DOCSLIB.ORG

Program Book

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Program Book TABLE OF CONTENTS 5 Welcome Message 6 Administrative Program 7 Social Program 9 General Information 13 Program Welcome Message On behalf of the Organizing Committee, I welcome you to Mérida and the 15th Latin American Congress on Probability and Mathematical Statistics. We are truly honored by your presence and sincerely hope that the experience will prove to be professionally rewarding, as well as memorable on a personal level. It goes without saying that your participation is highly significant for promoting the development of this subject matter in our region. Please do not hesitate to ask any member of the staff for assistance during your stay, information regarding academic activities and conference venues, or any other questions you may have. The city of Mérida is renowned within Mexico for its warm hospitality, amid gastronomical, archaeological, and cultural treasures. Do take advantage of any free time to explore the city and its surroundings! Dr. Daniel Hernández Chair of the Organizing Committee, XV CLAPEM Administrative Program REGISTRATION The registration will be at the venue Gamma Mérida El Castellano Hotel. There will be a registration desk at the Lobby. Sunday, December 1, 2019 From 16:00 hrs to 22:00 hrs. Monday, December 2, 2019 From 8:00 to 17:00 hrs. Tuesday, December 3, 2019 From 8:00 to 17:00 hrs Thursday, December 4, 2019 From 8:00 to 16:00 hrs. DO YOU NEED AN INVOICE FOR YOUR REGISTRATION FEE? Please ask for it at the Registration Desk at your arrival. COFFEE BREAKS During the XV CLAPEM there will be coffee break services which will be announced in the program and will be displayed in both venues: Gamma Mérida El Castellano Hotel and CCU, UADY. 6 clapem2019.eventos.cimat.mx Social Program 1) Opening ceremony & welcoming cocktail Monday, December 2, 2019 Auditorio “Manuel Cepeda Peraza” Centro Cultural Universitario (CCU), UADY 17:00 hrs. “Vaquería Yucateca” Performance by Ballet Folclórico – Universidad Autónoma de Yucatán 2) Conference dinner Thursday, December 5, 2019 Started: 21:00 hrs. Hacienda YA-AXKA Hacienda Ya-axka, named after it characterised blue colour. A peculiar colour of the ancient Mayan cities which is represented on the mural paintings in the archaeological sites of the region. Inspired by the majesty and fascination of the haciendas of our beautiful state of Yucatan, recreating the old main houses of the henequen haciendas which reached their maximum splendour at the endo of the 20th century. The dinner is a three course meal that includes two glasses of wine, two regionals beers, tequila, live music and round trip transportation to the city center of Merida. * The cost of the dinner is $50 USD and it can be paid at the registration desk from Sunday 1st of December up to 14:00 hrs of Wednesday 4th of December. Transportation to conference dinner Please, show your conference dinner ticket when you get on the bus. Downtown – Hacienda Ya-axka - Downtown Thursday, December 5, 2019 Downtown to Hacienda Ya-aska Departure time: 20:15 hrs. Departure site: Parking cross the street from Hotel Gamma Mérida El Castellano Hacienda Ya-aska to Downtown Bus 1: departure time: 22:30 hrs. Bus 2: departure time 24:00 hrs. Bus 3 and Bus 4: departure time: 02:00 hrs. 7 clapem2019.eventos.cimat.mx General Information 9 clapem2019.eventos.cimat.mx General Information WHERE CAN YOU EAT? Restaurant Address Food COST (MXP) $ El Trapiche 62 St # 491Downtown Traditional food Cafetería Pop 57 St #501 between 60 St and 62 St Mexican food $ La Chaya Maya 62 St. # 481 x 57 Downtown Traditional food $$ 62 St # 498 X 59 and 61 $$ 100% Natural Vegetarian food Downtown 59 St # 502 X 60 $$ Los trompos Mexican tacos Downtown 59 St # 507 X 60 and 62 $$ Amaro Italian food Downtown 59 St #509 $$ Pancho´s Mexican food Santa Lucía Park 62 St #488B $$ El Marlín Azul Sea food Santa Lucía Park 60 St # 488 X 57 $$ Bristrola 57 Restaurant & bar (Downtown) 55 St # 502 X 60 St and 62 St $$ Peruano Peruvian food (Downtown) Pita Mediterranean 55 St # 496 $$ Mediterranean food Cuisine & Bar Santa Lucía Park La Tratto Santa Lucía 60 St # 471 X 53 St and 55 St Italian food $$ Don Spaghetto Departamento a X 63 St and 65 St $$ Italian food Centro Downtown 60 St #491 between 55 St and 57 St $$$ Piñuela Alta cocina (Downtown) La Pigua Av Cupules 62 Sea food $$$ BANKS (near venues) 10 clapem2019.eventos.cimat.mx General Information WHAT TO DO IN MERIDA CITY DURING EVENINGS Monday Thursday Vaquería Yucateca Serenata (Serenade) (Tradicional regional dance of Santa Lucía park Yucatán) 21:00 hrs. City House “En el Corazón de Mérida” 21:00 hrs. From Thursday to Saturday From 20:00 to 2:00 hrs Tuesday It consists of closing a complete street “Remembranzas Musicales” of the city center so that restaurants, (Popular music from the 1940 musical groups, local artists and artisans can exhibit their products in mostly Danzon) full public roads during a period of Santiago’s park, Downtown time of three hours. 20:30 hrs. Friday Wednesday Video mapping “Piedras Sagradas” Recorrido por el Cathedral of Merida Cementerio de Mérida 20:30 hrs. (Guide tour to the cementery of Merida) 20:00 hrs. Saturday Mexican night “Noche de las Culturas” meeting At the end of Paseo Montejo Francisco de Montejo Starting at 20:00 hrs. (Cultural Nights) Montejo’s house (Downtown) Mayan ball game “Pok Ta Pok” 20:30 hrs. 20:30 hrs Besides the cathedral of Merida We hope you will enjoy this CLAPEM and Mérida City!!! Emergency Phone: 911 At this time of the year, 30°C / 18°C WEATHER temperature at Mérida is about (86°F/64°F) 11 clapem2019.eventos.cimat.mx Program PROGRAM Auditorium, CCU-UADY 8:30 – 9:30 Plenary Talk Average Gromov hyperbolicity and the Parisi ansatz, Sourav Chatterjee (Stanford University, US) Monday, December 2 9:30 – 12:00 Thematic Session TS Random processes on networks and their limits Organizer: Louigi Addario-Berry (MacGill University, CA) Christina Goldschmidt, (University of Oxford, UK) The scaling limit of a critical random directed graph Anja Sturm (Georg-August-Universität Göttingen, DE) Recursive tree processes and mean-field limits of interacting particle systems (10:30 – 11:00 Coffee break - both venues) Roberto Imbuzeiro Oliveira, (IMPA, BR) Interacting diffusions over random graphs and the role of sparsity Simon Griffiths (PUC-Río, BR) Moderate deviation probabilities for subgraphs and other discrete structures Hall 1, CCU-UADY 9:30 – 12:00 Contributed Session CS, Random dynamical systems with jumps I Organizer: Juan Carlos Pardo Millán (CIMAT, MX) Random events occur in nature throughout our everyday experiences. Taking stochastic effects into account is of central importance for the development of mathematical models of complex phenomena under uncertainty arising in applications. Macroscopic models in the form of differential equations for these systems contain randomness in many ways, 14 clapem2019.eventos.cimat.mx such as stochastic forcing, uncertain parameters, random sources or inputs, and random initial and boundary conditions. The theory of random dynamical systems and stochastic differential equations provides fundamental ideas and tools for the modeling, analysis, and prediction of complex phenomena. The aim of this contributed session is to showcast new developments on the theory of random dynamical systems whose driven noise has a jump structure. The three speakers on this session will deal with different aspects of stochastic differential equations driven by Lévy processes. Gerardo Barrera, (University of Alberta, CA) Cut-off phenomenon for Ornstein--Uhlenbeck processes driven by Lévy processes Joaquín Fontbona (Universidad de Chile, CL) Synchronization of stochastic mean field networks of Hodgkin-Huxley neurons with noisy channels Ilya Pavlyukevich, (University of Jena, DE) Monday, December 2 Lévy-driven transport equations Hall 2, CCU-UADY 9:30 – 12:00 Contributed Talks CT, Felipe Muñoz (Universidad de Chile and Université Paris-Saclay, CL) Rate of convergence of a spatial branching process in the large population limit using optimal transport CT, Laura Eslava, (IIMAS, UNAM, MX) Branching processes with cousin merges and locality of hypercube´s critical percolation (10:30 – 11:00 Coffee break - both venues) CT, Freddy Palma Mancilla (IMUNAM, MX) Intertwining of Galton-Watson processes CT, Peter Pflaumer (TU Dortmund, DE) Euler´s and Süßmilchs´s Population Growth Model Hall 3, CCU-UADY 9:30 – 12:00 Contributed Talks CT, Alexander Alvarez (University of Prince Edward Island, CA) A robust approach to construct coherent risk measures CT, Laszlo Markus (Eötvös Loránd University, Budapest, HU) Stochastic correlation for modelling association of stock prices 15 clapem2019.eventos.cimat.mx (10:30 – 11:00 Coffee break - both venues) CT, Jonathan Chavez Casillas (University of Rhode Island, US) A level-1 Limit Order book with time dependent arrival rates CT, Adriana Ocejo (University of North Carolina at Charlotte, US) Optimal investment portfolio of a variable annuity policyholder Hall 1, Gamma Mérida El Castellano Hotel 9:30 – 12:00 Contributed Session CS, Probabilistic Methods in PDEs and SPEDEs Organizer: José Alfredo López Mimbela (CIMAT, MX) Asymptotic properties of semi-linear partial differential equations, such as Monday, December 2 explosion in finite time an existence of solutions defined globally in time, is a current and very active field of research in Mathematics. Moreover, existence and regularity results of solutions of stochastic partial differential equations perturbed by Gaussian noises more general than Brownian motion has been intensively studied in recent years. Probabilistic methods have been shown to be a powerful tool to understand these properties, both in PDEs and SPDEs, including reaction difussion equations with non-autonomous generators, or generators of anomalous difussions and systems of semi- linear PDEs and SPDEs. The aim of this session is to report several recent developments in these fields, where the probabilistic methods are crucial.
Load more

Recommended publications
  • Methods of Monte Carlo Simulation II
    Methods of Monte Carlo Simulation II Ulm University Institute of Stochastics Lecture Notes Dr. Tim Brereton Summer Term 2014 Ulm, 2014 2 Contents 1 SomeSimpleStochasticProcesses 7 1.1 StochasticProcesses . 7 1.2 RandomWalks .......................... 7 1.2.1 BernoulliProcesses . 7 1.2.2 RandomWalks ...................... 10 1.2.3 ProbabilitiesofRandomWalks . 13 1.2.4 Distribution of Xn .................... 13 1.2.5 FirstPassageTime . 14 2 Estimators 17 2.1 Bias, Variance, the Central Limit Theorem and Mean Square Error................................ 19 2.2 Non-AsymptoticErrorBounds. 22 2.3 Big O and Little o Notation ................... 23 3 Markov Chains 25 3.1 SimulatingMarkovChains . 28 3.1.1 Drawing from a Discrete Uniform Distribution . 28 3.1.2 Drawing From A Discrete Distribution on a Small State Space ........................... 28 3.1.3 SimulatingaMarkovChain . 28 3.2 Communication .......................... 29 3.3 TheStrongMarkovProperty . 30 3.4 RecurrenceandTransience . 31 3.4.1 RecurrenceofRandomWalks . 33 3.5 InvariantDistributions . 34 3.6 LimitingDistribution. 36 3.7 Reversibility............................ 37 4 The Poisson Process 39 4.1 Point Processes on [0, )..................... 39 ∞ 3 4 CONTENTS 4.2 PoissonProcess .......................... 41 4.2.1 Order Statistics and the Distribution of Arrival Times 44 4.2.2 DistributionofArrivalTimes . 45 4.3 SimulatingPoissonProcesses. 46 4.3.1 Using the Infinitesimal Definition to Simulate Approx- imately .......................... 46 4.3.2 SimulatingtheArrivalTimes . 47 4.3.3 SimulatingtheInter-ArrivalTimes . 48 4.4 InhomogenousPoissonProcesses. 48 4.5 Simulating an Inhomogenous Poisson Process . 49 4.5.1 Acceptance-Rejection. 49 4.5.2 Infinitesimal Approach (Approximate) . 50 4.6 CompoundPoissonProcesses . 51 5 ContinuousTimeMarkovChains 53 5.1 TransitionFunction. 53 5.2 InfinitesimalGenerator . 54 5.3 ContinuousTimeMarkovChains .
    [Show full text]
  • 12 : Conditional Random Fields 1 Hidden Markov Model
    10-708: Probabilistic Graphical Models 10-708, Spring 2014 12 : Conditional Random Fields Lecturer: Eric P. Xing Scribes: Qin Gao, Siheng Chen 1 Hidden Markov Model 1.1 General parametric form In hidden Markov model (HMM), we have three sets of parameters, j i transition probability matrix A : p(yt = 1jyt−1 = 1) = ai;j; initialprobabilities : p(y1) ∼ Multinomial(π1; π2; :::; πM ); i emission probabilities : p(xtjyt) ∼ Multinomial(bi;1; bi;2; :::; bi;K ): 1.2 Inference k k The inference can be done with forward algorithm which computes αt ≡ µt−1!t(k) = P (x1; :::; xt−1; xt; yt = 1) recursively by k k X i αt = p(xtjyt = 1) αt−1ai;k; (1) i k k and the backward algorithm which computes βt ≡ µt t+1(k) = P (xt+1; :::; xT jyt = 1) recursively by k X i i βt = ak;ip(xt+1jyt+1 = 1)βt+1: (2) i Another key quantity is the conditional probability of any hidden state given the entire sequence, which can be computed by the dot product of forward message and backward message by, i i i i X i;j γt = p(yt = 1jx1:T ) / αtβt = ξt ; (3) j where we define, i;j i j ξt = p(yt = 1; yt−1 = 1; x1:T ); i j / µt−1!t(yt = 1)µt t+1(yt+1 = 1)p(xt+1jyt+1)p(yt+1jyt); i j i = αtβt+1ai;jp(xt+1jyt+1 = 1): The implementation in Matlab can be vectorized by using, i Bt(i) = p(xtjyt = 1); j i A(i; j) = p(yt+1 = 1jyt = 1): 1 2 12 : Conditional Random Fields The relation of those quantities can be simply written in pseudocode as, T αt = (A αt−1): ∗ Bt; βt = A(βt+1: ∗ Bt+1); T ξt = (αt(βt+1: ∗ Bt+1) ): ∗ A; γt = αt: ∗ βt: 1.3 Learning 1.3.1 Supervised Learning The supervised learning is trivial if only we know the true state path.
    [Show full text]
  • Hyperwage Theory
    Hyperwage Theory About the cover The cover is a glowing red-hot bark of a tree embedded with the greatest equations of nature that tremendously impacted the thought of mankind and the course of civilization. These are the Maxwell’s electromagnetic field equations, the Navier-Stokes Theorem, Euler’s identity, Newton’s second law of motion, Newton’s law of gravitation, the ideal gas equation of state, Stefan’s law, the Second Law of Thermodynamics, Einstein’s mass-energy equivalence, Einstein’s gravity tensor equation, Lorenz time dilation, Planck’s Law, Heisenberg’s Uncertainty Principle, Schrodinger’s equation, Shannon’s Theorem, and Feynman diagrams in quantum electrodynamics. Concept and design by Thads Bentulan Hyperwage Theory The Misadventures of the Street Strategist Volume 10 Thads Bentulan Street Strategist First Edition 2008 Street Strategist Publications Limited Hyperwage Theory The Misadventures of the Street Strategist Volume 10 by Thads Bentulan ISBN 978-988-17536-9-4 This book is a compilation of articles that first appeared in BusinessWorld, unless otherwise noted. While the author endeavored to credit sources whenever possible, he welcomes corrections for any unacknowledged material. No part of this book may be reproduced, stored, or utilized in any form or by any means, electronic or mechanical, including photocopying, or recording, or by any information storage and retrieval system, including internet websites, without prior written permission. Copyright 2005-2008 by Thads Bentulan [email protected] 08/24/09
    [Show full text]
  • The 7Th Workshop on MARKOV PROCESSES and RELATED TOPICS
    The 7th Workshop on MARKOV PROCESSES AND RELATED TOPICS July 19 - 23, 2010 No.6 Lecture room on 3th floor, Jingshi Building (京京京师师师大大大厦厦厦) Beijing Normal University Organizers: Mu-Fa Chen, Zeng-Hu Li, Feng-Yu Wang Supported by National Natural Science Foundation of China (No. 10721091) Probability Group, Stochastic Research Center School of Mathematical Sciences, Beijing Normal University No.19, Xinjiekouwai St., Beijing 100875, China Phone and Fax: 86-10-58809447 E-mail: [email protected] Website: http://math.bnu.edu.cn/probab/Workshop2010 Schedule 1 July 19 July 20 July 21 July 22 July 23 Chairman Mu-Fa Chen Fu-Zhou Gong Shui Feng Jie Xiong Dayue Chen Opening Shuenn-Jyi Sheu Anyue Chen Leonid Mytnik Zengjing Chen 8:30{8:40 8:30{9:00 8:30{9:00 8:30{9:00 8:30{9:00 M. Fukushima Feng-Yu Wang Jiashan Tang Quansheng Liu Dong Han 8:40{9:30 9:00{9:30 9:00{9:30 9:00{9:30 9:00{9:30 Speaker Tea Break Zhen-Qing Chen Renming Song Xia Chen Hao Wang Zongxia Liang 10:00{10:30 10:00{10:30 10:00{10:30 10:00{10:305 10:00{10:30 Panki Kim Christian Leonard Yutao Ma Xiaowen Zhou Fubao Xi 10:30{11:00 10:30{11:00 10:30{11:00 10:30{11:00 10:30{11:00 Jinghai Shao Xu Zhang Liang-Hui Xia Hui He Liqun Niu 11:00{11:30 11:00{11:20 11:00{11:20 11:00{11:20 11:00{11:20 Lunch Chairman Feng-Yu Wang Shizan Fang Zengjing Chen Zeng-Hu Li Chii-Ruey Hwang Tusheng Zhang Dayue Chen Shizan Fang 14:30{15:00 14:30{15:00 14:30{15:00 14:30{15:00 Ivan Gentil Xiang-Dong Li Alok Goswami Yimin Xiao 15:00{15:30 15:00{15:30 15:00{15:30 15:00{15:30 Speaker Tea Break Fu-Zhou Gong Jinwen
    [Show full text]
  • MCMC Learning (Slides)
    Uniform Distribution Learning Markov Random Fields Harmonic Analysis Experiments and Questions MCMC Learning Varun Kanade Elchanan Mossel UC Berkeley UC Berkeley August 30, 2013 Uniform Distribution Learning Markov Random Fields Harmonic Analysis Experiments and Questions Outline Uniform Distribution Learning Markov Random Fields Harmonic Analysis Experiments and Questions Uniform Distribution Learning Markov Random Fields Harmonic Analysis Experiments and Questions Uniform Distribution Learning • Unknown target function f : {−1; 1gn ! {−1; 1g from some class C • Uniform distribution over {−1; 1gn • Random Examples: Monotone Decision Trees [OS06] • Random Walk: DNF expressions [BMOS03] • Membership Query: DNF, TOP [J95] • Main Tool: Discrete Fourier Analysis X Y f (x) = f^(S)χS (x); χS (x) = xi S⊆[n] i2S • Can utilize sophisticated results: hypercontractivity, invariance, etc. • Connections to cryptography, hardness, de-randomization etc. • Unfortunately, too much of an idealization. In practice, variables are correlated. Uniform Distribution Learning Markov Random Fields Harmonic Analysis Experiments and Questions Markov Random Fields • Graph G = ([n]; E). Each node takes some value in finite set A. n • Distribution over A : (for φC non-negative, Z normalization constant) 1 Y Pr((σ ) ) = φ ((σ ) ) v v2[n] Z C v v2C clique C Uniform Distribution Learning Markov Random Fields Harmonic Analysis Experiments and Questions Markov Random Fields • MRFs widely used in vision, computational biology, biostatistics etc. • Extensive Algorithmic Theory for sampling from MRFs, recovering parameters and structures • Learning Question: Given f : An ! {−1; 1g. (How) Can we learn with respect to MRF distribution? • Can we utilize the structure of the MRF to aid in learning? Uniform Distribution Learning Markov Random Fields Harmonic Analysis Experiments and Questions Learning Model • Let M be a MRF with distribution π and f : An ! {−1; 1g the target function • Learning algorithm gets i.i.d.
    [Show full text]
  • Superpositions and Products of Ornstein-Uhlenbeck Type Processes: Intermittency and Multifractality
    Superpositions and Products of Ornstein-Uhlenbeck Type Processes: Intermittency and Multifractality Nikolai N. Leonenko School of Mathematics Cardiff University The second conference on Ambit Fields and Related Topics Aarhus August 15 Abstract Superpositions of stationary processes of Ornstein-Uhlenbeck (supOU) type have been introduced by Barndorff-Nielsen. We consider the constructions producing processes with long-range dependence and infinitely divisible marginal distributions. We consider additive functionals of supOU processes that satisfy the property referred to as intermittency. We investigate the properties of multifractal products of supOU processes. We present the general conditions for the Lq convergence of cumulative processes and investigate their q-th order moments and R´enyifunctions. These functions are nonlinear, hence displaying the multifractality of the processes. We also establish the corresponding scenarios for the limiting processes, such as log-normal, log-gamma, log-tempered stable or log-normal tempered stable scenarios. Acknowledgments Joint work with Denis Denisov, University of Manchester, UK Danijel Grahovac, University of Osijek, Croatia Alla Sikorskii, Michigan State University, USA Murad Taqqu, Boston University, USA OU type process I OU Type process is the unique strong solution of the SDE: dX (t) = −λX (t)dt + dZ(λt) where λ > 0, fZ(t)gt≥0 is a (non-decreasing, for this talk) L´eviprocess, and an initial condition X0 is taken to be independent of Z(t). Note, in general Zt doesn't have to be a non-decreasing L´evyprocess. I For properties of OU type processes and their generalizations see Mandrekar & Rudiger (2007), Barndorff-Nielsen (2001), Barndorff-Nielsen & Stelzer (2011). I The a.s.
    [Show full text]
  • Markov Random Fields: – Geman, Geman, “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images”, IEEE PAMI 6, No
    MarkovMarkov RandomRandom FieldsFields withwith ApplicationsApplications toto MM--repsreps ModelsModels Conglin Lu Medical Image Display and Analysis Group University of North Carolina, Chapel Hill MarkovMarkov RandomRandom FieldsFields withwith ApplicationsApplications toto MM--repsreps ModelsModels Outline: Background; Definition and properties of MRF; Computation; MRF m-reps models. MarkovMarkov RandomRandom FieldsFields Model a large collection of random variables with complex dependency relationships among them. MarkovMarkov RandomRandom FieldsFields • A model based approach; • Has been applied to a variety of problems: - Speech recognition - Natural language processing - Coding - Image analysis - Neural networks - Artificial intelligence • Usually used within the Bayesian framework. TheThe BayesianBayesian ParadigmParadigm X = space of the unknown variables, e.g. labels; Y = space of data (observations), e.g. intensity values; Given an observation y∈Y, want to make inference about x∈X. TheThe BayesianBayesian ParadigmParadigm Prior PX : probability distribution on X; Likelihood PY|X : conditional distribution of Y given X; Statistical inference is based on the posterior distribution PX|Y ∝ PX •PY|X . TheThe PriorPrior DistributionDistribution • Describes our assumption or knowledge about the model; • X is usually a high dimensional space. PX describes the joint distribution of a large number of random variables; • How do we define PX? MarkovMarkov RandomRandom FieldsFields withwith ApplicationsApplications toto MM--repsreps ModelsModels Outline: 9 Background; Definition and properties of MRF; Computation; MRF m-reps models. AssumptionsAssumptions •X = {Xs}s∈S, where each Xs is a random variable; S is an index set and is finite; • There is a common state space R:Xs∈R for all s ∈ S; | R | is finite; • Let Ω = {ω=(x , ..., x ): x ∈ , 1≤i≤N} be s1 sN si R the set of all possible configurations.
    [Show full text]
  • Anomaly Detection Based on Wavelet Domain GARCH Random Field Modeling Amir Noiboar and Israel Cohen, Senior Member, IEEE
    IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 45, NO. 5, MAY 2007 1361 Anomaly Detection Based on Wavelet Domain GARCH Random Field Modeling Amir Noiboar and Israel Cohen, Senior Member, IEEE Abstract—One-dimensional Generalized Autoregressive Con- Markov noise. It is also claimed that objects in imagery create a ditional Heteroscedasticity (GARCH) model is widely used for response over several scales in a multiresolution representation modeling financial time series. Extending the GARCH model to of an image, and therefore, the wavelet transform can serve as multiple dimensions yields a novel clutter model which is capable of taking into account important characteristics of a wavelet-based a means for computing a feature set for input to a detector. In multiscale feature space, namely heavy-tailed distributions and [17], a multiscale wavelet representation is utilized to capture innovations clustering as well as spatial and scale correlations. We periodical patterns of various period lengths, which often ap- show that the multidimensional GARCH model generalizes the pear in natural clutter images. In [12], the orientation and scale casual Gauss Markov random field (GMRF) model, and we de- selectivity of the wavelet transform are related to the biological velop a multiscale matched subspace detector (MSD) for detecting anomalies in GARCH clutter. Experimental results demonstrate mechanisms of the human visual system and are utilized to that by using a multiscale MSD under GARCH clutter modeling, enhance mammographic features. rather than GMRF clutter modeling, a reduced false-alarm rate Statistical models for clutter and anomalies are usually can be achieved without compromising the detection rate. related to the Gaussian distribution due to its mathematical Index Terms—Anomaly detection, Gaussian Markov tractability.
    [Show full text]
  • A Novel Approach for Markov Random Field with Intractable Normalising Constant on Large Lattices
    A novel approach for Markov Random Field with intractable normalising constant on large lattices W. Zhu ∗ and Y. Fany February 19, 2018 Abstract The pseudo likelihood method of Besag (1974), has remained a popular method for estimating Markov random field on a very large lattice, despite various documented deficiencies. This is partly because it remains the only computationally tractable method for large lattices. We introduce a novel method to estimate Markov random fields defined on a regular lattice. The method takes advantage of conditional independence structures and recur- sively decomposes a large lattice into smaller sublattices. An approximation is made at each decomposition. Doing so completely avoids the need to com- pute the troublesome normalising constant. The computational complexity arXiv:1601.02410v1 [stat.ME] 11 Jan 2016 is O(N), where N is the the number of pixels in lattice, making it computa- tionally attractive for very large lattices. We show through simulation, that the proposed method performs well, even when compared to the methods using exact likelihoods. Keywords: Markov random field, normalizing constant, conditional indepen- dence, decomposition, Potts model. ∗School of Mathematics and Statistics, University of New South Wales, Sydney 2052 Australia. Communicating Author Wanchuang Zhu: Email [email protected]. ySchool of Mathematics and Statistics, University of New South Wales, Sydney 2052 Australia. Email [email protected]. 1 1 Introduction Markov random field (MRF) models have an important role in modelling spa- tially correlated datasets. They have been used extensively in image and texture analyses ( Nott and Ryden´ 1999, Hurn et al. 2003), image segmentation (Pal and Pal 1993, Van Leemput et al.
    [Show full text]
  • Markov Random Fields and Stochastic Image Models
    Markov Random Fields and Stochastic Image Models Charles A. Bouman School of Electrical and Computer Engineering Purdue University Phone: (317) 494-0340 Fax: (317) 494-3358 email [email protected] Available from: http://dynamo.ecn.purdue.edu/»bouman/ Tutorial Presented at: 1995 IEEE International Conference on Image Processing 23-26 October 1995 Washington, D.C. Special thanks to: Ken Sauer Suhail Saquib Department of Electrical School of Electrical and Computer Engineering Engineering University of Notre Dame Purdue University 1 Overview of Topics 1. Introduction (b) Non-Gaussian MRF's 2. The Bayesian Approach i. Quadratic functions ii. Non-Convex functions 3. Discrete Models iii. Continuous MAP estimation (a) Markov Chains iv. Convex functions (b) Markov Random Fields (MRF) (c) Parameter Estimation (c) Simulation i. Estimation of σ (d) Parameter estimation ii. Estimation of T and p parameters 4. Application of MRF's to Segmentation 6. Application to Tomography (a) The Model (a) Tomographic system and data models (b) Bayesian Estimation (b) MAP Optimization (c) MAP Optimization (c) Parameter estimation (d) Parameter Estimation 7. Multiscale Stochastic Models (e) Other Approaches (a) Continuous models 5. Continuous Models (b) Discrete models (a) Gaussian Random Process Models 8. High Level Image Models i. Autoregressive (AR) models ii. Simultaneous AR (SAR) models iii. Gaussian MRF's iv. Generalization to 2-D 2 References in Statistical Image Modeling 1. Overview references [100, 89, 50, 54, 162, 4, 44] 4. Simulation and Stochastic Optimization Methods [118, 80, 129, 100, 68, 141, 61, 76, 62, 63] 2. Type of Random Field Model 5. Computational Methods used with MRF Models (a) Discrete Models i.
    [Show full text]
  • A Note on Probability Theory
    A Note on Probability Theory Ying Nian Wu, Note for STATS 200A Contents 1 Probability 3 1.1 Why probability? . .3 1.2 Three canonical examples . .4 1.3 Long run frequency . .4 1.4 Basic language and notation . .4 1.5 Axioms . .5 1.6 Sigma algebra . .5 1.7 Why sigma-algebra . .6 2 Measure 6 2.1 What is measure? . .6 2.2 Lebesgue measure . .7 2.3 Law of large number . .7 2.4 Concentration of measure . .8 2.5 Lebesgue integral . .9 2.6 Simple functions . 10 2.7 Convergence theorems . 10 3 Univariate distribution and expectation 11 3.1 Discrete random variable, expectation, long run average . 11 3.2 Continuous random variable, basic event, discretization . 12 3.3 How to think about density . 13 3.4 Existence of probability density function . 13 3.5 Cumulative density . 14 3.6 Uniform distribution . 14 3.7 Inversion method . 14 3.8 Transformation . 15 3.9 Polar method for normal random variable . 16 3.10 Counting techniques . 17 3.11 Bernoulli . 17 3.12 Binomial . 18 3.13 Normal approximation . 18 3.14 Geometric . 22 3.15 Poisson process . 22 3.16 Survival analysis . 24 1 4 Joint distribution and covariance 25 4.1 Joint distribution . 25 4.2 Expectation, variance, covariance . 26 4.3 Correlation as cosine of angle . 27 4.4 Correlation as the strength of regression . 28 4.5 Least squares derivation of regression . 28 4.6 Regression in terms of projections . 29 4.7 Independence and uncorrelated . 29 4.8 Multivariate statistics . 30 4.9 Multivariate normal .
    [Show full text]
  • A Review on Statistical Inference Methods for Discrete Markov Random Fields Julien Stoehr, Richard Everitt, Matthew T
    A review on statistical inference methods for discrete Markov random fields Julien Stoehr, Richard Everitt, Matthew T. Moores To cite this version: Julien Stoehr, Richard Everitt, Matthew T. Moores. A review on statistical inference methods for discrete Markov random fields. 2017. hal-01462078v2 HAL Id: hal-01462078 https://hal.archives-ouvertes.fr/hal-01462078v2 Preprint submitted on 11 Apr 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. A review on statistical inference methods for discrete Markov random fields Julien Stoehr1 1School of Mathematical Sciences & Insight Centre for Data Analytics, University College Dublin, Ireland Abstract Developing satisfactory methodology for the analysis of Markov random field is a very challenging task. Indeed, due to the Markovian dependence structure, the normalizing constant of the fields cannot be computed using standard analytical or numerical methods. This forms a central issue for any statistical approach as the likelihood is an integral part of the procedure. Furthermore, such unobserved fields cannot be integrated out and the likelihood evaluation becomes a doubly intractable problem. This report gives an overview of some of the methods used in the literature to analyse such observed or unobserved random fields.
    [Show full text]