Lognormal and gamma mixed negative binomial regression

In regression analysis of counts, a lack of simple and efficient algorithms for posterior computation has made Bayesian approaches appear unattractive and thus underdeveloped. We propose a lognormal and gamma mixed negative binomial (NB) regression model for counts, and present efficient closed-form Bayesian inference; unlike conventional Poisson models, the proposed approach has two free parameters to include two different kinds of random effects, and allows the incorporation of prior information, such as sparsity in the regression coefficients. By placing a gamma distribution prior on the NB dispersion parameter r, and connecting a log-normal distribution prior with the logit of the NB probability parameter p, efficient Gibbs sampling and variational Bayes inference are both developed. The closed-form updates are obtained by exploiting conditional conjugacy via both a compound Poisson representation and a Polya-Gamma distribution based data augmentation approach. The proposed Bayesian inference can be implemented routinely, while being easily generalizable to more complex settings involving multivariate dependence structures. The algorithms are illustrated using real examples. Copyright 2012 by the author(s)/owner(s).

Seeing the forest for the fuel

We demonstrate a new approach to understanding the role of fuelwood in the rural household economy by applying insights from travel cost modeling to author-compiled household survey data and meso-scale environmental statistics from Ruteng Park in Flores, Indonesia. We characterize Manggarai farming households' fuelwood collection trips as inputs into household production of the utility yielding service of cooking and heating. The number of trips taken by households depends on the shadow price of fuelwood collection or the travel cost, which is endogenous. Econometric analyses using truncated negative binomial regression models and correcting for endogeneity show that the Manggarai are 'economically rational' about fuelwood collection and access to the forests for fuelwood makes substantial contributions to household welfare. Increasing cost of forest access, wealth, use of alternative fuels, ownership of kerosene stoves, trees on farm, park staff activity, primary schools and roads, and overall development could all reduce dependence on collecting fuelwood from forests. © 2004 Cambridge University Press.

Weighted and two-stage least squares estimation of semiparametric truncated regression models

This paper provides a root-n consistent, asymptotically normal weighted least squares estimator of the coefficients in a truncated regression model. The distribution of the errors is unknown and permits general forms of unknown heteroskedasticity. Also provided is an instrumental variables based two-stage least squares estimator for this model, which can be used when some regressors are endogenous, mismeasured, or otherwise correlated with the errors. A simulation study indicates that the new estimators perform well in finite samples. Our limiting distribution theory includes a new asymptotic trimming result addressing the boundary bias in first-stage density estimation without knowledge of the support boundary. © 2007 Cambridge University Press.

A memory-based model of posttraumatic stress disorder: evaluating basic assumptions underlying the PTSD diagnosis.

In the mnemonic model of posttraumatic stress disorder (PTSD), the current memory of a negative event, not the event itself, determines symptoms. The model is an alternative to the current event-based etiology of PTSD represented in the Diagnostic and Statistical Manual of Mental Disorders (4th ed., text rev.; American Psychiatric Association, 2000). The model accounts for important and reliable findings that are often inconsistent with the current diagnostic view and that have been neglected by theoretical accounts of the disorder, including the following observations. The diagnosis needs objective information about the trauma and peritraumatic emotions but uses retrospective memory reports that can have substantial biases. Negative events and emotions that do not satisfy the current diagnostic criteria for a trauma can be followed by symptoms that would otherwise qualify for PTSD. Predisposing factors that affect the current memory have large effects on symptoms. The inability-to-recall-an-important-aspect-of-the-trauma symptom does not correlate with other symptoms. Loss or enhancement of the trauma memory affects PTSD symptoms in predictable ways. Special mechanisms that apply only to traumatic memories are not needed, increasing parsimony and the knowledge that can be applied to understanding PTSD.

Structured Illumination Microscopy and a Quantitative Image Analysis for the Detection of Positive Margins in a Pre-Clinical Genetically Engineered Mouse Model of Sarcoma.

Intraoperative assessment of surgical margins is critical to ensuring residual tumor does not remain in a patient. Previously, we developed a fluorescence structured illumination microscope (SIM) system with a single-shot field of view (FOV) of 2.1 × 1.6 mm (3.4 mm2) and sub-cellular resolution (4.4 μm). The goal of this study was to test the utility of this technology for the detection of residual disease in a genetically engineered mouse model of sarcoma. Primary soft tissue sarcomas were generated in the hindlimb and after the tumor was surgically removed, the relevant margin was stained with acridine orange (AO), a vital stain that brightly stains cell nuclei and fibrous tissues. The tissues were imaged with the SIM system with the primary goal of visualizing fluorescent features from tumor nuclei. Given the heterogeneity of the background tissue (presence of adipose tissue and muscle), an algorithm known as maximally stable extremal regions (MSER) was optimized and applied to the images to specifically segment nuclear features. A logistic regression model was used to classify a tissue site as positive or negative by calculating area fraction and shape of the segmented features that were present and the resulting receiver operator curve (ROC) was generated by varying the probability threshold. Based on the ROC curves, the model was able to classify tumor and normal tissue with 77% sensitivity and 81% specificity (Youden's index). For an unbiased measure of the model performance, it was applied to a separate validation dataset that resulted in 73% sensitivity and 80% specificity. When this approach was applied to representative whole margins, for a tumor probability threshold of 50%, only 1.2% of all regions from the negative margin exceeded this threshold, while over 14.8% of all regions from the positive margin exceeded this threshold.