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We introduce a new approach to latent state filtering and parameter estimation for a class of stochastic volatility models (SVMs) for which the likelihood function is unknown. The $\alpha$ -stable stochastic volatility model provides a flexible framework for capturing asymmetry and heavy tails, which is useful when modeling financial returns. However, the $\alpha$ -stable distribution lacks a closed form for the probability density function, which prevents the direct application of standard Bayesian filtering and estimation techniques such as sequential Monte Carlo and Markov chain Monte Carlo. To obtain filtered volatility estimates, we develop a novel approximate Bayesian computation (ABC) based auxiliary particle filter, which provides improved performance through better proposal distributions. Further, we propose a new particle based MCMC (PMCMC) method for joint estimation of the parameters and latent volatility states. With respect to other extensions of PMCMC, we introduce an efficient single filter particle Metropolis-within-Gibbs algorithm which can be applied for obtaining inference on the parameters of an asymmetric $\alpha$ -stable stochastic volatility model. We show the increased efficiency in the estimation process through a simulation study. Finally, we highlight the necessity for modeling asymmetric $\alpha$ -stable SVMs through an application to propane weekly spot prices.

A comprehensive regional investigation of the Eagle Ford Shale linking productivity to porosity-thickness (PHIH), lithology ([Formula: see text]), pore volume (PHIT), organic matter (TOC), and water-saturation ([Formula: see text]) variations has not been presented to date. Therefore, isopach maps across the Eagle Ford Shale play west of the San Marcos Arch were constructed using thickness and log-calculated attributes such as TOC, [Formula: see text], [Formula: see text], and porosity to identify sweet spots and spatial distribution of these geologic characteristics that influence productivity in shale plays. The Upper Cretaceous Eagle Ford Shale in South Texas is an organic-rich, calcareous mudrock deposited during a second-order transgression of global sea level on a carbonate-dominated shelf updip from the older Sligo and Edwards (Stuart City) reef margins. Lithology and organic-matter deposition were controlled by fluvial input from the Woodbine delta in the northeast, upwelling along the Cretaceous shelf edge, and volcanic and clastic input from distant Laramide events to the north and west. Local oxygen minimum events along the South Texas margin contributed to the preservation of this organic-rich source rock related to the Cenomanian/Turonian global organic anoxic event (OAE2). Paleogeographic and deep-seated tectonic elements controlled the variations of lithology, amount and distribution of organic matter, and facies that have a profound impact on production quality. Petrophysical modeling was conducted to calculate total organic carbon, water saturation, lithology, and porosity of the Eagle Ford Group. Thickness maps, as well as PHIH maps, show multiple sweet spots across the study area. Components of the database were used as variables in kriging, and multivariate statistical analyses evaluated the impact of these variables on productivity. For example, TOC and clay volume ([Formula: see text]) show an inverse relationship that is related to production. Mapping petrophysical parameters across a play serves as a tool to predict geologic drivers of productivity across the Eagle Ford taking the geologic heterogeneity into account.

OBJECTIVEOligodendroglioma is a rare primary CNS neoplasm in the pediatric population, and only a limited number of studies in the literature have characterized this entity. Existing studies are limited by small sample sizes and discrepant interstudy findings in identified prognostic factors. In the present study, the authors aimed to increase the statistical power in evaluating for potential prognostic factors of pediatric oligodendrogliomas and sought to reconcile the discrepant findings present among existing studies by performing an individual-patient-data (IPD) meta-analysis and using multiple imputation to address data not directly available from existing studies.METHODSA systematic search was performed, and all studies found to be related to pediatric oligodendrogliomas and associated outcomes were screened for inclusion. Each study was searched for specific demographic and clinical characteristics of each patient and the duration of event-free survival (EFS) and overall survival (OS). Given that certain demographic and clinical information of each patient was not available within all studies, a multivariable imputation via chained equations model was used to impute missing data after the mechanism of missing data was determined. The primary end points of interest were hazard ratios for EFS and OS, as calculated by the Cox proportional-hazards model. Both univariate and multivariate analyses were performed. The multivariate model was adjusted for age, sex, tumor grade, mixed pathologies, extent of resection, chemotherapy, radiation therapy, tumor location, and initial presentation. A p value of less than 0.05 was considered statistically significant.RESULTSA systematic search identified 24 studies with both time-to-event and IPD characteristics available, and a total of 237 individual cases were available for analysis. A median of 19.4% of the values among clinical, demographic, and outcome variables in the compiled 237 cases were missing. Multivariate Cox regression analysis revealed subtotal resection (p = 0.007 [EFS] and 0.043 [OS]), initial presentation of headache (p = 0.006 [EFS] and 0.004 [OS]), mixed pathologies (p = 0.005 [EFS] and 0.049 [OS]), and location of the tumor in the parietal lobe (p = 0.044 [EFS] and 0.030 [OS]) to be significant predictors of tumor progression or recurrence and death.CONCLUSIONSThe use of IPD meta-analysis provides a valuable means for increasing statistical power in investigations of disease entities with a very low incidence. Missing data are common in research, and multiple imputation is a flexible and valid approach for addressing this issue, when it is used conscientiously. Undergoing subtotal resection, having a parietal tumor, having tumors with mixed pathologies, and suffering headaches at the time of diagnosis portended a poorer prognosis in pediatric patients with oligodendroglioma.

Gradually increasing production of natural gas from shale formations has surpassed the production from all other sources, including conventional, coal-bed, and tight formations in the U.S. (EIA, Monthly Energy Review, Jan. 2016). In fact, thanks to shale, natural gas production in the U.S. increased much faster than demand growth. Lower gas prices since 2010-11 owing to excess supply, has been encouraging more natural gas utilization in power generation and industrial sector, and exports via pipelines to Mexico and the rest of the world via liquefaction facilities. Many of these facilities are still under construction; and demand growth may not be fully felt until 2018 or later. In the meantime, shale drilling has slowed down considerably owing to low oil (and NGL) prices in addition to low natural gas prices. This situation raises concerns about the shale gas resource potential and future production capabilities. To address these concerns, the understanding of the two key resource characteristics is essential: (1) the total resource-in-place, and (2) the extractability of the resource under the given technological and economic conditions. The Marcellus play is the largest shale gas play in the U.S.; gas production from the play continued to increase despite declining prices and drilling activity. In this study, we focus on the Marcellus play to study these two characteristics. The resource base estimate for the Marcellus has been provided by geologic studies (e.g. Smye et al., in review). The recovery remains a subject of discussion in numerous engineering studies (Malpani et al., 2015; Xie and Li, 2014; Arogundade and Sohrabi, 2012). These studies, however, are mostly focused on the best drilling and completion practices, rather than looking at changes in productivity over time or comparison of marginal contribution of different inputs to productivity, which is more relevant for economic studies of the resource extraction. The present paper attempts to fill this gap, preparing the base for further economic viability analyses.