Luke Tierney - Academia.edu (original) (raw)

Papers by Luke Tierney

Journal of Statistical Software, 2009

R is a mature open-source programming language for statistical computing and graphics. Many areas... more R is a mature open-source programming language for statistical computing and graphics. Many areas of statistical research are experiencing rapid growth in the size of data sets. Methodological advances drive increased use of simulations. A common approach is to use parallel computing.

Journal of Statistical Software, 2008

This paper presents R utilities for computing and displaying isosurfaces, or threedimensional con... more This paper presents R utilities for computing and displaying isosurfaces, or threedimensional contour surfaces, from a three-dimensional array of function values. A version of the marching cubes algorithm that takes into account face and internal ambiguities is used to compute the isosurfaces. Vectorization is used to ensure adequate performance using only R code. Examples are presented showing contours of theoretical densities, density estimates, and medical imaging data. Rendering can use the rgl package or standard or grid graphics, and a set of tools for representing and rendering surfaces using standard or grid graphics is presented. R> library("rgl") R> points3d(quakes$long/22, quakes$lat/28, -quakes$depth/640, size = 2) R> box3d(col = "gray") R> title3d(xlab = "long", ylab = "lat", zlab = "depth")

This appendix for the paper \State of the Art in Parallel Computing with R" (Schmid- berger,... more This appendix for the paper \State of the Art in Parallel Computing with R" (Schmid- berger, Morgan, Eddelbuettel, Yu, Tierney, and Mansmann 2009) gives some short code examples for all in the paper presented R packages in order to introduce the reader to the basic functionality. Furthermore, the full R code for performance evaluation is provided and some additional tables

Encyclopedia of Statistical Sciences, 2004

ABSTRACT We briefly describe Markov chain Monte Carlo algorithms, such as the Gibbs sampler and t... more ABSTRACT We briefly describe Markov chain Monte Carlo algorithms, such as the Gibbs sampler and the Metropolis-Hastings (1953, 1970) algorithm, which are frequently used in the statistics literature to explore complicated probability distributions. We present a general method for proving rigorous, a priori bounds an the number of iterations required to achieve convergence of the algorithms

Genome biology, 2004

The Bioconductor project is an initiative for the collaborative creation of extensible software f... more The Bioconductor project is an initiative for the collaborative creation of extensible software for computational biology and bioinformatics. The goals of the project include: fostering collaborative development and widespread use of innovative software, reducing barriers to entry into interdisciplinary scientific research, and promoting the achievement of remote reproducibility of research results. We describe details of our aims and methods, identify current challenges, compare Bioconductor to other open bioinformatics projects, and provide working examples.

Statistics in Medicine, 2014

Various works have used magnetic resonance imaging (MRI) tissue classification extensively to stu... more Various works have used magnetic resonance imaging (MRI) tissue classification extensively to study a number of neurological and psychiatric disorders. Various noise characteristics and other artifacts make this classification a challenging task. Instead of splitting the procedure into different steps, we extend a previous work to develop a unified Bayesian hierarchical model, which addresses both the partial volume effect and intensity non-uniformity, the two major acquisition artifacts, simultaneously. We adopted a normal mixture model with the means and variances depending on the tissue types of voxels to model the observed intensity values. We modeled the relationship among the components of the index vector of tissue types by a hidden Markov model, which captures the spatial similarity of voxels. Furthermore, we addressed the partial volume effect by construction of a higher resolution image in which each voxel is divided into subvoxels. Finally, We achieved the bias field correction by using a Gaussian Markov random field model with a band precision matrix designed in light of image filtering. Sparse matrix methods and parallel computations based on conditional independence are exploited to improve the speed of the Markov chain Monte Carlo simulation. The unified model provides more accurate tissue classification results for both simulated and real data sets.

Journal of the American Statistical Association, 2012

Magnetic resonance imaging (MRI) is used to identify the major tissues within a subject's brain. ... more Magnetic resonance imaging (MRI) is used to identify the major tissues within a subject's brain. Classification is usually based on a single image providing one measurement for each volume element, or voxel, in a discretization of the brain. A simple model views each voxel as homogeneous, belonging entirely to one of the three major tissue types (gray matter, white matter, and cerebro-spinal fluid); the measurements are normally distributed with means and variances depending on the tissue types of their voxels. Since nearby voxels tend to be of the same tissue type, a Markov random field model can be used to capture the spatial similarity of voxels. A more realistic model would take into account the fact that some voxels are not homogeneous and contain tissues of more than one type. Our approach to this problem is to construct a higher resolution image in which each voxel is divided into subvoxels, and subvoxels are in turn assumed to be homogeneous and follow a Markov random field model. This paper uses a Bayesian hierarchical model to conduct MRI tissue classification.

Journal of the American Statistical Association, 1989

Tierney and Kadane (1986) presented a simple second-order approximation for posterior expectation... more Tierney and Kadane (1986) presented a simple second-order approximation for posterior expectations of positive functions. They used Laplace's method for asymptotic evaluation of integrals, in which the integrand is written as f(θ)exp(-nh(θ)) and the function h is approximated by a quadratic. The form in which they applied Laplace's method, however, was fully exponential: The integrand was written instead as exp[− nh(θ) + log f(θ)]; this allowed first-order approximations to be used in the numerator and denominator of a ratio of integrals to produce a second-order expansion for the ratio. Other second-order expansions (Hartigan 1965; Johnson 1970; Lindley 1961, 1980; Mosteller and Wallace 1964) require computation of more derivatives of the log-likelihood function. In this article we extend the fully exponential method to apply to expectations and variances of nonpositive functions. To obtain a second-order approximation to an expectation E(g(θ)), we use the fully exponential method to approximate the moment-generating function E(exp(sg(θ))), whose integrand is positive, and then differentiate the result. This method is formally equivalent to that of Lindley and that of Mosteller and Wallace, yet does not require third derivatives of the likelihood function. It is also equivalent to another alternative approach to the approximation of E(g(θ)): We may add a large constant c to g(θ), apply the fully exponential method to E(c + g(θ)), and subtract c; on passing to the limit as c tends to infinity we regain the approximation based on the moment-generating function. Furthermore, the second derivative of the logarithm of the approximation E(exp(sg(θ))), which is an approximate cumulant-generating function, yields a simple second-order approximation to the variance. In deriving these results we omit rigorous justification of formal manipulations, which may be found in Kass, Tierney, and Kadane (in press). Although our point of view is Bayesian, our results have applications to non-Bayesian inference as well (DiCiccio 1986).

Journal of the American Statistical Association, 1995

In Markov chain Monte Carlo, a distribution ir is exam-ined by obtaining sample paths from a Mark... more In Markov chain Monte Carlo, a distribution ir is exam-ined by obtaining sample paths from a Markov chain con-structed to have equilibrium distribution ir. This approach, introduced by Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller (1953), has recently received ...

Journal of Computational and Graphical Statistics, 2010

Computational Statistics & Data Analysis, 1992

... graphics. Purchase this Book. Source, Pages: 397. Year of Publication: 1990. ISBN:0-471-50916... more ... graphics. Purchase this Book. Source, Pages: 397. Year of Publication: 1990. ISBN:0-471-50916-7. Author, Luke Tierney, Univ. of Minnesota, Minneapolis. Publisher, Wiley-Interscience New York, NY, USA. Bibliometrics, Downloads ...

CHEST Journal, 1986

Pulmonary mucormycosis is an uncommon, but important, opportunistic fungal pneumonia which is oft... more Pulmonary mucormycosis is an uncommon, but important, opportunistic fungal pneumonia which is often diagnosed post-mortem. This review emphasizes clinical and pathologic characteristics of pulmonary mucormycosis that differentiate this infection from other fungal pneumonias. The most common clinical presentation of pulmonary mucormycosis is a rapidly progressive pneumonia with diffuse infiltrates on chest radiographic examination of a patient with an underlying hematologic malignancy treated with immunosuppressive drugs. Other immunocompromised hosts at risk for pulmonary mucormycosis include patients with diabetes mellitus who may develop a distinctive endobronchial form of this disease. Early consideration of this diagnosis, along with aggressive diagnostic evaluation, are critical to effective therapy and patient survival. While treatment with amphotericin B is the mainstay of therapy for pulmonary mucormycosis, diabetics with endobronchial disease may benefit from early, aggressive surgical resection of the involved lung tissue.

Biometrika, 1989

... J. Am. Statist. Assoc. 81, 82-6. TIERNEY, L., KASS, RE & KADANE, JB (1987). Interactive B... more ... J. Am. Statist. Assoc. 81, 82-6. TIERNEY, L., KASS, RE & KADANE, JB (1987). Interactive Bayesian analysis using accurate asymptotic approximations. In Proc. of 19th Symp. on the Interface, Ed. RM Heiberger, pp. 15-21. Alexandria: ASA. [Received February 1988. ...

Biometrika, 1989

... We begin further analysis by assessing the appropriateness of the first-order approximation t... more ... We begin further analysis by assessing the appropriateness of the first-order approximation to the marginal posteriors on the various quantities of interest g. We then assess influence of each case, and ... We might also consider the effect of moving the prior mean while ...

Journal of Statistical Software, 2009

R is a mature open-source programming language for statistical computing and graphics. Many areas... more R is a mature open-source programming language for statistical computing and graphics. Many areas of statistical research are experiencing rapid growth in the size of data sets. Methodological advances drive increased use of simulations. A common approach is to use parallel computing.

Journal of Statistical Software, 2008

This paper presents R utilities for computing and displaying isosurfaces, or threedimensional con... more This paper presents R utilities for computing and displaying isosurfaces, or threedimensional contour surfaces, from a three-dimensional array of function values. A version of the marching cubes algorithm that takes into account face and internal ambiguities is used to compute the isosurfaces. Vectorization is used to ensure adequate performance using only R code. Examples are presented showing contours of theoretical densities, density estimates, and medical imaging data. Rendering can use the rgl package or standard or grid graphics, and a set of tools for representing and rendering surfaces using standard or grid graphics is presented. R> library("rgl") R> points3d(quakes$long/22, quakes$lat/28, -quakes$depth/640, size = 2) R> box3d(col = "gray") R> title3d(xlab = "long", ylab = "lat", zlab = "depth")

This appendix for the paper \State of the Art in Parallel Computing with R" (Schmid- berger,... more This appendix for the paper \State of the Art in Parallel Computing with R" (Schmid- berger, Morgan, Eddelbuettel, Yu, Tierney, and Mansmann 2009) gives some short code examples for all in the paper presented R packages in order to introduce the reader to the basic functionality. Furthermore, the full R code for performance evaluation is provided and some additional tables

Encyclopedia of Statistical Sciences, 2004

ABSTRACT We briefly describe Markov chain Monte Carlo algorithms, such as the Gibbs sampler and t... more ABSTRACT We briefly describe Markov chain Monte Carlo algorithms, such as the Gibbs sampler and the Metropolis-Hastings (1953, 1970) algorithm, which are frequently used in the statistics literature to explore complicated probability distributions. We present a general method for proving rigorous, a priori bounds an the number of iterations required to achieve convergence of the algorithms

Genome biology, 2004

The Bioconductor project is an initiative for the collaborative creation of extensible software f... more The Bioconductor project is an initiative for the collaborative creation of extensible software for computational biology and bioinformatics. The goals of the project include: fostering collaborative development and widespread use of innovative software, reducing barriers to entry into interdisciplinary scientific research, and promoting the achievement of remote reproducibility of research results. We describe details of our aims and methods, identify current challenges, compare Bioconductor to other open bioinformatics projects, and provide working examples.

Statistics in Medicine, 2014

Various works have used magnetic resonance imaging (MRI) tissue classification extensively to stu... more Various works have used magnetic resonance imaging (MRI) tissue classification extensively to study a number of neurological and psychiatric disorders. Various noise characteristics and other artifacts make this classification a challenging task. Instead of splitting the procedure into different steps, we extend a previous work to develop a unified Bayesian hierarchical model, which addresses both the partial volume effect and intensity non-uniformity, the two major acquisition artifacts, simultaneously. We adopted a normal mixture model with the means and variances depending on the tissue types of voxels to model the observed intensity values. We modeled the relationship among the components of the index vector of tissue types by a hidden Markov model, which captures the spatial similarity of voxels. Furthermore, we addressed the partial volume effect by construction of a higher resolution image in which each voxel is divided into subvoxels. Finally, We achieved the bias field correction by using a Gaussian Markov random field model with a band precision matrix designed in light of image filtering. Sparse matrix methods and parallel computations based on conditional independence are exploited to improve the speed of the Markov chain Monte Carlo simulation. The unified model provides more accurate tissue classification results for both simulated and real data sets.

Journal of the American Statistical Association, 2012

Magnetic resonance imaging (MRI) is used to identify the major tissues within a subject's brain. ... more Magnetic resonance imaging (MRI) is used to identify the major tissues within a subject's brain. Classification is usually based on a single image providing one measurement for each volume element, or voxel, in a discretization of the brain. A simple model views each voxel as homogeneous, belonging entirely to one of the three major tissue types (gray matter, white matter, and cerebro-spinal fluid); the measurements are normally distributed with means and variances depending on the tissue types of their voxels. Since nearby voxels tend to be of the same tissue type, a Markov random field model can be used to capture the spatial similarity of voxels. A more realistic model would take into account the fact that some voxels are not homogeneous and contain tissues of more than one type. Our approach to this problem is to construct a higher resolution image in which each voxel is divided into subvoxels, and subvoxels are in turn assumed to be homogeneous and follow a Markov random field model. This paper uses a Bayesian hierarchical model to conduct MRI tissue classification.

Journal of the American Statistical Association, 1989

Tierney and Kadane (1986) presented a simple second-order approximation for posterior expectation... more Tierney and Kadane (1986) presented a simple second-order approximation for posterior expectations of positive functions. They used Laplace's method for asymptotic evaluation of integrals, in which the integrand is written as f(θ)exp(-nh(θ)) and the function h is approximated by a quadratic. The form in which they applied Laplace's method, however, was fully exponential: The integrand was written instead as exp[− nh(θ) + log f(θ)]; this allowed first-order approximations to be used in the numerator and denominator of a ratio of integrals to produce a second-order expansion for the ratio. Other second-order expansions (Hartigan 1965; Johnson 1970; Lindley 1961, 1980; Mosteller and Wallace 1964) require computation of more derivatives of the log-likelihood function. In this article we extend the fully exponential method to apply to expectations and variances of nonpositive functions. To obtain a second-order approximation to an expectation E(g(θ)), we use the fully exponential method to approximate the moment-generating function E(exp(sg(θ))), whose integrand is positive, and then differentiate the result. This method is formally equivalent to that of Lindley and that of Mosteller and Wallace, yet does not require third derivatives of the likelihood function. It is also equivalent to another alternative approach to the approximation of E(g(θ)): We may add a large constant c to g(θ), apply the fully exponential method to E(c + g(θ)), and subtract c; on passing to the limit as c tends to infinity we regain the approximation based on the moment-generating function. Furthermore, the second derivative of the logarithm of the approximation E(exp(sg(θ))), which is an approximate cumulant-generating function, yields a simple second-order approximation to the variance. In deriving these results we omit rigorous justification of formal manipulations, which may be found in Kass, Tierney, and Kadane (in press). Although our point of view is Bayesian, our results have applications to non-Bayesian inference as well (DiCiccio 1986).

Journal of the American Statistical Association, 1995

In Markov chain Monte Carlo, a distribution ir is exam-ined by obtaining sample paths from a Mark... more In Markov chain Monte Carlo, a distribution ir is exam-ined by obtaining sample paths from a Markov chain con-structed to have equilibrium distribution ir. This approach, introduced by Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller (1953), has recently received ...

Journal of Computational and Graphical Statistics, 2010

Computational Statistics & Data Analysis, 1992

... graphics. Purchase this Book. Source, Pages: 397. Year of Publication: 1990. ISBN:0-471-50916... more ... graphics. Purchase this Book. Source, Pages: 397. Year of Publication: 1990. ISBN:0-471-50916-7. Author, Luke Tierney, Univ. of Minnesota, Minneapolis. Publisher, Wiley-Interscience New York, NY, USA. Bibliometrics, Downloads ...

CHEST Journal, 1986

Pulmonary mucormycosis is an uncommon, but important, opportunistic fungal pneumonia which is oft... more Pulmonary mucormycosis is an uncommon, but important, opportunistic fungal pneumonia which is often diagnosed post-mortem. This review emphasizes clinical and pathologic characteristics of pulmonary mucormycosis that differentiate this infection from other fungal pneumonias. The most common clinical presentation of pulmonary mucormycosis is a rapidly progressive pneumonia with diffuse infiltrates on chest radiographic examination of a patient with an underlying hematologic malignancy treated with immunosuppressive drugs. Other immunocompromised hosts at risk for pulmonary mucormycosis include patients with diabetes mellitus who may develop a distinctive endobronchial form of this disease. Early consideration of this diagnosis, along with aggressive diagnostic evaluation, are critical to effective therapy and patient survival. While treatment with amphotericin B is the mainstay of therapy for pulmonary mucormycosis, diabetics with endobronchial disease may benefit from early, aggressive surgical resection of the involved lung tissue.

Biometrika, 1989

... J. Am. Statist. Assoc. 81, 82-6. TIERNEY, L., KASS, RE & KADANE, JB (1987). Interactive B... more ... J. Am. Statist. Assoc. 81, 82-6. TIERNEY, L., KASS, RE & KADANE, JB (1987). Interactive Bayesian analysis using accurate asymptotic approximations. In Proc. of 19th Symp. on the Interface, Ed. RM Heiberger, pp. 15-21. Alexandria: ASA. [Received February 1988. ...

Biometrika, 1989

... We begin further analysis by assessing the appropriateness of the first-order approximation t... more ... We begin further analysis by assessing the appropriateness of the first-order approximation to the marginal posteriors on the various quantities of interest g. We then assess influence of each case, and ... We might also consider the effect of moving the prior mean while ...