The Bayesian Decision Tree Technique with a Sweeping Strategy

The uncertainty of classification outcomes is of crucial importance for many safety critical applications including, for example, medical diagnostics. In such applications the uncertainty of classification can be reliably estimated within a Bayesian model averaging technique that allows the use of prior information. Decision Tree (DT) classification models used within such a technique gives experts additional information by making this classification scheme observable. The use of the Markov Chain Monte Carlo (MCMC) methodology of stochastic sampling makes the Bayesian DT technique feasible to perform. However, in practice, the MCMC technique may become stuck in a particular DT which is far away from a region with a maximal posterior. Sampling such DTs causes bias in the posterior estimates, and as a result the evaluation of classification uncertainty may be incorrect. In a particular case, the negative effect of such sampling may be reduced by giving additional prior information on the shape of DTs. In this paper we describe a new approach based on sweeping the DTs without additional priors on the favorite shape of DTs. The performances of Bayesian DT techniques with the standard and sweeping strategies are compared on a synthetic data as well as on real datasets. Quantitatively evaluating the uncertainty in terms of entropy of class posterior probabilities, we found that the sweeping strategy is superior to the standard strategy

Basin structure in the two-dimensional dissipative circle map

Fractal basin structure in the two-dimensional dissipative circle map is examined in detail. Numerically obtained basin appears to be riddling in the parameter region where two periodic orbits co-exist near a boundary crisis, but it is shown to consist of layers of thin bands.Comment: published in J. Phys. Soc. Jpn., 72, 1943-1947 (2003

Closed-Form Bayesian Inferences for the Logit Model via Polynomial Expansions

Articles in Marketing and choice literatures have demonstrated the need for incorporating person-level heterogeneity into behavioral models (e.g., logit models for multiple binary outcomes as studied here). However, the logit likelihood extended with a population distribution of heterogeneity doesn't yield closed-form inferences, and therefore numerical integration techniques are relied upon (e.g., MCMC methods). We present here an alternative, closed-form Bayesian inferences for the logit model, which we obtain by approximating the logit likelihood via a polynomial expansion, and then positing a distribution of heterogeneity from a flexible family that is now conjugate and integrable. For problems where the response coefficients are independent, choosing the Gamma distribution leads to rapidly convergent closed-form expansions; if there are correlations among the coefficients one can still obtain rapidly convergent closed-form expansions by positing a distribution of heterogeneity from a Multivariate Gamma distribution. The solution then comes from the moment generating function of the Multivariate Gamma distribution or in general from the multivariate heterogeneity distribution assumed. Closed-form Bayesian inferences, derivatives (useful for elasticity calculations), population distribution parameter estimates (useful for summarization) and starting values (useful for complicated algorithms) are hence directly available. Two simulation studies demonstrate the efficacy of our approach.Comment: 30 pages, 2 figures, corrected some typos. Appears in Quantitative Marketing and Economics vol 4 (2006), no. 2, 173--20

Three-dimensional modeling of acoustic backscattering from fluid-like zooplankton

Author Posting. © Acoustical Society of America, 2002. This article is posted here by permission of Acoustical Society of America for personal use, not for redistribution. The definitive version was published in Journal of the Acoustical Society of America 111 (2002): 1197-1210, doi:10.1121/1.1433813.Scattering models that correctly incorporate organism size and shape are a critical component for the remote detection and classification of many marine organisms. In this work, an acoustic scattering model has been developed for fluid-like zooplankton that is based on the distorted wave Born approximation (DWBA) and that makes use of high-resolution three-dimensional measurements of the animal's outer boundary shape. High-resolution computerized tomography (CT) was used to determine the three-dimensional digitizations of animal shape. This study focuses on developing the methodology for incorporating high-resolution CT scans into a scattering model that is generally valid for any body with fluid-like material properties. The model predictions are compared to controlled laboratory measurements of the acoustic backscattering from live individual decapod shrimp. The frequency range used was 50 kHz to 1 MHz and the angular characteristics of the backscattering were investigated with up to a 1° angular resolution. The practical conditions under which it is necessary to make use of high-resolution digitizations of shape are assessed.This work was supported in part by the Woods Hole Oceanographic Institution Education Office

Peritoneal and hemodialysis: I. Differences in patient characteristics at initiation

Peritoneal and hemodialysis: I. Differences in patient characteristics at initiation.BackgroundComparisons of mortality outcomes between peritoneal dialysis (PD) and hemodialysis (HD) patients have shown varying results, which may be caused by the unequally distributed clinical conditions of patients at initiation. To address this issue, we evaluated the clinical characteristics of 105,954 patients at the initiation of PD and HD, using the U.S. national incidence data on treated end-stage renal disease from the Medical Evidence Form, 1995 to 1997.MethodsA general linear model was used to analyze differences of age, albumin, creatinine, blood urea nitrogen (BUN), and hematocrit; categorical data analysis to evaluate body mass index (BMI), grouped into four categories: !19, 19–25 (!25), 25–30 (!30), and 30+; and logistic regression to assess the likelihood of initiating PD versus HD. Diabetics (DM) were analyzed separately from non-diabetics (NDM). Explanatory variables in the logistic regression included incidence year, race, gender, age, BMI, albumin, creatinine, BUN, and hematocrit. Race included white and black. Age was categorized into four groups: 20–44, 45–64, 65–74, and 75+.ResultsAt the initiation of dialysis PD patients were approximately 6 years younger (P ! 0.0001) than HD patients. PD patients also had higher (P ! 0.0001) albumin (+0.35 g/dL for DM and +0.23 g/dL for NDM) and hematocrit (+1.64% for DM and +1.71% for NDM) levels, and lower (P ! 0.04) BUN (-8.75 mg/dL for DM and -5.24 mg/dL for NDM) and creatinine (-0.51 mg/dL for DM and -0.23 mg/dL for NDM) levels than HD patients. Whites had a higher (P ! 0.0001) likelihood of starting PD than blacks, and patients with BMI !19 had a lower (P ! 0.0001) chance of beginning on PD.ConclusionPD patients had favorable clinical conditions at the initiation of dialysis, which should be taken into consideration when comparing dialysis outcomes between the two modalities