Many machine learning algorithms require the features to be categorical. Hence, they require all numeric-valued data to be discretized into intervals. In this paper, we present a new discretization method based on the receiver operating characteristics (ROC) Curve (AUC) measure. Maximum area under ROC curve-based discretization (MAD) is a global, static and supervised discretization method. MAD...

Statistical inference is reviewed for survival data applications with hazard models having one parameter per distinct failure time and using Jeffreys' (1961) vague priors. Distinction between a discrete hazard and a piecewise exponential model is made. Bayes estimators of survival probabilities ace derived. For a single sample and a discrete hazard, the Bayes estimator is shown to be larger tha...

Of those things that can be estimated well in an inverse problem, which are best to estimate? Backus-Gilbert resolution theory answers a version of this question for linear (or linearized) inverse problems in Hilbert spaces with additive zero-mean errors with known, finite covariance, and no constraints on the unknown other than the data. This paper extends Backus-Gilbert resolution: it defines...

We consider both frequentist and empirical Bayes forecasts of a single time series using a linear model with T observations and K orthonormal predictors. The frequentist formulation considers estimators that are equivariant under permutations (reorderings) of the regressors. The empirical Bayes formulation (both parametric and nonparametric) treats the coefficients as i.i.d. and estimates their...

We analyze the relationship between a Minimum Description Length (MDL) estimator (posterior mode) and a Bayes estimator for exponential families. We show the following results concerning these estimators: a) Both the Bayes estimator with Jeffreys prior and the MDL estimator with the uniform prior with respect to the expectation parameter are nearly equivalent to a bias-corrected maximum-likelih...

In this paper, we propose a class of general pretest estimators for the univariate normal mean. The main mathematical idea proposed is adaptation randomized tests, where randomization probability related to shrinkage parameter. Consequently, includes many existing estimators, such as pretest, shrinkage, Bayes, and empirical Bayes special cases. Furthermore, can be easily tuned users by adjustin...