• Communications for Statistical Applications and Methods
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• v.30 no.3
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• pp.291-309
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• 2023

Longitudinal count data has been widely collected in biomedical research, public health, and clinical trials. These repeated measurements over time on the same subjects need to account for an appropriate dependency. The Poisson regression model is the first choice to model the expected count of interest, however, this may not be an appropriate when data exhibit over-dispersion or under-dispersion. Recently, Conway-Maxwell-Poisson (CMP) distribution is popularly used as the distribution offers a flexibility to capture a wide range of dispersion in the data. In this article, we propose a Bayesian CMP regression model to accommodate over and under-dispersion in modeling longitudinal count data. Specifically, we develop a regression model with random intercept and slope to capture subject heterogeneity and estimate covariate effects to be different across subjects. We implement a Bayesian computation via Hamiltonian MCMC (HMCMC) algorithm for posterior sampling. We then compute Bayesian model assessment measures for model comparison. Simulation studies are conducted to assess the accuracy and effectiveness of our methodology. The usefulness of the proposed methodology is demonstrated by a well-known example of epilepsy data.

• The Bulletin of The Korean Astronomical Society
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• v.41 no.2
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• pp.61.1-61.1
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• 2016

Black hole (BH) mass is a fundamental quantity to understand BH growth, galaxy evolution, and connection between them. Thus, obtaining accurate and precise BH mass estimates over cosmic time is of paramount importance. The rest-frame UV CIV ${\lambda}1549$ broad emission line is commonly used for BH mass estimates in high-redshift AGNs (i.e., $2{\leq}z{\leq}5$) when single-epoch (SE) optical spectra are available. Achieving correct and accurate calibration for CIV-based SE BH mass estimators against the most reliable reverberation-mapping based BH mass estimates is thus practically important and still useful. By performing multi-component spectral decomposition analysis to obtained high-quality HST UV spectra for the updated sample of local reverberation-mapped AGNs including new HST STIS observations, CIV emission line widths and continuum luminosities are consistently measured. Using a Bayesian hierarchical model with MCMC sampling based on Hamiltonian Monte Carlo algorithm (Stan NUTS), we provide the most consistent and accurate calibration of CIV-based BH mass estimators for the three line width characterizations, i.e., full width at half maximum (FWHM), line dispersion (${\sigma}_{line}$), and mean absolute deviation (MAD), in the extended BH mass dynamic range of log $M_{BH}/M_{\odot}=6.5-9.1$.