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21
A Sequential Particle Filter Method for Static Models
, 2000
"... Particle filter methods are complex inference procedures, which combine importance sampling and Monte Carlo schemes, in order to consistently explore a sequence of multiple distributions of interest. The purpose of this article is to show that such methods can also offer an efficient estimation tool ..."
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Cited by 61 (2 self)
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Particle filter methods are complex inference procedures, which combine importance sampling and Monte Carlo schemes, in order to consistently explore a sequence of multiple distributions of interest. The purpose of this article is to show that such methods can also offer an efficient estimation tool in "static" setups; in this case, π(θy_1, ..., y_N) is the only posterior distribution of interest but the preliminary exploration of partial posteriors π(θy_1, ..., y_N) (n < N) makes computing time savings possible. A complete "blackbox" algorithm is proposed for independent or Markov models. Our method is shown to possibly challenge other common estimation procedures, in terms of robustness and execution time, especially when the sample size is important. Two classes of examples are discussed and illustrated by numerical results: mixture models and discrete generalized linear models.
The Mode Tree: A Tool for Visualization of Nonparametric Density Features
 Journal of Computational and Graphical Statistics
, 1993
"... Recognition and extraction of features in a nonparametric density estimate is highly dependent on correct calibration. The datadriven choice of bandwidth h in kernel density estimation is a difficult one, compounded by the fact that the globally optimal h is not generally optimal for all values of ..."
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Cited by 35 (4 self)
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Recognition and extraction of features in a nonparametric density estimate is highly dependent on correct calibration. The datadriven choice of bandwidth h in kernel density estimation is a difficult one, compounded by the fact that the globally optimal h is not generally optimal for all values of x. In recognition of this fact, a new type of graphical tool, the mode tree, is proposed. The basic mode tree plot relates the locations of modes in density estimates with the bandwidths of those estimates. Additional information can be included on the plot indicating such factors as the size of modes, how modes split, and the locations of antimodes and bumps. The use of a mode tree in adaptive multimodality investigations is proposed, and an example is given to show the value in using a Normal kernel, as opposed to the biweight or other kernels, in such investigations. Examples of such investigations are provided for Ahrens' chondrite data and van Winkle's Hidalgo stamp data. Finally, the b...
Approximate Dirichlet Process Computing in Finite Normal Mixtures: Smoothing and Prior Information
 JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
, 2000
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Universal smoothing factor selection in density estimation: theory and practice (with discussion
 Test
, 1997
"... In earlier work with Gabor Lugosi, we introduced a method to select a smoothing factor for kernel density estimation such that, for all densities in all dimensions, the L1 error of the corresponding kernel estimate is not larger than 3+e times the error of the estimate with the optimal smoothing fac ..."
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Cited by 23 (10 self)
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In earlier work with Gabor Lugosi, we introduced a method to select a smoothing factor for kernel density estimation such that, for all densities in all dimensions, the L1 error of the corresponding kernel estimate is not larger than 3+e times the error of the estimate with the optimal smoothing factor plus a constant times Ov~~n/n, where n is the sample size, and the constant only depends on the complexity of the kernel used in the estimate. The result is nonasymptotic, that is, the bound is valid for each n. The estimate uses ideas from the minimum distance estimation work of Yatracos. We present a practical implementation of this estimate, report on some comparative results, and highlight some key properties of the new method.
Bayesian Model Selection in Finite Mixtures by Marginal Density Decompositions
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2001
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Estimating the Number of Clusters
, 2000
"... Hartigan (1975) defines the number q of clusters in a dvariate statistical population as the number of connected components of the set {f>c}, where f denotes the underlying density function on R^d and c is a given constant. Some usual cluster algorithms treat q as an input which must be given in ad ..."
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Cited by 10 (0 self)
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Hartigan (1975) defines the number q of clusters in a dvariate statistical population as the number of connected components of the set {f>c}, where f denotes the underlying density function on R^d and c is a given constant. Some usual cluster algorithms treat q as an input which must be given in advance. The authors propose a method for estimating this parameter which is based on the computation of the number of connected components of an estimate of {f>c}. This set estimator is constructed as a union of balls with centres at an appropriate subsample which is selected via a nonparametric density estimator of f. The asymptotic behaviour of the proposed method is analyzed. A simulation study and an example with real data are also included.
Generalized Crossentropy Methods with Applications to Rareevent Simulation and Optimization
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Adaptive Kernel Density Estimation
, 1994
"... The need for improvements over the fixed kernel density estimator in certain situations has been discussed extensively in the literature, particularly in the application of density estimation to mode hunting. Problem densities often exhibit skewness or multimodality with differences in scale for eac ..."
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Cited by 8 (0 self)
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The need for improvements over the fixed kernel density estimator in certain situations has been discussed extensively in the literature, particularly in the application of density estimation to mode hunting. Problem densities often exhibit skewness or multimodality with differences in scale for each mode. By varying the bandwidth in some fashion, it is possible to achieve significant improvements over the fixed bandwidth approach. In general, variable bandwidth kernel density estimators can be divided into two categories: those that vary the bandwidth with the estimation point (balloon estimators) and those that vary the bandwidth with each data point (sample point estimators). For univariate balloon estimators, it can be shown that there exists a bandwidth in regions of f where f is convex (e.g. the tails) such that the bias is exactly zero. Such a bandwidth leads to a MSE = O(n \Gamma1 ) for points in the appropriate regions. A global implementation strategy using a local crossv...
The Bumpy Road to the Mode Forest
"... The mode tree of Minnotte and Scott (1993) provides a valuable method of investigating features such as modes and bumps in a unknown density. By examining kernel density estimates for a range of bandwidths, we can learn a lot about the structure of a data set. Unfortunately, the basic mode tree can ..."
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Cited by 7 (0 self)
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The mode tree of Minnotte and Scott (1993) provides a valuable method of investigating features such as modes and bumps in a unknown density. By examining kernel density estimates for a range of bandwidths, we can learn a lot about the structure of a data set. Unfortunately, the basic mode tree can be strongly affected by small changes in the data, and gives no way to differentiate between important modes and those caused, for example, by outliers. The mode forest overcomes these difficulties by looking simultaneously at a large collection of mode trees, all based on some variation of the original data, by means such as resampling or jittering. The result is both visually appealing and informative.
CLUSTER ANALYSIS AND CLASSIFICATION TREE METHODOLOGY AS AN AID TO IMPROVE UNDERSTANDING OF BENIGN PROSTATIC HYPERPLASIA
, 1994
"... Clear scientifically dermed guidelines for diagnosing benign prostatic hyperplasia have not been developed, and commonly used urologic measures characterizing the disease have shown lack of correlation. However, most reports in the literature are based on studies in referred patients or other nonre ..."
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Cited by 6 (0 self)
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Clear scientifically dermed guidelines for diagnosing benign prostatic hyperplasia have not been developed, and commonly used urologic measures characterizing the disease have shown lack of correlation. However, most reports in the literature are based on studies in referred patients or other nonrepresentative samples and additionally have not considered the multivariate relationship among these measures. Such commonly used measures were collected during the baseline phase of a communitybased study initiated in Olmsted County,. Minnesota to study the prevalence and progression of disease in a randomly selected sample of untreated men aged 4079 without history of prostate cancer or prior prostate surgery. In the absence of a clinical diagnosis, hierarchical group average cluster analysis and the kth nearest neighbor nonparametric density estimation (NPDE) approach were applied to group men after fIrst standardizing variables using a robust measure. As the number of clusters has been shown to be a monotonically decreasing function ofsmoothing parameter k, graphical tools