Journal of Data Science

In this paper, a comparison is provided for volatility estimation in Bayesian and frequentist settings. We compare the predictive performance of these two approaches under the generalized autoregressive conditional heteroscedasticity (GARCH) model. Our results indicate that the frequentist estimation provides better predictive potential than the Bayesian approach. The finding is contrary to some of the work in this line of research. To illustrate our finding, we used the six major foreign exchange rate datasets.

Abstract: A prospective, multi-institutional and randomized surgical trial involving 724 early stage melanoma patients was conducted to determine whether excision margins for intermediate-thickness melanomas (1.0 to 4.0 mm) could be safely reduced from the standard 4-cm radius. Patients with 1- to 4-mm-thick melanomas on the trunk or proximal extremities were randomly assigned to receive either a 2- or 4-cm surgical margin with or without immediate node dissection (i.e. immediate vs. later -within 6 months). The median follow-up time was 6 years. Recurrence rates did not correlate with surgical margins, even among stratified thickness groups. The hospital stay was shortened from 7.0 days for patients receiving 4-cm surgical margins to 5.2 days for those receiving 2-cm margins (p = 0.0001). This reduction was largely due to reduced need for skin grafting in the 2cm group. The overall conclusion was that the narrower margins significantly reduced the need for skin grafting and shortened the hospital stay. Due to the adequacy of subject follow up, recently a statistical focus was on what prognostics factors usually called covariates actually determined recurrence. As was anticipated, the thickness of the lesion (p = 0.0091) and whether or not the lesion was ulcerated (p = 0.0079), were determined to be significantly associated with recurrence events using the logistic regression model. This type of fixed effect analysis is rather a routine. The authors have determined that a Bayesian consideration of the results would afford a more coherent interpretation of the effect of the model assuming a random effect of the covariates of thickness and ulceration. Thus, using a Markov Chain Monte Carlo method of parameter estimation with non informative priors, one is able to obtain the posterior estimates and credible regions of estimates of these effects as well as their interaction on recurrence outcome. Graphical displays of convergence history and posterior densities affirm the stability of the results. We demonstrate how the model performs under relevant clinical conditions. The conditions are all tested using a Bayesian statistical approach allowing for the robust testing of the model parameters under various recursive partitioning conditions of the covariates and hyper parameters which we introduce into the model. The convergence of the parameters to stable values are seen in trace plots which follow the convergence patterns This allows for precise estimation for determining clinical conditions under which the response pattern will change.

Abstract: Particulate matter smaller than 2.5 microns (PM2.5) is a com monly measured parameter in ground-based sampling networks designed to assess short and long-term air quality. The measurement techniques for ground based PM2.5 are relatively accurate and precise, but monitoring lo cations are spatially too sparse for many applications. Aerosol Optical Depth (AOD) is a satellite based air quality measurement that can be computed for more spatial locations, but measures light attenuation by particulates throughout in entire air column, not just near the ground. The goal of this paper is to better characterize the spatio-temporal relationship between the two measurements. An informative relationship will aid in imputing PM2.5 values for health studies in a way that accounts for the variability in both sets of measurements, something physics based models cannot do. We use a data set of Chicago air quality measurements taken during 2007 and 2008 to construct a weekly hierarchical model. We also demonstrate that AOD measurements and a latent spatio-temporal process aggregated weekly can be used to aid in the prediction of PM2.5measurements.

Abstract: The assessment of modality or “bumps” in distributions is of in terest to scientists in many areas. We compare the performance of four statistical methods to test for departures from unimodality in simulations, and further illustrate the four methods using well-known ecological datasets on body mass published by Holling in 1992 to illustrate their advantages and disadvantages. Silverman’s kernel density method was found to be very conservative. The excess mass test and a Bayesian mixture model approach showed agreement among the data sets, whereas Hall and York’s test pro vided strong evidence for the existence of two or more modes in all data sets. The Bayesian mixture model also provided a way to quantify the un certainty associated with the number of modes. This work demonstrates the inherent richness of animal body mass distributions but also the difficulties for characterizing it, and ultimately understanding the processes underlying them.

The complexity of energy infrastructure at large institutions increasingly calls for data-driven monitoring of energy usage. This article presents a hybrid monitoring algorithm for detecting consumption surges using statistical hypothesis testing, leveraging the posterior distribution and its information about uncertainty to introduce randomness in the parameter estimates, while retaining the frequentist testing framework. This hybrid approach is designed to be asymptotically equivalent to the Neyman-Pearson test. We show via extensive simulation studies that the hybrid approach enjoys control over type-1 error rate even with finite sample sizes whereas the naive plug-in method tends to exceed the specified level, resulting in overpowered tests. The proposed method is applied to the natural gas usage data at the University of Connecticut.