Previous divide-and-conquer segmentation analyses of DNA sequences do not provide a satisfactory stopping criterion for the recursion. This paper proposes that segmentation be considered as a model selection process. Using the tools in model selection, a limit for the stopping criterion on the relaxed end can be determined. The Bayesian information criterion, in particular, provides a much more stringent stopping criterion than what is currently used. Such a stringent criterion can be used to delineate larger DNA domains. A relationship between the stopping criterion and the average domain size is empirically determined, which may aid in the determination of isochore borders. 1.

We describe two methodologies for obtaining segmented regression estimators from massive training data sets. The first methodology, called Linear Regression Tree (LRT), is used for continuous response variables, and the second and complementary methodology, called Naive Bayes Tree (NBT), is used for categorical response variables. These are implemented in the IBM ProbE TM (Probabilistic Estimation) data mining engine, which is an object-oriented framework for building classes of segmented predictive models from massive training data sets. Based on this methodology, an application called ATM-SE TM for direct-mail targeted marketing has been developed jointly with Fingerhut Business Intelligence [1]).

Abstract — A standard approach to automatic speech recognition uses Hidden Markov Models whose state dependent distributions are Gaussian mixture models. Each Gaussian can be viewed as an exponential model whose features are linear and quadratic monomials in the acoustic vector. We consider here models in which the weight vectors of these exponential models are constrained to lie in an affine subspace shared by all the Gaussians. This class of models includes Gaussian models with linear constraints placed on the precision (inverse covariance) matrices (such as diagonal covariance, MLLT, or EMLLT) as well as the LDA/HLDA models used for feature selection which tie the part of the Gaussians in the directions not used for discrimination. In this paper we present algorithms for training these models using a maximum likelihood criterion. We present experiments on both small vocabulary, resource constrained, grammar based tasks as well as large vocabulary, unconstrained resource tasks to explore the rather large parameter space of models that fit within our framework. In particular, we demonstrate significant improvements can be obtained in both word error rate and computational complexity. I.

Choosing the number of hidden states and their topology (model selection) and estimating model parameters (learning) are important problems for Hidden Markov Models. This paper presents a new state-splitting algorithm that addresses both these problems. The algorithm models more information about the dynamic context of a state during a split, enabling it to discover underlying states more effectively. Compared to previous top-down methods, the algorithm also touches a smaller fraction of the data per split, leading to faster model search and selection. Because of its efficiency and ability to avoid local minima, the state-splitting approach is a good way to learn HMMs even if the desired number of states is known beforehand. We compare our approach to previous work on synthetic data as well as several real-world data sets from the literature, revealing significant improvements in efficiency and test-set likelihoods. We also compare to previous algorithms on a sign-language recognition task, with positive results. 1

ABSTRACT: Probabilistic design of structures is usually based on estimates of a design load with a high average return period. Design loads are often estimated using classical statistical methods. A shortcoming of this approach is that statistical uncertainties are not taken into account. In this paper, a method based on Bayesian statistics is presented. Using Bayes ’ theorem, the prior distribution representing information about the uncertainty of the statistical parameters can be updated to the posterior distribution as soon as data becomes available. Seven predictive probability distributions are considered for determining extreme quantiles of loads: the exponential, Rayleigh, normal, lognormal, gamma, Weibull and Gumbel. The Bayesian method has been successfully applied to estimate the design discharge of the river Rhine while taking account of the statistical uncertainties involved. As a prior the non-informative Jeffreys prior was chosen. The Bayes estimates are compared to the classical maximum-likelihood estimates. Furthermore, so-called Bayes factors are used to determine weights corresponding to how well a probability distribution fits the observed data; that is, the better the fit, the higher the weighting. 1

This paper considers the problem of testing for structural changes in the trend function of a univariate time series without any prior knowledge as to whether the noise component is stationary or contains an autoregressive unit root. We propose a new approach that builds on the work of Perron and Yabu (2005), based on a Feasible Quasi Generalized Least Squares procedure that uses a superefficient estimate of the sum of the autoregressive parameters α when α =1. In the case of a known break date, the resulting Wald test has a chi-square limit distribution in both the I(0) and I(1) cases. When the break date is unknown, the Exp functional of Andrews and Ploberger (1994) yields a test with nearly identical limit distributions in the two cases so that a testing procedure with nearly the same size in the I(0) and I(1) cases can be obtained. To improve the finite sample properties of the tests, we use the bias corrected version of the OLS estimate of α proposed by Roy and Fuller (2001). We show our procedure to be substantially more powerful than currently available alternatives and also to have a power function that is close to that attainable if we knew the true value of α in many cases. The extension to the case of multiple breaks is also discussed. JEL Classification Number: C22.

Predictive modeling techniques are now being used in application domains where the training data sets are potentially enormous. For example, certain marketing databases that we have encountered contain millions of customer records with thousands of attributes per record. The development of statistical modeling algorithms

This paper poses the problem of model order determination of an autoregressive (AR) process within a Bayesian framework. Several original hierarchical prior models are proposed that allow for the stability of the model to be enforced and account for a possible unknown initial state. Obtaining the posterior model order probabilities requires integration of the resulting posterior distribution, an operation which is analytically intractable. Here stochastic reversible jump Markov chain Monte Carlo (MCMC) algorithms are developed to perform the required integration by simulating from the posterior distribution. The methods developed are evaluated in simulation studies on a number of synthetic and real data sets, and compared to standard model selection criteria. 1 I Introduction When tting an autoregressive (AR) model to real data, e.g. speech, the correct model order is often unknown. Using too low a value for the model order would lead to an undesired smoothing of the data, whereas o...

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