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Fred Huffer

Florida State University, Statistics, Department Member

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Steven J. Miller

Williams College

Anoop Chaturvedi

University of Allahabad

Prof.Amjad Al-Nasser

Yarmouk University

Sevcan Demir Atalay

Ege University

Universitas Syiah Kuala Banda Aceh

José Francisco Pessanha

UERJ - Universidade do Estado do Rio de Janeiro / Rio de Janeiro State University

Yogendra Chaubey

Concordia University (Canada)

Srinivasa Rao Gadde

The University of Dodoma, Tanzania

Universidade Federal de Pernambuco

E.i.abdul Sathar

University of Kerala

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Papers by Fred Huffer

Detecting Shapes in 2 D Point Clouds Generated from Images

We present a novel statistical framework for detecting pre-determined shape classes in 2D clutter... more We present a novel statistical framework for detecting pre-determined shape classes in 2D cluttered point clouds, that are in turn extracted from images. In this model-based approach, we use a 1D Poisson process for sampling points on shapes, a 2D Poisson process for points from background clutter, and an additive Gaussian model for noise. Combining these with a past stochastic models on shapes of continuous 2D contours, and optimization over unknown pose and scale, we develop a generalized likelihood ratio test for shape detection. We demonstrate the efficiency of this method and its robustness to clutter using both simulated and real data.

New Development of Bayesian Variable Selection Criteria for Spatial Point Process with Applications

arXiv: Applications, 2019

Selecting important spatial-dependent variables under the nonhomogeneous spatial Poisson process ... more Selecting important spatial-dependent variables under the nonhomogeneous spatial Poisson process model is an important topic of great current interest. In this paper, we use the Deviance Information Criterion (DIC) and Logarithm of the Pseudo Marginal Likelihood (LPML) for Bayesian variable selection under the nonhomogeneous spatial Poisson process model. We further derive the new Monte Carlo estimation formula for LPML in the spatial Poisson process setting. Extensive simulation studies are carried out to evaluate the empirical performance of the proposed criteria. The proposed methodology is further applied to the analysis of two large data sets, the Earthquake Hazards Program of United States Geological Survey (USGS) earthquake data and the Forest of Barro Colorado Island (BCI) data.

Is Extinction Age Dependent?

PALAIOS, 2006

Abstract Age-dependent extinction is an observation with important biological implications. Van V... more Abstract Age-dependent extinction is an observation with important biological implications. Van Valen's Red Queen hypothesis triggered three decades of research testing its primary implication: that age is independent of extinction. In contrast to this, later studies with species-level data have indicated the possible presence of age dependence. Since the formulation of the Red Queen hypothesis, more powerful tests of survivorship models have been developed. This is the first report of the application of the Cox Proportional Hazards model to paleontological data. Planktonic foraminiferal morphospecies allow the taxonomic and precise stratigraphic resolution necessary for the Cox model. As a whole, planktonic foraminiferal morphospecies clearly show age-dependent extinction. In particular, the effect is attributable to the presence of shorter-ranged species (range < 4 myr) following extinction events. These shorter-ranged species also possess tests with unique morphological architecture. The morphological differences are probably epiphenomena of underlying developmental and heterochronic processes of shorter-ranged species that survived various extinction events. Extinction survivors carry developmental and morphological characteristics into postextinction recovery times, and this sets them apart from species populations established independently of extinction events.

An explanatory differential item functioning (DIF) model by the WinBUG 1.4

This study proposed a multilevel logistic regression model to evaluate a source of DIF. The model... more This study proposed a multilevel logistic regression model to evaluate a source of DIF. The model accounts for the three levels nested structure of the data and combines results of logistic regression analysesto identify level-3 unit characteristic variables that explain a DIF variation. A simulation study is presented to assess the adequacy of the proposed models. The parameters of the proposed models were estimated by usinga Bayesian approach implemented by the WinBUGS 1.4.

Using Moments to Approximate the Distribution of the Scan Statistic

Scan Statistics and Applications, 1999

Let C w denote the number ofm:wclumps amongNrandom points uniformly distributed in the interval (... more Let C w denote the number ofm:wclumps amongNrandom points uniformly distributed in the interval (01]. (We say that anm:wclump exists whenmpoints fall within an interval of lengthw.) The previous chapter described how to compute the lower-order moments ofC w . In the present chapter, we discuss ways these moments can be used to obtain bounds and approximations for the distribution

Modelling the distribution of plant species using the autologistic regression model

Environmental and Ecological Statistics, 1997

For modeling the distribution of plant species in terms of climate covariates, we consider an aut... more For modeling the distribution of plant species in terms of climate covariates, we consider an autologistic regression model for spatial binary data on a regularly spaced lattice. This model belongs to the class of autologistic models introduced by Besag (1974). Three estimation methods, the coding method, maximum pseudolikelihood method and Markov chain Monte Carlo method are studied and comparedvia simulation

An Approach to Computations Involving Spacings With Applications to the Scan Statistic

Scan Statistics and Applications, 1999

Consider the order statistics fromNi.i.d. random variables uniformly distributed on the interval ... more Consider the order statistics fromNi.i.d. random variables uniformly distributed on the interval (0,1]. We present a general method for computing probabilities involving differences of the order statistics or linear combinations of the spacings between the order statistics. This method is based on repeated use of a basic recursion to break up the joint distribution of linear combinations of spacings into

Approximating the Distribution of the Scan Statistic Using Moments of the Number of Clumps

Journal of the American Statistical Association, 1997

Let X 1 ; X 2 ; : : : ; X n be randomly distributed points on the unit interval. LetN x;x+d be th... more Let X 1 ; X 2 ; : : : ; X n be randomly distributed points on the unit interval. LetN x;x+d be the number of these points contained in the interval (x; x + d). Thescan statistic N d is defined as the maximum number of points in a window oflength d, that is, N d = sup x N x;x+d . This statistic is used to test for the presenceof non-random clustering. We say that m points form an m : d clump if thesepoints are all contained in some interval of length d. Let Y denote the number ofm : d...

Computing the exact distribution of the extremes of sums of consecutive spacings

Computational Statistics & Data Analysis, 1997

Consider the spacings between i.i.d, uniform observations in the interval (0,1). We develop a gen... more Consider the spacings between i.i.d, uniform observations in the interval (0,1). We develop a general method for evaluating the distribution of the minimum or the maximum of random variables which are sums of consecutive spacings. We then present some applications of this method. The main idea underlying our approach was given by Huffer (1988): a recursion is used to break up the joint distribution of several linear combinations of spacings into a sum of simpler components. We continue applying this recursion until we obtain components which are simple and easily expressed in closed form. In this paper we propose an algorithm for the systematic application of this recursion. Our method can be used to solve a variety of problems involving sums of spacings or exponential random variables. In particular, our method gives another way to obtain the distribution of the scan statistic. Because the output of our procedure is a polynomial whose coefficients are computed exactly, we can supply numerical answers which are accurate to any required degree of precision.

Additive Risk Model Using Piecewise Constant Hazard Function

Communications in Statistics - Simulation and Computation, 2011

We study a weighted least squares estimator for Aalen's additive risk model with right-censor... more We study a weighted least squares estimator for Aalen's additive risk model with right-censored survival data which allows for a very flexible handling of covariates. We divide the follow-up period into intervals and assume a constant hazard rate in each interval. The model is motivated as a piecewise approximation of a hazard function composed of three parts: arbitrary nonparametric functions for some covariate effects, smoothly varying functions for others, and known (or constant) functions for yet others. The proposed estimator is an extension of the grouped data version of the Huffer and McKeague (1991) estimator. For our model, since the number of parameters is finite (although large), conventional approaches (such as maximum likelihood) are easy to formulate and implement. The approach is illustrated by simulations, and is compared to the previous studies. The method is also applied to the Framingham study data.

Markov Chain Monte Carlo for Autologistic Regression Models with Application to the Distribution of Plant Species

Biometrics, 1998

ABSTRACT

A test for elliptical symmetry

Journal of Multivariate Analysis, 2007

This paper presents a statistic for testing the hypothesis of elliptical symmetry. The statistic ... more This paper presents a statistic for testing the hypothesis of elliptical symmetry. The statistic also provides a specialized test of multivariate normality. We obtain the asymptotic distribution of this statistic under the null hypothesis of multivariate normality, and give a bootstrapping procedure for approximating the null distribution of the statistic under an arbitrary elliptically symmetric distribution. We present simulation results to examine the accuracy of the asymptotic distribution and the performance of the bootstrapping procedure. Finally, for selected alternatives, we compare the power of our test statistic with that of recently proposed tests for elliptical symmetry given by Manzotti et al. [A statistic for testing the null hypothesis of elliptical symmetry, J. Multivariate Anal. 81 (2002) 274-285] and Schott [Testing for elliptical symmetry in covariance-matrix-based analyses, Statist. Probab. Lett. 60 (2002) 395-404], and with that of the well known tests for multivariate normality of Mardia [Measures of multivariate skewness and kurtosis with applications, Biometrika 57 (1970) 519-530] and Baringhaus and Henze [A consistent test for multivariate normality based on the empirical characteristic function, Metrika 35 (1988) 339-348].

The Limiting Distribution of a Test for Multivariate

We define a chi-squared statistic for p-dimensional data as follows. First, we transform the data... more

A Comparison of Bayesian Accelerated Failure Time Models with Spatially Varying Coefficients

Sankhya B

Bayesian Estimation of Three-Dimensional Chromosomal Structure from Single-Cell Hi-C Data

Journal of Computational Biology

The problem of three-dimensional (3D) chromosome structure inference from Hi-C data sets is impor... more The problem of three-dimensional (3D) chromosome structure inference from Hi-C data sets is important and challenging. While bulk Hi-C data sets contain contact information derived from millions of cells and can capture major structural features shared by the majority of cells in the sample, they do not provide information about local variability between cells. Single-cell Hi-C can overcome this problem, but contact matrices are generally very sparse, making structural inference more problematic. We have developed a Bayesian multiscale approach, named Structural Inference via Multiscale Bayesian Approach, to infer 3D structures of chromosomes from singlecell Hi-C while including the bulk Hi-C data and some regularization terms as a prior. We study the landscape of solutions for each single-cell Hi-C data set as a function of prior strength and demonstrate clustering of solutions using data from the same cell.

Bayesian Estimation of 3D Chromosomal Structure from Single Cell Hi-C Data

The problem of 3D chromosome structure inference from Hi-C datasets is important and challenging.... more The problem of 3D chromosome structure inference from Hi-C datasets is important and challenging. While bulk Hi-C datasets contain contact information derived from millions of cells, and can capture major structural features shared by the majority of cells in the sample, they do not provide information about local variability between cells. Single cell Hi-C can overcome this problem, but contact matrices are generally very sparse, making structural inference more problematic. We have developed a Bayesian multiscale approach, named SIMBA3D, to infer 3D structures of chromosomes from single cell Hi-C while including the bulk Hi-C data and some regularization terms as a prior. We study the landscape of solutions for each single-cell Hi-C dataset as a function of prior strength and demonstrate clustering of solutions using data from the same cell.

Modified Kaplan-Meier Estimator and Nelson-Aalen Estimator with Geographical Weighting for Survival Data

Geographical Analysis

A Preliminary Test for Structure in Large, High-Dimensional Data Sets

GINOM: A statistical framework for assessing interval overlap of multiple genomic features

PLoS computational biology, 2017

A common problem in genomics is to test for associations between two or more genomic features, ty... more A common problem in genomics is to test for associations between two or more genomic features, typically represented as intervals interspersed across the genome. Existing methodologies can test for significant pairwise associations between two genomic intervals; however, they cannot test for associations involving multiple sets of intervals. This limits our ability to uncover more complex, yet biologically important associations between multiple sets of genomic features. We introduce GINOM (Genomic INterval Overlap Model), a new method that enables testing of significant associations between multiple genomic features. We demonstrate GINOM's ability to identify higher-order associations with both simulated and real data. In particular, we used GINOM to explore L1 retrotransposable element insertion bias in lung cancer and found a significant pairwise association between L1 insertions and heterochromatic marks. Unlike other methods, GINOM also detected an association between L1 in...

A fully statistical framework for shape detection in image primitives

2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Workshops, 2010

ABSTRACT We present a fully statistical framework for detecting pre-determined shape classes in 2... more ABSTRACT We present a fully statistical framework for detecting pre-determined shape classes in 2D clouds of primitives (points, edges, and arcs), which are in turn extracted from images. An important goal is to provide a likelihood, and thus a confidence, of finding a shape class in a given data. This requires a model-based approach. We use a composite Poisson process: 1D Poisson process for primitives belonging to shapes and a 2D Poisson process for primitives belonging to clutter. An additive Gaussian model is assumed for noise in shape primitives. Combining these with a past stochastic model on shapes of continuous 2D contours, and optimization over unknown pose and scale, we develop a generalized likelihood ratio test for shape detection. We demonstrate the efficiency of this method and its robustness to clutter using both simulated and real data.

Detecting Shapes in 2 D Point Clouds Generated from Images

We present a novel statistical framework for detecting pre-determined shape classes in 2D clutter... more We present a novel statistical framework for detecting pre-determined shape classes in 2D cluttered point clouds, that are in turn extracted from images. In this model-based approach, we use a 1D Poisson process for sampling points on shapes, a 2D Poisson process for points from background clutter, and an additive Gaussian model for noise. Combining these with a past stochastic models on shapes of continuous 2D contours, and optimization over unknown pose and scale, we develop a generalized likelihood ratio test for shape detection. We demonstrate the efficiency of this method and its robustness to clutter using both simulated and real data.

New Development of Bayesian Variable Selection Criteria for Spatial Point Process with Applications

arXiv: Applications, 2019

Selecting important spatial-dependent variables under the nonhomogeneous spatial Poisson process ... more Selecting important spatial-dependent variables under the nonhomogeneous spatial Poisson process model is an important topic of great current interest. In this paper, we use the Deviance Information Criterion (DIC) and Logarithm of the Pseudo Marginal Likelihood (LPML) for Bayesian variable selection under the nonhomogeneous spatial Poisson process model. We further derive the new Monte Carlo estimation formula for LPML in the spatial Poisson process setting. Extensive simulation studies are carried out to evaluate the empirical performance of the proposed criteria. The proposed methodology is further applied to the analysis of two large data sets, the Earthquake Hazards Program of United States Geological Survey (USGS) earthquake data and the Forest of Barro Colorado Island (BCI) data.

Is Extinction Age Dependent?

PALAIOS, 2006

Abstract Age-dependent extinction is an observation with important biological implications. Van V... more Abstract Age-dependent extinction is an observation with important biological implications. Van Valen's Red Queen hypothesis triggered three decades of research testing its primary implication: that age is independent of extinction. In contrast to this, later studies with species-level data have indicated the possible presence of age dependence. Since the formulation of the Red Queen hypothesis, more powerful tests of survivorship models have been developed. This is the first report of the application of the Cox Proportional Hazards model to paleontological data. Planktonic foraminiferal morphospecies allow the taxonomic and precise stratigraphic resolution necessary for the Cox model. As a whole, planktonic foraminiferal morphospecies clearly show age-dependent extinction. In particular, the effect is attributable to the presence of shorter-ranged species (range < 4 myr) following extinction events. These shorter-ranged species also possess tests with unique morphological architecture. The morphological differences are probably epiphenomena of underlying developmental and heterochronic processes of shorter-ranged species that survived various extinction events. Extinction survivors carry developmental and morphological characteristics into postextinction recovery times, and this sets them apart from species populations established independently of extinction events.

An explanatory differential item functioning (DIF) model by the WinBUG 1.4

This study proposed a multilevel logistic regression model to evaluate a source of DIF. The model... more This study proposed a multilevel logistic regression model to evaluate a source of DIF. The model accounts for the three levels nested structure of the data and combines results of logistic regression analysesto identify level-3 unit characteristic variables that explain a DIF variation. A simulation study is presented to assess the adequacy of the proposed models. The parameters of the proposed models were estimated by usinga Bayesian approach implemented by the WinBUGS 1.4.

Using Moments to Approximate the Distribution of the Scan Statistic

Scan Statistics and Applications, 1999

Let C w denote the number ofm:wclumps amongNrandom points uniformly distributed in the interval (... more Let C w denote the number ofm:wclumps amongNrandom points uniformly distributed in the interval (01]. (We say that anm:wclump exists whenmpoints fall within an interval of lengthw.) The previous chapter described how to compute the lower-order moments ofC w . In the present chapter, we discuss ways these moments can be used to obtain bounds and approximations for the distribution

Modelling the distribution of plant species using the autologistic regression model

Environmental and Ecological Statistics, 1997

For modeling the distribution of plant species in terms of climate covariates, we consider an aut... more For modeling the distribution of plant species in terms of climate covariates, we consider an autologistic regression model for spatial binary data on a regularly spaced lattice. This model belongs to the class of autologistic models introduced by Besag (1974). Three estimation methods, the coding method, maximum pseudolikelihood method and Markov chain Monte Carlo method are studied and comparedvia simulation

An Approach to Computations Involving Spacings With Applications to the Scan Statistic

Scan Statistics and Applications, 1999

Consider the order statistics fromNi.i.d. random variables uniformly distributed on the interval ... more Consider the order statistics fromNi.i.d. random variables uniformly distributed on the interval (0,1]. We present a general method for computing probabilities involving differences of the order statistics or linear combinations of the spacings between the order statistics. This method is based on repeated use of a basic recursion to break up the joint distribution of linear combinations of spacings into

Approximating the Distribution of the Scan Statistic Using Moments of the Number of Clumps

Journal of the American Statistical Association, 1997

Let X 1 ; X 2 ; : : : ; X n be randomly distributed points on the unit interval. LetN x;x+d be th... more Let X 1 ; X 2 ; : : : ; X n be randomly distributed points on the unit interval. LetN x;x+d be the number of these points contained in the interval (x; x + d). Thescan statistic N d is defined as the maximum number of points in a window oflength d, that is, N d = sup x N x;x+d . This statistic is used to test for the presenceof non-random clustering. We say that m points form an m : d clump if thesepoints are all contained in some interval of length d. Let Y denote the number ofm : d...

Computing the exact distribution of the extremes of sums of consecutive spacings

Computational Statistics & Data Analysis, 1997

Consider the spacings between i.i.d, uniform observations in the interval (0,1). We develop a gen... more Consider the spacings between i.i.d, uniform observations in the interval (0,1). We develop a general method for evaluating the distribution of the minimum or the maximum of random variables which are sums of consecutive spacings. We then present some applications of this method. The main idea underlying our approach was given by Huffer (1988): a recursion is used to break up the joint distribution of several linear combinations of spacings into a sum of simpler components. We continue applying this recursion until we obtain components which are simple and easily expressed in closed form. In this paper we propose an algorithm for the systematic application of this recursion. Our method can be used to solve a variety of problems involving sums of spacings or exponential random variables. In particular, our method gives another way to obtain the distribution of the scan statistic. Because the output of our procedure is a polynomial whose coefficients are computed exactly, we can supply numerical answers which are accurate to any required degree of precision.

Additive Risk Model Using Piecewise Constant Hazard Function

Communications in Statistics - Simulation and Computation, 2011

We study a weighted least squares estimator for Aalen's additive risk model with right-censor... more We study a weighted least squares estimator for Aalen's additive risk model with right-censored survival data which allows for a very flexible handling of covariates. We divide the follow-up period into intervals and assume a constant hazard rate in each interval. The model is motivated as a piecewise approximation of a hazard function composed of three parts: arbitrary nonparametric functions for some covariate effects, smoothly varying functions for others, and known (or constant) functions for yet others. The proposed estimator is an extension of the grouped data version of the Huffer and McKeague (1991) estimator. For our model, since the number of parameters is finite (although large), conventional approaches (such as maximum likelihood) are easy to formulate and implement. The approach is illustrated by simulations, and is compared to the previous studies. The method is also applied to the Framingham study data.

Markov Chain Monte Carlo for Autologistic Regression Models with Application to the Distribution of Plant Species

Biometrics, 1998

ABSTRACT

A test for elliptical symmetry

Journal of Multivariate Analysis, 2007

This paper presents a statistic for testing the hypothesis of elliptical symmetry. The statistic ... more This paper presents a statistic for testing the hypothesis of elliptical symmetry. The statistic also provides a specialized test of multivariate normality. We obtain the asymptotic distribution of this statistic under the null hypothesis of multivariate normality, and give a bootstrapping procedure for approximating the null distribution of the statistic under an arbitrary elliptically symmetric distribution. We present simulation results to examine the accuracy of the asymptotic distribution and the performance of the bootstrapping procedure. Finally, for selected alternatives, we compare the power of our test statistic with that of recently proposed tests for elliptical symmetry given by Manzotti et al. [A statistic for testing the null hypothesis of elliptical symmetry, J. Multivariate Anal. 81 (2002) 274-285] and Schott [Testing for elliptical symmetry in covariance-matrix-based analyses, Statist. Probab. Lett. 60 (2002) 395-404], and with that of the well known tests for multivariate normality of Mardia [Measures of multivariate skewness and kurtosis with applications, Biometrika 57 (1970) 519-530] and Baringhaus and Henze [A consistent test for multivariate normality based on the empirical characteristic function, Metrika 35 (1988) 339-348].

The Limiting Distribution of a Test for Multivariate

We define a chi-squared statistic for p-dimensional data as follows. First, we transform the data... more

A Comparison of Bayesian Accelerated Failure Time Models with Spatially Varying Coefficients

Sankhya B

Bayesian Estimation of Three-Dimensional Chromosomal Structure from Single-Cell Hi-C Data

Journal of Computational Biology

The problem of three-dimensional (3D) chromosome structure inference from Hi-C data sets is impor... more The problem of three-dimensional (3D) chromosome structure inference from Hi-C data sets is important and challenging. While bulk Hi-C data sets contain contact information derived from millions of cells and can capture major structural features shared by the majority of cells in the sample, they do not provide information about local variability between cells. Single-cell Hi-C can overcome this problem, but contact matrices are generally very sparse, making structural inference more problematic. We have developed a Bayesian multiscale approach, named Structural Inference via Multiscale Bayesian Approach, to infer 3D structures of chromosomes from singlecell Hi-C while including the bulk Hi-C data and some regularization terms as a prior. We study the landscape of solutions for each single-cell Hi-C data set as a function of prior strength and demonstrate clustering of solutions using data from the same cell.

Bayesian Estimation of 3D Chromosomal Structure from Single Cell Hi-C Data

The problem of 3D chromosome structure inference from Hi-C datasets is important and challenging.... more The problem of 3D chromosome structure inference from Hi-C datasets is important and challenging. While bulk Hi-C datasets contain contact information derived from millions of cells, and can capture major structural features shared by the majority of cells in the sample, they do not provide information about local variability between cells. Single cell Hi-C can overcome this problem, but contact matrices are generally very sparse, making structural inference more problematic. We have developed a Bayesian multiscale approach, named SIMBA3D, to infer 3D structures of chromosomes from single cell Hi-C while including the bulk Hi-C data and some regularization terms as a prior. We study the landscape of solutions for each single-cell Hi-C dataset as a function of prior strength and demonstrate clustering of solutions using data from the same cell.

Modified Kaplan-Meier Estimator and Nelson-Aalen Estimator with Geographical Weighting for Survival Data

Geographical Analysis

A Preliminary Test for Structure in Large, High-Dimensional Data Sets

GINOM: A statistical framework for assessing interval overlap of multiple genomic features

PLoS computational biology, 2017

A common problem in genomics is to test for associations between two or more genomic features, ty... more A common problem in genomics is to test for associations between two or more genomic features, typically represented as intervals interspersed across the genome. Existing methodologies can test for significant pairwise associations between two genomic intervals; however, they cannot test for associations involving multiple sets of intervals. This limits our ability to uncover more complex, yet biologically important associations between multiple sets of genomic features. We introduce GINOM (Genomic INterval Overlap Model), a new method that enables testing of significant associations between multiple genomic features. We demonstrate GINOM's ability to identify higher-order associations with both simulated and real data. In particular, we used GINOM to explore L1 retrotransposable element insertion bias in lung cancer and found a significant pairwise association between L1 insertions and heterochromatic marks. Unlike other methods, GINOM also detected an association between L1 in...

A fully statistical framework for shape detection in image primitives

2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Workshops, 2010

ABSTRACT We present a fully statistical framework for detecting pre-determined shape classes in 2... more ABSTRACT We present a fully statistical framework for detecting pre-determined shape classes in 2D clouds of primitives (points, edges, and arcs), which are in turn extracted from images. An important goal is to provide a likelihood, and thus a confidence, of finding a shape class in a given data. This requires a model-based approach. We use a composite Poisson process: 1D Poisson process for primitives belonging to shapes and a 2D Poisson process for primitives belonging to clutter. An additive Gaussian model is assumed for noise in shape primitives. Combining these with a past stochastic model on shapes of continuous 2D contours, and optimization over unknown pose and scale, we develop a generalized likelihood ratio test for shape detection. We demonstrate the efficiency of this method and its robustness to clutter using both simulated and real data.