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Term(s):1998
Results:40
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Title:A lattice path model for the Bessel polynomials
Author(s):Pitman, Jim;
Date issued:Mar 1998
http://nma.berkeley.edu/ark:/28722/bk0000n225b (PDF)
http://nma.berkeley.edu/ark:/28722/bk0000n226w (PostScript)
Abstract:The (n-1)th Bessel polynomial is represented by an exponential generating function derived from the number of returns to $0$ of a sequence with 2n increments of +1 or -1 which starts and ends at 0.
Keyword note:Pitman__Jim
Report ID:551
Relevance:100

Title:Brownian motion, bridge, excursion, and meander characterized by sampling at independent uniform times
Author(s):Pitman, Jim;
Date issued:Feb 1998
Abstract:For a random process $X$ consider the random vector defined by the values of $X$ at times $0 < U_(n,1) < ... < U_(n,n) < 1$ and the minimal values of $X$ on each of the intervals between consecutive pairs of these times, where the $U_(n,i)$ are the order statistics of $n$ independent uniform $(0,1)$ variables, independent of $X$. The joint law of this random vector is explicitly described when $X$ is a Brownian motion. Corresponding results for Brownian bridge, excursion, and meander are deduced by appropriate conditioning. These descriptions yield numerous new identities involving the laws of these processes, and simplified proofs of various known results, including Aldous's characterization of the random tree constructed by sampling the excursion at $n$ independent uniform times, Vervaat's transformation of Brownian bridge into Brownian excursion, and Denisov's decomposition of the Brownian motion at the time of its minimum into two independent Brownian meanders. Other consequences of the sampling formulae are Brownian representions of various special functions, including Bessel polynomials, some hypergeometric polynomials, and the Hermite function. Various combinatorial identities involving random partitions and generalized Stirling numbers are also obtained.
Pub info:Electronic Journal of Probability, Vol. 4 (1999) Paper no. 11, pages 1-33
Keyword note:Pitman__Jim
Report ID:545
Relevance:100

Title:Continuum-sites stepping-stone models, coalescing exchangeable partitions, and random trees
Author(s):Donnelly, Peter; Evans, Steven N.; Fleischmann, Klaus; Kurtz, Thomas G.; Zhou, Xiaowen;
Date issued:Nov 1998
http://nma.berkeley.edu/ark:/28722/bk0000n3x7v (PDF)
http://nma.berkeley.edu/ark:/28722/bk0000n3x8d (PostScript)
Abstract:Analogues of stepping--stone models are considered where the site--space is continuous, the migration process is a general Markov process, and the type--space is infinite. Such processes were defined in previous work of the second author by specifying a Feller transition semigroup in terms of expectations of suitable functionals for systems of coalescing Markov processes. An alternative representation is obtained here in terms of a limit of interacting particle systems. It is shown that, under a mild condition on the migration process, the continuum--sites stepping--stone process has continuous sample paths. The case when the migration process is Brownian motion on the circle is examined in detail using a duality relation between coalescing and annihilating Brownian motion. This duality relation is also used to show that a random compact metric space that is naturally associated to an infinite family of coalescing Brownian motions on the circle has Hausdorff and packing dimension both almost surely equal to $\frac(1)(2)$ and, moreover, this space is capacity equivalent to the middle--1/2 Cantor set (and hence also to the Brownian zero set).
Keyword note:Donnelly__Peter Evans__Steven_N Fleischmann__Klaus Kurtz__Thomas_G Zhou__Xiaowen
Report ID:540
Relevance:100

Title:The distribution of local times of a Brownian bridge
Author(s):Pitman, Jim;
Date issued:Nov 1998
http://nma.berkeley.edu/ark:/28722/bk0000n278k (PDF)
http://nma.berkeley.edu/ark:/28722/bk0000n2794 (PostScript)
Abstract:L\'evy's approach to Brownian local times is used to give a simple derivation of a formula of Borodin which determines the distribution of the local time at level x up to time 1 for a Brownian bridge of length 1 from 0 to b. A number of identities in distribution involving functionals of the bridge are derived from this formula. A stationarity property of the bridge local times is derived by a simple path transformation, and related to Ray's description of the local time process of Brownian motion stopped at an independent exponential time.
Pub info:S\'{e}minaire de Probabilit\'{e}s XXXIII, 388-394, Lecture Notes in Math. 1709, Springer, 1999
Keyword note:Pitman__Jim
Report ID:539
Relevance:100

Title:The Histogram Method for Nonlinear Mixed Effects Models
Author(s):Zhiyu, Ge; Bickel, Peter J.; Rice, John A.;
Date issued:October 1998
Keyword note:Zhiyu__Ge Bickel__Peter_John Rice__John_Andrew
Report ID:538
Relevance:100

Title:Statistical Controversies in Census 2000
Author(s):Brown, Lawrence D.; Eaton, Morris L.; Freedman, David A.; Klein, Stephen P.; Olshen, Richard A.; Wachter, Kenneth W.; Wells, Martin T.; Ylvisaker, Donald;
Date issued:Oct 1998
http://nma.berkeley.edu/ark:/28722/bk0000n3m76 (PDF)
http://nma.berkeley.edu/ark:/28722/bk0000n3m8r (PostScript)
Abstract:This paper is a discussion of Census 2000, focusing on planned use of sampling techniques for non-response followup and adjustment. Past experience with adjustment methods suggests that the design for Census 2000 is quite risky.
Keyword note:Brown__Lawrence_D Eaton__Morris_L Freedman__David Klein__Stephen_P Olshen__Richard_A Wachter__Kenneth Wells__Martin_T Ylvisaker__Donald
Report ID:537
Relevance:100

Title:Half&Half Bagging and Hard Boundary Points
Author(s):Breiman, Leo;
Date issued:Sep 1998
http://nma.berkeley.edu/ark:/28722/bk0000n3b95 (PDF)
http://nma.berkeley.edu/ark:/28722/bk0000n3c0q (PostScript)
Abstract:Half&half bagging is a method for generating an ensemble of classifiers and combining them that does not resemble any method proposed to date. It is simple and intuitive in concept and its accuracy is very competitive with Adaboost. Certain instances that are used repeatedly turn out to be located in the boundaries between classes and we refer to these as hard boundary points. The effectiveness of half&half bagging leads to the conjecture that the accuracy of any combination method is based on its ability to locate the hard boundary points.
Keyword note:Breiman__Leo
Report ID:535
Relevance:100

Title:The law of the maximum of a Bessel bridge
Author(s):Pitman, Jim; Yor, Marc;
Date issued:Oct 1998
Abstract:Let $M_d$ be the maximum of a standard Bessel bridge of dimension $d$. A series formula for $P(M_d < a)$ due to Gikhman and Kiefer for $d = 1,2, \ldots$ is shown to be valid for all real $d >0$. Various other characterizations of the distribution of $M_d$ are given, including formulae for its Mellin transform, which is an entire function. The asymptotic distribution of $M_d$ as is described both as $d$ tends to $\infty$ and as $d$ tends to $0$. Keywords: Brownian bridge, Brownian excursion, Brownian scaling, local time, Bessel process, zeros of Bessel functions, Riemann zeta function.
Pub info:Electronic Journal of Probability, Vol. 4 (1999) Paper no. 15, pages 1-35
Keyword note:Pitman__Jim Yor__Marc
Report ID:534
Relevance:100

Title:tochastic optimization methods for fitting polyclass and feed-forward neural network models
Author(s):Stone, C. J.; Kooperberg, C.;
Date issued:August 1998
Pub info:Submitted to Journal of Computational and Graphical Statistics.
Keyword note:Stone__Charles Kooperberg__Charles_Louis
Report ID:533
Relevance:100

Title:Path decompositions of a Brownian bridge related to the ratio of its maximum and amplitude
Author(s):Pitman, Jim; Yor, Marc;
Date issued:Aug 1998
http://nma.berkeley.edu/ark:/28722/bk0000n377h (PDF)
http://nma.berkeley.edu/ark:/28722/bk0000n3782 (PostScript)
Abstract:We give two new proofs of Csaki's formula for the law of the ratio 1-Q of the maximum relative to the amplitude (i.e. the maximum minus minimum) for a standard Brownian bridge. The second of these proofs is based on an absolute continuity relation between the law of the Brownian bridge restricted to the event (Q < v) and the law of a process obtained by a Brownian scaling operation after back-to back joining of two independent three-dimensional Bessel processes, each started at v and run until it first hits 1. Variants of this construction and some properties of the joint law of Q and the amplitude are described.
Keyword note:Pitman__Jim Yor__Marc
Report ID:532
Relevance:100

Title:Kingman's coalescent as a random metric space
Author(s):Evans, Steven N.;
Date issued:Aug 1998
http://nma.berkeley.edu/ark:/28722/bk0000n264v (PDF)
http://nma.berkeley.edu/ark:/28722/bk0000n265d (PostScript)
Abstract:Kingman's coalescent is a Markov process with state--space the collection of partitions of the positive integers. Its initial state is the trivial partition of singletons and it evolves by successive pairwise mergers of blocks. The coalescent induces a metric on the positive integers: the distance between two integers is the time until they both belong to the same block. We investigate the completion of this (random) metric space. We show that almost surely it is a compact metric space with Hausdorff and packing dimension both $1$, and it has positive capacities in precisely the same gauges as the unit interval.
Keyword note:Evans__Steven_N
Report ID:531
Relevance:100

Title:Testing and the Method of Sieves
Author(s):Bickel, Peter; Ritov, Ya'acov; Stoker, Thomas;
Date issued:Jul 1998
http://nma.berkeley.edu/ark:/28722/bk0000n231n (PDF)
http://nma.berkeley.edu/ark:/28722/bk0000n2326 (PostScript)
Abstract:This paper develops test statistics based on scores for the specification of regression in nonparametric and semiparametric contexts. We study how different types of test statistics focus power on different directions of departure from the null hypothesis. We consider index models as basic examples, and utilize sieves for nonparametric approximation. We examine various goodness-of-fit statistics, including Cramer-von Mises and Kolmogorov-Smirnov forms. For a "box-style" sieve approximation, we establish limiting distributions of these statistics. We develop a bootstrap resampling method for estimating critical values for the test statistics, and illustrate their performance with a Monte Carlo simulation.
Keyword note:Bickel__Peter_John Ritov__Yaacov Stoker__Thomas
Report ID:530
Relevance:100

Title:An Edgeworth expansion for the m out of n bootstrapped median.
Author(s):Sakov, Anat; Bickel, Peter J.;
Date issued:Jul 1998
http://nma.berkeley.edu/ark:/28722/bk0000n1w8x (PDF)
http://nma.berkeley.edu/ark:/28722/bk0000n1w9g (PostScript)
Abstract:It is well known Singh (1981) that the bootstrap distribution of the median has the correct limiting distribution. In this note we prove the existence of the next term in the Edgeworth expansion if the bootstrap sample size is m = o(n).
Keyword note:Sakov__Anat Bickel__Peter_John
Report ID:529
Relevance:100

Title:A score test for linkage using identity by descent data from sibships
Author(s):Dudoit, Sandrine; Speed, Terence P.;
Date issued:Jul 1998
http://nma.berkeley.edu/ark:/28722/bk0000n218g (PDF)
http://nma.berkeley.edu/ark:/28722/bk0000n2191 (PostScript)
Abstract:We consider score tests of the null hypothesis $(\rm H)_0: \theta = \frac(1)(2)$ against the alternative hypothesis $(\rm H)_1: 0 \leq \theta < \frac(1)(2)$, based upon counts multinomially distributed with parameters $n$ and $\rho(\theta,\pi)_( 1 \times m) = \pi_(1 \times m) T(\theta)_(m \times m)$, where $T(\theta)$ is a transition matrix with $T(0) = I$, the identity matrix, and $T(\frac(1)(2)) = (\bf 1)^T \alpha$, $(\bf 1) = (1,\ldots, 1)$. This type of testing problem arises in human genetics when testing the null hypothesis of no linkage between a marker and a disease susceptibility gene, using identity by descent data from families with affected members. In important cases in this genetic context, the score test is independent of the nuisance parameter $\pi$ and is based on a widely used test statistic in linkage analysis. The proof of this result involves embedding the states of the multinomial distribution into a continuous time Markov chain with infinitesimal generator $Q$. The second largest eigenvalue of $Q$ and its multiplicity are key in determining the form of the score statistic. We relate $Q$ to the adjacency matrix of a quotient graph, in order to derive its eigenvalues and eigenvectors.
Keyword note:Dudoit__Sandrine Speed__Terry_P
Report ID:528
Relevance:100

Title:Triangle constraints for sib-pair identity by descent probabilities under a general multilocus model for disease susceptibility
Author(s):Dudoit, Sandrine; Speed, Terence P.;
Date issued:Jul 1998
http://nma.berkeley.edu/ark:/28722/bk0000n1w58 (PDF)
http://nma.berkeley.edu/ark:/28722/bk0000n1w6t (PostScript)
Abstract:In this paper, we study sib-pair IBD probabilities under a general multilocus model for disease susceptibility which doesn't assume random mating, linkage equilibrium or Hardy-Weinberg equilibrium. We derive the triangle constraints satisfied by affected, discordant and unaffected sib-pair IBD probabilities, as well as constraints distinguishing between sharing of maternal and paternal DNA, under general monotonicity assumptions concerning the penetrance probabilities. The triangle constraints are valid for age and sex-dependent penetrances, and in the presence of parental imprinting. We study the parameterization of sib-pair IBD probabilities for common models, and present examples to demonstrate the impact of non-random mating and the necessity of our assumptions for the triangle constraints. We prove that the affected sib-pair possible triangle is covered by the IBD probabilities of two types of models, one with fixed mode of inheritance and general mating type frequencies, the other with varying mode of inheritance and random mating. Finally, we consider IBD probabilities at marker loci linked to disease susceptibility loci and derive the triangle constraints satisfied by these probabilities.
Keyword note:Dudoit__Sandrine Speed__Terry_P
Report ID:527
Relevance:100

Title:A family of random trees with random edge lengths
Author(s):Aldous, David; Pitman, Jim;
Date issued:Jun 1998
http://nma.berkeley.edu/ark:/28722/bk0000n3n1d (PDF)
http://nma.berkeley.edu/ark:/28722/bk0000n3n2z (PostScript)
Abstract:We introduce a family of probability distributions on the space of trees with I labeled vertices and possibly extra unlabeled vertices of degree 3, whose edges have positive real lengths. Formulas for distributions of quantities such as degree sequence, shape, and total length are derived. An interpretation is given in terms of sampling from the inhomogeneous continuum random tree of Aldous and Pitman (1998). Key words and phrases: continuum tree, enumeration, random tree, spanning tree, weighted tree, Cayley's multinomial expansion.
Pub info:Random Structures and Algorithms Vol 15, 176-195 (1999)
Keyword note:Aldous__David_J Pitman__Jim
Report ID:526
Relevance:100

Title:Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent
Author(s):Aldous, D.; Pitman, J.;
Date issued:June 1998
Keyword note:Aldous__David_J Pitman__Jim
Report ID:525
Relevance:100

Title:Asymptotics for k-fold repeats in the birthday problem with unequal probabilities
Author(s):Camarri, Michael;
Date issued:Jul 1998
http://nma.berkeley.edu/ark:/28722/bk0000n2w69 (PDF)
http://nma.berkeley.edu/ark:/28722/bk0000n2w7v (PostScript)
Abstract:In a previous paper Camarri and Pitman studied the asymptotics for repeat times in random sampling by a method of Poisson embedding. Here we extend these results to k-fold repeats and also indicate the relationships between the repeat processes of various orders.
Keyword note:Camarri__Michael_Brett
Report ID:524
Relevance:100

Title:Limit distributions and random trees derived from the birthday problem with unequal probabilities
Author(s):Camarri, Michael; Pitman, Jim;
Date issued:Jun 1998
Abstract:Given an arbitrary distribution on a countable set, consider the number of independent samples required until the first repeated value is seen. Exact and asymptotic formulae are derived for the distribution of this time and of the times until subsequent repeats. Asymptotic properties of the repeat times are derived by embedding in a Poisson process. In particular, necessary and sufficient conditions for convergence are given and the possible limits explicitly described. Under the same conditions the finite dimensional distributions of the repeat times converge to the arrival times of suitably modified Poisson processes, and random trees derived from the sequence of independent trials converge in distribution to an inhomogeneous continuum random tree.
Pub info:Electronic Journal of Probability, Vol. 5 (2000) Paper no. 2, pages 1-18
Keyword note:Camarri__Michael_Brett Pitman__Jim
Report ID:523
Relevance:100

Title:Nonparametric mixed effects models for unequally sampled noisy curves
Author(s):Rice, John; Wu, Colin;
Date issued:Jun 1998
http://nma.berkeley.edu/ark:/28722/bk0000n3t2j (PDF)
http://nma.berkeley.edu/ark:/28722/bk0000n3t33 (PostScript)
Abstract:We propose a method of analyzing collections of related curves in which the individual curves are modeled as spline functions with random coefficients. The method is applicable when the individual curves are sampled at variable and irregularly spaced points. This produces a low rank, low frequency approximation to the covariance structure, which can be estimated naturally by the EM algorithm. Smooth curves for individual trajectories are constructed as BLUP estimates, combining data from that individual and the entire collection. This framework leads naturally to methods for examining the effects of covariates on the shapes of the curves. We use model selection techniques---AIC, BIC, and cross-validation---to select the number of breakpoints for the spline approximation. We believe that the methodology we propose provides a simple, flexible, and computationally efficient means of functional data analysis. We illustrate it with two sets of data.
Keyword note:Rice__John_Andrew Wu__Chien-Fu
Report ID:522
Relevance:100

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