Bayesian predictive densities based on latent information priors

Construction methods for prior densities are investigated from a predictive viewpoint. Predictive densities for future observables are constructed by using observed data. The simultaneous distribution of future observables and observed data is assumed to belong to a parametric submodel of a multinomial model. Future observables and data are possibly dependent. The discrepancy of a predictive density to the true conditional density of future observables given observed data is evaluated by the Kullback-Leibler divergence. It is proved that limits of Bayesian predictive densities form an essentially complete class. Latent information priors are defined as priors maximizing the conditional mutual information between the parameter and the future observables given the observed data. Minimax predictive densities are constructed as limits of Bayesian predictive densities based on prior sequences converging to the latent information priors.     

On Parametric Bootstrapping and Bayesian Prediction

Abstract.  We investigate bootstrapping and Bayesian methods for prediction. The observations and the variable being predicted are distributed according to different distributions. Many important problems can be formulated in this setting. This type of prediction problem appears when we deal with a Poisson process. Regression problems can also be formulated in this setting. First, we show that bootstrap predictive distributions are equivalent to Bayesian predictive distributions in the second-order expansion when some conditions are satisfied. Next, the performance of predictive distributions is compared with that of a plug-in distribution with an estimator. The accuracy of prediction is evaluated by using the Kullback–Leibler divergence. Finally, we give some examples.     

Comorbidities as predictors of incidental prostate cancer after Holmium laser enucleation of the prostate: diabetes and high-risk cancer

Prostate cancer can be diagnosed as an incidental finding during the pathological examination of benign prostatic hyperplasia (BPH) specimens by Holmium laser enucleation of the prostate (HoLEP). BPH and comorbidities such as hypertension, diabetes, and dyslipidemia often coexist in elderly people. We identified which comorbidities can be used to predict the presence of incidental prostate cancer, particularly high-risk cancer, in men who had undergone HoLEP. On the basis of pathological findings of HoLEP specimens, patients with incidental cancer were categorized as low-risk (Gleason ≤6 and T1a) or high-risk (all others). Of the 654 patients who underwent HoLEP, 41 patients (6.3%) were identified as having incidental cancer (25 low-risk and 16 high-risk). There were no significant factors for overall prostate cancers. However, a significantly higher frequency of diabetes was observed in patients with high-risk cancer compared to those with BPH (31% vs. 13%; p?=?.033). Logistic regression analysis using prostate-specific antigen (PSA) and prostate volume (PV), and smoking showed that diabetes was an independent predictor of high-risk cancer (odds ratio, 3.15; 95% confidence interval, 1.06–9.43). Diabetes may be an important predictor of the presence of high-risk prostate cancer in men with BPH who have undergone HoLEP.     

A Behavioral Approach to Organizational Change: Reinforcing Those Responsible for Facilitating the Climate and Hence Promoting Diversity

Despite the passage of the U.S. Civil Rights Act in 1964, cries can still be heard for a more diverse workforce. Among the difficulties are retaining often sought-after women and minorities. In this 2-year demonstration, change agents—the provost, deans, and heads of departments/schools of a large public university—were helped to deliberately and directly change the milieu of their departments and schools so as to encourage faculty to remain. Uniquely suited to organizational change, the behavioral approach identifies constructive actions for change agents and, most importantly, provides proven strategies for motivating them. Fostering a supportive climate was defined in terms of change agents’ behaviors. The Building Behaviorally Based Climate Survey was developed and validated. Recognition and feedback were provided in what is typically a feedback desert. This reinforcement model can be used to create and sustain inviting atmospheres, hence enticing all faculty, including women and minority faculty, to stay, hence enabling a diverse workforce.     

Edge selection based on the geometry of dually flat spaces for Gaussian graphical models

We propose a method for selecting edges in undirected Gaussian graphical models. Our algorithm takes after our previous work, an extension of Least Angle Regression (LARS), and it is based on the information geometry of dually flat spaces. Non-diagonal elements of the inverse of the covariance matrix, the concentration matrix, play an important role in edge selection. Our iterative method estimates these elements and selects covariance models simultaneously. A sequence of pairs of estimates of the concentration matrix and an independence graph is generated, whose length is the same as the number of non-diagonal elements of the matrix. In our algorithm, the next estimate of the graph is the nearest graph to the latest estimate of the concentration matrix. The next estimate of the concentration matrix is not just the projection of the latest estimate, and it is shrunk to the origin. We describe the algorithm and show results for some datasets. Furthermore, we give some remarks on model identification and prediction.