Mixtures of g-priors in Generalized Linear Models

Mixtures of Zellner's g-priors have been studied extensively in linear models and have been shown to have numerous desirable properties for Bayesian variable selection and model averaging. Several extensions of g-priors to Generalized Linear Models (GLMs) have been proposed in the literature; however, the choice of prior distribution of g and resulting properties for inference have received considerably less attention. In this paper, we unify mixtures of g-priors in GLMs by assigning the truncated Compound Confluent Hypergeometric (tCCH) distribution to 1/(1 + g), which encompasses as special cases several mixtures of g-priors in the literature, such as the hyper-g, Beta-prime, truncated Gamma, incomplete inverse-Gamma, benchmark, robust, hyper-g/n, and intrinsic priors. Through an integrated Laplace approximation, the posterior distribution of 1/(1 + g) is in turn a tCCH distribution, and approximate marginal likelihoods are thus available analytically, leading to "Compound Hypergeometric Information Criteria" for model selection. We discuss the local geometric properties of the g-prior in GLMs and show how the desiderata for model selection proposed by Bayarri et al, such as asymptotic model selection consistency, intrinsic consistency, and measurement invariance may be used to justify the prior and specific choices of the hyper parameters. We illustrate inference using these priors and contrast them to other approaches via simulation and real data examples. The methodology is implemented in the R package BAS and freely available on CRAN

On the Use of Cauchy Prior Distributions for Bayesian Logistic Regression

In logistic regression, separation occurs when a linear combination of the predictors can perfectly classify part or all of the observations in the sample, and as a result, finite maximum likelihood estimates of the regression coefficients do not exist. Gelman et al. (2008) recommended independent Cauchy distributions as default priors for the regression coefficients in logistic regression, even in the case of separation, and reported posterior modes in their analyses. As the mean does not exist for the Cauchy prior, a natural question is whether the posterior means of the regression coefficients exist under separation. We prove theorems that provide necessary and sufficient conditions for the existence of posterior means under independent Cauchy priors for the logit link and a general family of link functions, including the probit link. We also study the existence of posterior means under multivariate Cauchy priors. For full Bayesian inference, we develop a Gibbs sampler based on Polya-Gamma data augmentation to sample from the posterior distribution under independent Student-t priors including Cauchy priors, and provide a companion R package in the supplement. We demonstrate empirically that even when the posterior means of the regression coefficients exist under separation, the magnitude of the posterior samples for Cauchy priors may be unusually large, and the corresponding Gibbs sampler shows extremely slow mixing. While alternative algorithms such as the No-U-Turn Sampler in Stan can greatly improve mixing, in order to resolve the issue of extremely heavy tailed posteriors for Cauchy priors under separation, one would need to consider lighter tailed priors such as normal priors or Student-t priors with degrees of freedom larger than one

Are Innovation Output and Economic Output Strongly Related in Emerging Industrial Clusters? Evidence from China

For many countries, innovation-driven development has become a prevalent consensus because innovation can effectively stimulate economic growth. Emerging industries are innovation-intensive with high potential economic benefit. However, is it assured that high innovation output means high economic benefit? In October of 2010, China State Council initiated the Decision of Speeding up Cultivation and Development of Strategic Emerging Industries, signifying top-down policy mobilization to advance emerging industries. According to seven types of emerging industries defined in the Decision, we collected data from official industrial databases to figure out spatial divergence of emerging industries in terms of innovation output and economic benefit over the years from 2000 to 2011. We construct twodimension scatter diagrams based on number of granted patents as the indicator of innovation output and industrial locational quotient as the indicator of industrial economic benefit. The result shows that China has seen preliminary spatial clustering of key emerging industries across regions and industries in the light of innovation output and economic benefit. However, not all regions with high innovation output have high economic benefit. The spatial divergence is closely related to region-specific and industry-specific characteristics. We offer policy implications to facilitate targeted emerging industries with more detailed policy and regional endowment

Bayesian Hierarchical Models for Model Choice

<p>With the development of modern data collection approaches, researchers may collect hundreds to millions of variables, yet may not need to utilize all explanatory variables available in predictive models. Hence, choosing models that consist of a subset of variables often becomes a crucial step. In linear regression, variable selection not only reduces model complexity, but also prevents over-fitting. From a Bayesian perspective, prior specification of model parameters plays an important role in model selection as well as parameter estimation, and often prevents over-fitting through shrinkage and model averaging.</p><p>We develop two novel hierarchical priors for selection and model averaging, for Generalized Linear Models (GLMs) and normal linear regression, respectively. They can be considered as "spike-and-slab" prior distributions or more appropriately "spike- and-bell" distributions. Under these priors we achieve dimension reduction, since their point masses at zero allow predictors to be excluded with positive posterior probability. In addition, these hierarchical priors have heavy tails to provide robust- ness when MLE's are far from zero.</p><p>Zellner's g-prior is widely used in linear models. It preserves correlation structure among predictors in its prior covariance, and yields closed-form marginal likelihoods which leads to huge computational savings by avoiding sampling in the parameter space. Mixtures of g-priors avoid fixing g in advance, and can resolve consistency problems that arise with fixed g. For GLMs, we show that the mixture of g-priors using a Compound Confluent Hypergeometric distribution unifies existing choices in the literature and maintains their good properties such as tractable (approximate) marginal likelihoods and asymptotic consistency for model selection and parameter estimation under specific values of the hyper parameters.</p><p>While the g-prior is invariant under rotation within a model, a potential problem with the g-prior is that it inherits the instability of ordinary least squares (OLS) estimates when predictors are highly correlated. We build a hierarchical prior based on scale mixtures of independent normals, which incorporates invariance under rotations within models like ridge regression and the g-prior, but has heavy tails like the Zeller-Siow Cauchy prior. We find this method out-performs the gold standard mixture of g-priors and other methods in the case of highly correlated predictors in Gaussian linear models. We incorporate a non-parametric structure, the Dirichlet Process (DP) as a hyper prior, to allow more flexibility and adaptivity to the data.</p>Dissertatio

Berberine hydrochloride: anticancer activity and nanoparticulate delivery system

Wen Tan, Yingbo Li, Meiwan Chen, Yitao WangState Key Laboratory of Quality Research in Chinese Medicine, Institute of Chinese Medical Sciences, University of Macau, Macao Special Administrative Region, ChinaBackground: Berberine hydrochloride is a conventional component in Chinese medicine, and is characterized by a diversity of pharmacological effects. However, due to its hydrophobic properties, along with poor stability and bioavailability, the application of berberine hydrochloride was hampered for a long time. In recent years, the pharmaceutical preparation of berberine hydrochloride has improved to achieve good prospects for clinical application, especially for novel nanoparticulate delivery systems. Moreover, anticancer activity and novel mechanisms have been explored, the chance of regulating glucose and lipid metabolism in cancer cells showing more potential than ever. Therefore, it is expected that appropriate pharmaceutical procedures could be applied to the enormous potential for anticancer efficacy, to give some new insights into anticancer drug preparation in Chinese medicine.Methods and results: We accessed conventional databases, such as PubMed, Scope, and Web of Science, using &amp;ldquo;berberine hydrochloride&amp;rdquo;, &amp;ldquo;anti-cancer mechanism&amp;rdquo;, and &amp;ldquo;nanoparticulate delivery system&amp;rdquo; as search words, then summarized the progress in research, illustrating the need to explore reprogramming of cancer cell metabolism using nanoparticulate drug delivery systems.Conclusion: With increasing research on regulation of cancer cell metabolism by berberine hydrochloride and troubleshooting of issues concerning nanoparticulate delivery preparation, berberine hydrochloride is likely to become a natural component of the nanoparticulate delivery systems used for cancer therapy. Meanwhile, the known mechanisms of berberine hydrochloride, such as decreased multidrug resistance and enhanced sensitivity of chemotherapeutic drugs, along with improvement in patient quality of life, could also provide new insights into cancer cell metabolism and nanoparticulate delivery preparation.Keywords: berberine hydrochloride, anticancer mechanisms, nanoparticulate drug progres