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Partition Weighted Approach for Estimating the Marginal Posterior Density with Applications.

ABSTRACT: The computation of marginal posterior density in Bayesian analysis is essential in that it can provide complete information about parameters of interest. Furthermore, the marginal posterior density can be used for computing Bayes factors, posterior model probabilities, and diagnostic measures. The conditional marginal density estimator (CMDE) is theoretically the best for marginal density estimation but requires the closed-form expression of the conditional posterior density, which is often not available in many applications. We develop the partition weighted marginal density estimator (PWMDE) to realize the CMDE. This unbiased estimator requires only a single MCMC output from the joint posterior distribution and the known unnormalized posterior density. The theoretical properties and various applications of the We carry out simulation studies to investigate the empirical performance of the PWMDE and further demonstrate the desirable features of the proposed method with two real data sets from a study of dissociative identity disorder patients and a prostate cancer study, respectively.

SUBMITTER: Wang YB

PROVIDER: S-EPMC6602590 | biostudies-literature | 2019

REPOSITORIES: biostudies-literature

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Partition Weighted Approach for Estimating the Marginal Posterior Density with Applications.

Wang Yu-Bo YB Chen Ming-Hui MH Kuo Lynn L Lewis Paul O PO

Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America 20190326 2

The computation of marginal posterior density in Bayesian analysis is essential in that it can provide complete information about parameters of interest. Furthermore, the marginal posterior density can be used for computing Bayes factors, posterior model probabilities, and diagnostic measures. The conditional marginal density estimator (CMDE) is theoretically the best for marginal density estimation but requires the closed-form expression of the conditional posterior density, which is often not ...[more]

PMID: 31263347

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Project description:Leaves acclimate to day-to-day fluctuating levels of photosynthetic photon flux density (PPFD) by adjusting their morphological and physiological parameters. Accurate estimation of these parameters under day-to-day fluctuating PPFD conditions benefits crop growth modeling and light environment management in greenhouses, although it remains challenging. We quantified the relationships between day-to-day PPFD changes over 6 days and light acclimation parameters for cucumber seedling leaves, including leaf mass per area (LMA), chlorophyll (Chl) a/b ratio, maximum net photosynthetic rate (P nmax), maximum rate of ribulose-1,5-bisphosphate (RuBP) carboxylase/oxygenase (V cmax), and maximum rate of electron transport (J max). The last two parameters reflect the capacity of the photosynthetic partial reactions. We built linear regression models of these parameters based on average or time-weighted averages of daily PPFDs. For time-weighted averages of daily PPFDs, the influence of daily PPFD was given a specific weight. We employed three types of functions to calculate this weight, including linear, quadratic, and sigmoid derivative types. We then determined the trend of weights that estimated each parameter most accurately. Moreover, we introduced saturating functions to calibrate the average or time-weighted averages of daily PPFDs, considering that light acclimation parameters are usually saturated under high PPFDs. We found that time-weighted average PPFDs, in which recent PPFD levels had larger weights than earlier levels, better estimated LMA than average PPFDs. This suggests that recent PPFDs contribute more to LMA than earlier PPFDs. Except for the Chl a/b ratio, the average PPFDs estimated P nmax, V cmax, and J max with acceptable accuracy. In contrast, time-weighted averages of daily PPFDs did not improve the estimation accuracy of these four parameters, possibly due to their low response rates and plasticity. Calibrating functions generally improved estimation of Chl a/b ratio, V cmax, and J max because of their saturating tendencies under high PPFDs. Our findings provide a reasonable approach to quantifying the extent to which the leaves acclimate to day-to-day fluctuating PPFDs, especially the extent of LMA.

Dataset Information

Partition Weighted Approach for Estimating the Marginal Posterior Density with Applications.

Publications

Partition Weighted Approach for Estimating the Marginal Posterior Density with Applications.

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