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Title:MISR Cloud Detection over Ice and Snow Based on Linear Correlation Matching
Author(s):Shi, Tao; Yu, Bin; Braverman, Amy; 
Date issued:Dec 2002 (PDF)
Abstract:Cloud detection is a crucial step in climate modeling and prediction. The Multi-angle Imaging SpectroRadiometer (MISR) was launched in 1999 by NASA in part to provide new and better methods for detecting clouds and estimating their heights. MISR looks at Earth and its atmosphere at view angles and four spectral bands thus providing a hyperstereo capability. Even so, cloud detection remains difficult in scenes covered with ice and snow. In this paper, we discuss a new methodology that bypasses the cloud height estimation step to directly tackle cloud detection using features of ice/snow (no cloud) pixels from obtained from different MISR view angles. We propose the linear correlation matching classification (LCMC) algorithm, which is based on Fisher linear correlation tests. We compare LCMC with the MISR Level 2 top-of-the atmosphere cloud algorithm (known as "L2TC"), and find that LCMC gives better coverage and more robust results as judged by visual inspection of finer resolution images. LCMC can also detect the very thin clouds in many cases. Moreover, LCMC is computationally much faster than L2TC and easier to implement. We hope to combine LCMC with L2TC in the future to improve the accuracy of the L2TC cloud height retrieval.
Keyword note:Shi__Tao Yu__Bin Braverman__Amy_J
Report ID:630

Title:Bivariate Uniqueness in the Logistic Recursive Distributional Equation
Author(s):Bandyopadhyay, Antar; 
Date issued:Nov 2002 (PDF)
Abstract:In this work we prove the \emph(bivariate uniqueness) property of the Logistic fixed-point equation, which arise in the study of the \emph(random assignment problem), as discussed by Aldous (2001). Using this and the general framework of Aldous and Bandyopadhyay (2002), we then conclude that the associated \emph(recursive tree process) is \emph(endogenous), and hence the Logistic variables defined in Aldous' 2001 paper are measurable with respect to the $\sigma$-field generated by the edge weights. The method involves construction of an explicit recursion to show the uniqueness of the associated integral equation.
Keyword note:Bandyopadhyay__Antar
Report ID:629

Title:Asymptotic Genealogy of a Critical Branching Process
Author(s):Popovic, Lea; 
Date issued:Oct 2002 (PDF) (PostScript)
Abstract:Let $\T_(t,n)$ be a continuous-time critical branching process conditioned to have population $n$ at time $t$. Consider $T_(t,n)$ as a random rooted tree with edge-lengths. We define the genealogy $\G(T_t)$ of the population at time $t$ to be the smallest subtree of $\T_(t,n)$ containing all the edges at a distance $t$ from the root. We also consider a Bernoulli($p$) sampling process on the leaves of $\T_(t,n)$, and define the $p$-sampled history $\H_p(\T_(t,n))$ to be the smallest subtree of $\T_(t,n)$ containing all the sampled leaves at a distance less than $t$ from the root. We first give a representation of $\G(\T_(t,n))$ and $\H_p(\T_(t,n))$ in terms of point-processes, and then prove their convergence as $n\rightarrow\infty$, $\frac(t)(n)\rightarrow t_0$, and $np\rightarrow p_0$. The resulting asymptotic processes are related to a Brownian excursion conditioned to have local time at $0$ equal to $1$, sampled at times of a Poisson($\frac(p_0)(2)$) process.
Keyword note:Popovic__Lea
Report ID:628

Title:Embedding a Markov chain into a random walk on a permutation group
Author(s):Evans, Steven N.; 
Date issued:Oct 2002
Date modified:revised June 2003 (PDF) (PostScript)
Abstract:Using representation theory, we obtain a necessary and sufficient condition for a discrete--time Markov chain on a finite state space $E$ to be representable as $\Psi_n \Psi_(n-1) \cdots \Psi_1 z$, $n \ge 0$, for any $z \in E$, where the $\Psi_i$ are independent, identically distributed random permutations taking values in some given transitive group of permutations on $E$. The condition is particularly simple when the group is $2$-transitive on $E$.
Keyword note:Evans__Steven_N
Report ID:627

Title:Statistical Methods for Detecting Stellar Occultations by Kuiper Belt Objects: the Taiwanese-American Occultation Survey
Author(s):Liang, Chyng-Lan; Rice, John A.; de Pater, Imke; Alcock, Charles; Axelrod, Tim; Wang, Andrew; Marshall, Stuart; 
Date issued:Sep 2002 (PDF)
Abstract:The Taiwanese-American Occultation Survey (TAOS) will detect objects in the Kuiper Belt, by measuring the rate of occultations of stars by these objects, using an array of three to four 50cm wide-field robotic telescopes. Thousands of stars will be monitored, resulting in hundreds of millions of photometric measurements per night. To optimize the success of TAOS, we have investigated various methods of gathering and processing the data and developed statistical methods for detecting occultations. In this paper we discuss these methods. The resulting estimated detection efficiencies will be used to guide the choice of various operational parameters determining the mode of actual observation when the telescopes come on line and begin routine observations. In particular we show how real-time detection algorithms may be constructed, taking advantage of having multiple telescopes. We also discuss a retrospective method for estimating the rate at which occultations occur.
Keyword note:Liang__Chyng-Lan Rice__John_Andrew Pater__Imke_de Alcock__Charles Axelrod__Tim Wang__Andrew Marshall__Stuart
Report ID:626

Title:Poisson-Kingman partitions
Author(s):Pitman, Jim; 
Date issued:Oct 2002 (PDF) (PostScript)
Abstract:This paper presents some general formulas for random partitions of a finite set derived by Kingman's model of random sampling from an interval partition generated by subintervals whose lengths are the points of a Poisson point process. These lengths can be also interpreted as the jumps of a subordinator, that is an increasing process with stationary independent increments. Examples include the two-parameter family of Poisson-Dirichlet models derived from the Poisson process of jumps of a stable subordinator. Applications are made to the random partition generated by the lengths of excursions of a Brownian motion or Brownian bridge conditioned on its local time at zero.
Keyword note:Pitman__Jim
Report ID:625

Title:Brownian Bridge Asymptotics for Random p-mappings
Author(s):Aldous, David; Pitman, Jim; Miermont, Gregory; 
Date issued:August 2002
Keyword note:Aldous__David_J Pitman__Jim Miermont__Gregory
Report ID:624

Title:[Title unavailable]
Author(s):Storey, J.; 
Date issued:July 2002
Keyword note:Storey__J
Report ID:623

Title:Detection of onset of neural activity using an empirical Bayes change point analysis
Author(s):Ritov, Y.; Raz, A.; Bergman, H.; 
Date issued:Jul 2002 (PDF) (PostScript)
Abstract:We consider situations in which there is a change point in the activity of a cell, that is, some time after an external event the firing rate of the cell changes. The change can occur after a random delay. The distribution of the time to change is considered unknown. Formally we deal with $n$ \iid random point processes, each of these is an inhomogeneous Poisson processes, with one intensity until a random time, and a different intensity thereafter. Thus, the change point is not explicitly observed. We present both a simple estimator and the non-parametric maximum likelihood estimator (NPMLE) of the change point distribution, both having the same rate of convergence. This rate is proved to be the best possible. The extension of the basic model to multiple processes per trial with different intensities and joint multiple change points is demonstrated using both simulated and neural data. We show that for realistic spike train data, trial by trial estimation of a change point may be misleading, while the distribution of the change point distribution can be well estimated.
Keyword note:Ritov__Yaacov Raz__A Bergman__H
Report ID:622

Title:Combinatorial Stochastic Processes
Author(s):Pitman, Jim; 
Date issued:Aug 2002 (PDF) (PostScript)
Abstract:This is a preliminary set of lecture notes for a course to be given at the St. Flour summer school in July 2002. The theme of the course is the study of various combinatorial models of random partitions and random trees, and the asymptotics of these models related to continuous parameter stochastic processes. Following is a list of the main topics treated: models for random combinatorial structures, such as trees, forests, permutations, mappings, and partitions; probabilistic interpretations of various combinatorial notions e.g. Bell polynomials, Stirling numbers, polynomials of binomial type, Lagrange inversion; Kingman's theory of exchangeable random partitions and random discrete distributions; connections between random combinatorial structures and processes with independent increments: Poisson-Dirichlet limits; random partitions derived from subordinators; asymptotics of random trees, graphs and mappings related to excursions of Brownian motion; continuum random trees embedded in Brownian motion; Brownian local times and squares of Bessel processes; various processes of fragmentation and coagulation, including Kingman's coalescent, the additive and multiplicative coalescents
Keyword note:Pitman__Jim
Report ID:621

Title:Microarray image compression: SLOCO and the effects of information loss
Author(s):Yu, Bin; Jornsten, R.; Wang, W.; Ramchandran, K.; 
Date issued:June 2002
Keyword note:Yu__Bin Jornsten__Rebecka Wang__Wei Ramchandran__K
Report ID:620

Title:Minimum Description Length Model Selection Criteria for Generalized Linear Models
Author(s):Yu, Bin; Hansen, Mark; 
Date issued:June 2002
Keyword note:Yu__Bin Hansen__Mark_Henry
Report ID:619

Title:Simultaneous Gene Clustering and Subset Selection for Classification via MDL
Author(s):Yu, Bin; Jornsten, Rebecka; 
Date issued:June 2002
Keyword note:Yu__Bin Jornsten__Rebecka
Report ID:618

Title:Minimax Expected Measure Confidence Sets for Restricted
Author(s):Evans, S. N.; Hansen, B.; Stark, P. B.; 
Date issued:May 2002
Date modified:revised 14 August 2002 (PDF) (PostScript)
Abstract:Location Parameters We study confidence sets for a parameter $\theta \in \Theta$ that have minimax expected measure among random sets with at least $1-\alpha$ coverage probability. We characterize the minimax sets using duality, which helps to find confidence sets with small expected measure and to bound improvements in expected measure compared with standard confidence sets. We construct explicit minimax expected length confidence sets for a variety of one-dimensional statistical models, including the bounded normal mean with known and with unknown variance. For the bounded normal mean with unit variance, the minimax expected measure 95% confidence interval has a simple form for $\Theta = [-\tau, \tau]$ with $\tau \le 3.25$. For $\Theta = [-3, 3]$, the maximum expected length of the minimax interval is about 14% less than that of the minimax fixed-length affine confidence interval and about 16% less than that of the truncated conventional interval $[X -1.96, X + 1.96] \cap [-3,3]$.
Keyword note:Evans__Steven_N Hansen__Ben Stark__Philip_B
Report ID:617

Title:Direct versus indirect designs for cDNA microarray experiments
Author(s):Speed, Terence P.; Yang, Yee Hwa; 
Date issued:Apr 2002 (PDF) (PostScript)
Abstract:We calculate the variances of two classes of estimates of differential gene expression based on log ratios of fluorescence intensities from cDNA microarray experiments: direct estimates, using measurements from the same slide, and indirect estimates, using measurements from different slides. These variances are compared and numerical estimates are obtained from a small experiment involving 4 slides. Some qualitative and quantitative conclusions are drawn which have potential relevance to the design of cDNA microarray experiments.
Keyword note:Speed__Terry_P Yang__Yee_Hwa
Report ID:616

Title:Diffusions on the simplex from Brownian motions on hypersurfaces
Author(s):Evans, Steven N.; 
Date issued:Apr 2002 (PDF) (PostScript)
Abstract:The $(n-1)$-dimensional simplex is the collection of probability measures on a set with $n$ points. Many applied situations result in simplex-valued data or in stochastic processes that have the simplex as their state space. In this paper we study a large class of simplex-valued diffusion processes that are constructed by first ``coordinatising'' the simplex with the points of a smooth hypersurface in such a way that several points on the hypersurface may correspond to a given point on the simplex, and then mapping forward the canonical Brownian motion on the hypersurface. For example, a particular instance of the Fleming-Viot process on $n$ points arises from Brownian motion on the $(n-1)$-dimensional sphere. The Brownian motion on the hypersurface has the normalised Riemannian volume as its equilibrium distribution. It is straightforward to compute the corresponding distribution on the simplex, and this provides a large class of interesting probability measures on the simplex.
Keyword note:Evans__Steven_N
Report ID:615

Title:Self-similar processes with independent increments associated with Levy and Bessel processes
Author(s):Jeanblanc, M.; Pitman, J.; Yor, M.; 
Date issued:January 2002 (PDF) (PostScript)
Abstract:Wolfe and Sato gave two different representations of a random variable X with a self-decomposable distribution in terms of processes with independent increments. This paper shows how either of these representations follows easily from the other, and makes these representations more explicit when X is either a first or last passage time for a Bessel process.
Keyword note:Jeanblanc__Monique Pitman__Jim Yor__Marc
Report ID:608

Title:The asymptotic distribution of the diameter of a random mapping
Author(s):Aldous, David; Pitman, Jim; 
Date issued:Feb 2002 (PDF) (PostScript)
Abstract:The asymptotic distribution of the diameter of the digraph of a uniformly distributed random mapping of an $n$-element set to itself is represented as the distribution of a functional of a reflecting Brownian bridge. This yields a formula for the Mellin transform of the asymptotic distribution, generalizing the evaluation of its mean by Flajolet and Odlyzko (1990).
Keyword note:Aldous__David_J Pitman__Jim
Report ID:606

Title:Two recursive decompositions of Brownian bridge related to the asymptotics of random mappings
Author(s):Aldous, David; Pitman, Jim; 
Date issued:Jul 2002 (PDF) (PostScript)
Abstract:Aldous and Pitman (1994) studied asymptotic distributions as $n \to \infty$, of various functionals of a uniform random mapping of the set $\(1, \ldots, n \)$, by constructing a mapping-walk and showing these random walks converge weakly to a reflecting Brownian bridge. Two different ways to encode a mapping as a walk lead to two different decompositions of the Brownian bridge, each defined by cutting the path of the bridge at an increasing sequence of recursively defined random times in the zero set of the bridge. The random mapping asymptotics entail some remarkable identities involving the random occupation measures of the bridge fragments defined by these decompositions. We derive various extensions of these identities for Brownian and Bessel bridges, and characterize the distributions of various path fragments involved, using the Levy-Ito theory of Poisson processes of excursions for a self-similar Markov process whose zero set is the range of a stable subordinator of index $\alpha \in (0,1)$.
Keyword note:Aldous__David_J Pitman__Jim
Report ID:595