we particularly deal with the probabilistic approaches for the steady-state or deterministic description of the biological systems when the systems are observed though time. Hence, we consider time s...
Estimation and hypothesis testing in multivariate linear regression models under non normality İslam, Muhammed Qamarul (Informa UK Limited, 2017-01-01) This paper discusses the problem of statistical inference in multivariate linear regression models when the errors involved are non normally distributed. We consider multivariate t-distribution, a fat-tailed distribution, for the errors as alternative to normal distribution. Such non normality is commonly observed in working with many data sets, e.g., financial data that are usually having excess kurtosis. This distribution has a number of applications in many other areas of research as well. We use modifie...
Low-Level Hierarchical Multiscale Segmentation Statistics of Natural Images Akbaş, Emre (2014-09-01) This paper is aimed at obtaining the statistics as a probabilistic model pertaining to the geometric, topological and photometric structure of natural images. The image structure is represented by its segmentation graph derived from the low-level hierarchical multiscale image segmentation. We first estimate the statistics of a number of segmentation graph properties from a large number of images. Our estimates confirm some findings reported in the past work, as well as provide some new ones. We then obtain ...

Citation Formats

H. Demirhan and Z. I. Kalaylıoğlu Akyıldız, “Joint prior distributions for variance parameters in Bayesian analysis of normal hierarchical models,” JOURNAL OF MULTIVARIATE ANALYSIS, pp. 163–174, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/49158.