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Kenny Q Ye - One of the best experts on this subject based on the ideXlab platform.

  • indicator function and its application in two level Factorial designs
    Annals of Statistics, 2003
    Co-Authors: Kenny Q Ye
    Abstract:

    A two-level Factorial design can be uniquely represented by a polynomial indicator function. Therefore, properties of Factorial designs can be studied through their indicator functions. This paper shows that the indicator function is an effective tool in studying two-level Factorial designs. The indicator function is used to generalize the aberration criterion of a regular two-level fractional Factorial design to all two-level Factorial designs. An important identity of generalized aberration is proved. The connection between a uniformity measure and aberration is also extended to all two-level Factorial designs.

Robert L Mason - One of the best experts on this subject based on the ideXlab platform.

  • fractional Factorial design
    Wiley Interdisciplinary Reviews: Computational Statistics, 2009
    Co-Authors: Richard F Gunst, Robert L Mason
    Abstract:

    Fractional Factorial designs are among the most important statistical contributions to the efficient exploration of the effects of several controllable factors on a response of interest. Fractional Factorials are widely used in experiments in fields as diverse as agriculture, industry, and medical research. A key feature of fractional Factorials that is not shared by more ad hoc methods for reducing the size of experiments is that the statistical properties are known in advance of experimentation. Consequently, an experimenter can investigate alternatives that enable the goals of the experiment to be met with the least cost, shortest time, or most effective use of resources. On occasion, an experimenter might decide not to conduct an experiment as originally planned once the statistical properties of the design are known. This article highlights the fundamental concepts, design strategies, and statistical properties of fractional Factorial designs. Copyright © 2009 John Wiley & Sons, Inc. For further resources related to this article, please visit the WIREs website.

Michael I Jordan - One of the best experts on this subject based on the ideXlab platform.

  • Factorial hidden markov models
    Neural Information Processing Systems, 1995
    Co-Authors: Zoubin Ghahramani, Michael I Jordan
    Abstract:

    Hidden Markov models (HMMs) have proven to be one of the most widely used tools for learning probabilistic models of time series data. In an HMM, information about the past is conveyed through a single discrete variable—the hidden state. We discuss a generalization of HMMs in which this state is factored into multiple state variables and is therefore represented in a distributed manner. We describe an exact algorithm for inferring the posterior probabilities of the hidden state variables given the observations, and relate it to the forward–backward algorithm for HMMs and to algorithms for more general graphical models. Due to the combinatorial nature of the hidden state representation, this exact algorithm is intractable. As in other intractable systems, approximate inference can be carried out using Gibbs sampling or variational methods. Within the variational framework, we present a structured approximation in which the the state variables are decoupled, yielding a tractable algorithm for learning the parameters of the model. Empirical comparisons suggest that these approximations are efficient and provide accurate alternatives to the exact methods. Finally, we use the structured approximation to model Bach‘s chorales and show that Factorial HMMs can capture statistical structure in this data set which an unconstrained HMM cannot.

M. Ploszajczak - One of the best experts on this subject based on the ideXlab platform.

  • The singular multiparticle correlation-function and the alpha model
    Physics Letters B, 1991
    Co-Authors: P. Bozek, M. Ploszajczak
    Abstract:

    A comparison is made between the two descriptions of multiparticle correlations using either the α-model or the scale-invariant distribution functions. The case of the strong and weak intermittency is discussed. These two descriptions show similar results for both the scaled Factorial moments and the scaled Factorial correlators. It is shown that the dimensional projection does not alter this similarity and moreover, it explains an experimentally observed difference between the slopes of Factorial moments and Factorial correlators.

A. E. Frid - One of the best experts on this subject based on the ideXlab platform.