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Statistical thinking: From Tukey to Vardi and beyond 统计思维:从土耳其到瓦尔第和其他地方
Ims Lecture Notes Monograph Series Pub Date : 2007-08-08 DOI: 10.1214/074921707000000210
L. Shepp
{"title":"Statistical thinking: From Tukey to Vardi and beyond","authors":"L. Shepp","doi":"10.1214/074921707000000210","DOIUrl":"https://doi.org/10.1214/074921707000000210","url":null,"abstract":"Data miners (minors?) and neural networkers tend to eschew modelling, misled perhaps by misinterpretation of strongly expressed views of John Tukey. I discuss Vardi's views of these issues as well as other aspects of Vardi's work in emision tomography and in sampling bias.","PeriodicalId":416422,"journal":{"name":"Ims Lecture Notes Monograph Series","volume":"286 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115422034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Spatial-temporal data mining procedure: LASR 时空数据挖掘程序:激光雷达
Ims Lecture Notes Monograph Series Pub Date : 2006-11-24 DOI: 10.1214/074921706000000707
Xiaofeng Wang, Jiayang Sun, K. Bogie
{"title":"Spatial-temporal data mining procedure: LASR","authors":"Xiaofeng Wang, Jiayang Sun, K. Bogie","doi":"10.1214/074921706000000707","DOIUrl":"https://doi.org/10.1214/074921706000000707","url":null,"abstract":"This paper is concerned with the statistical development of our spatial-temporal data mining procedure, LASR (pronounced \"laser\"). LASR is the abbreviation for Longitudinal Analysis with Self-Registration of large- p-small-n data. It was motivated by a study of \"Neuromuscular Electrical Stimulation\" experiments, where the data are noisy and heterogeneous, might not align from one session to another, and involve a large number of mul- tiple comparisons. The three main components of LASR are: (1) data seg- mentation for separating heterogeneous data and for distinguishing outliers, (2) automatic approaches for spatial and temporal data registration, and (3) statistical smoothing mapping for identifying \"activated\" regions based on false-discovery-rate controlled p-maps and movies. Each of the components is of interest in its own right. As a statistical ensemble, the idea of LASR is applicable to other types of spatial-temporal data sets beyond those from the NMES experiments.","PeriodicalId":416422,"journal":{"name":"Ims Lecture Notes Monograph Series","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132006887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Scale space consistency of piecewise constant least squares estimators - another look at the regressogram 分段常数最小二乘估计的尺度空间一致性-回归图的另一种看法
Ims Lecture Notes Monograph Series Pub Date : 2006-09-13 DOI: 10.1214/074921707000000274
L. Boysen, V. Liebscher, A. Munk, O. Wittich
{"title":"Scale space consistency of piecewise constant least squares estimators - another look at the regressogram","authors":"L. Boysen, V. Liebscher, A. Munk, O. Wittich","doi":"10.1214/074921707000000274","DOIUrl":"https://doi.org/10.1214/074921707000000274","url":null,"abstract":"We study the asymptotic behavior of piecewise constant least squares regression estimates, when the number of partitions of the estimate is penalized. We show that the estimator is consistent in the relevant metric if the signal is in L 2 ((0,1)), the space of cadlag functions equipped with the Skorokhod metric or C((0,1)) equipped with the supremum metric. Moreover, we consider the family of estimates under a varying smoothing parameter, also called scale space. We prove convergence of the empirical scale space towards its deterministic target.","PeriodicalId":416422,"journal":{"name":"Ims Lecture Notes Monograph Series","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124817442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 20
Markovianity in space and time 空间和时间的马尔可夫性
Ims Lecture Notes Monograph Series Pub Date : 2006-08-10 DOI: 10.1214/074921706000000185
V. Lieshout
{"title":"Markovianity in space and time","authors":"V. Lieshout","doi":"10.1214/074921706000000185","DOIUrl":"https://doi.org/10.1214/074921706000000185","url":null,"abstract":"Markov chains in time, such as simple random walks, are at the heart of probability. In space, due to the absence of an obvious definition of past and future, a range of definitions of Markovianity have been proposed. In this paper, after a brief review, we introduce a new concept of Markovianity that aims to combine spatial and temporal conditional independence. 1. From Markov chain to Markov point process, and beyond This paper is devoted to the fundamental concept of Markovianity. Although its precise definition depends on the context, common ingredients are conditional in- dependence and factorisation formulae that allow to break up complex, or high dimensional, probabilities into manageable, lower dimensional components. Thus, computations can be greatly simplified, sometimes to the point that a detailed probabilistic analysis is possible. If that cannot be done, feasible, efficient simula- tion algorithms that exploit the relatively simple building blocks may usually be designed instead.","PeriodicalId":416422,"journal":{"name":"Ims Lecture Notes Monograph Series","volume":"216 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133257469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 25
Proof of a conjecture of N. Konno for the 1D contact process 一维接触过程N. Konno猜想的证明
Ims Lecture Notes Monograph Series Pub Date : 2006-08-09 DOI: 10.1214/074921706000000031
J. Berg, O. Haggstrom, J. Kahn
{"title":"Proof of a conjecture of N. Konno for the 1D contact process","authors":"J. Berg, O. Haggstrom, J. Kahn","doi":"10.1214/074921706000000031","DOIUrl":"https://doi.org/10.1214/074921706000000031","url":null,"abstract":"Consider the one-dimensional contact process. About ten years ago, N. Konno stated the conjecture that, for all positive integers $n,m$, the upper invariant measure has the following property: Conditioned on the event that $O$ is infected, the events ${$All sites $-n,...,-1$ are healthy$}$ and ${$All sites $1,...,m$ are healthy$}$ are negatively correlated. We prove (a stronger version of) this conjecture, and explain that in some sense it is a dual version of the planar case of one of our results in citeBHK.","PeriodicalId":416422,"journal":{"name":"Ims Lecture Notes Monograph Series","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124973910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Linearly edge-reinforced random walks 线性边增强随机漫步
Ims Lecture Notes Monograph Series Pub Date : 2006-08-01 DOI: 10.1214/074921706000000103
F. Merkl, S. Rolles
{"title":"Linearly edge-reinforced random walks","authors":"F. Merkl, S. Rolles","doi":"10.1214/074921706000000103","DOIUrl":"https://doi.org/10.1214/074921706000000103","url":null,"abstract":"We review results on linearly edge-reinforced random walks. On finite graphs, the process has the same distribution as a mixture of reversible Markov chains. This has applications in Bayesian statistics and it has been used in studying the random walk on infinite graphs. On trees, one has a representation as a random walk in an independent random environment. We review recent results for the random walk on ladders: recurrence, a representation as a random walk in a random environment, and estimates for the position of the random walker.","PeriodicalId":416422,"journal":{"name":"Ims Lecture Notes Monograph Series","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126927111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 29
Localization and decay of correlations for a pinned lattice free field in dimension two 二维固定晶格自由场的局域化和相关衰减
Ims Lecture Notes Monograph Series Pub Date : 1900-01-01 DOI: 10.1214/LNMS/1215090066
E. Bolthausen, D. Brydges
{"title":"Localization and decay of correlations for a pinned lattice free field in dimension two","authors":"E. Bolthausen, D. Brydges","doi":"10.1214/LNMS/1215090066","DOIUrl":"https://doi.org/10.1214/LNMS/1215090066","url":null,"abstract":"We prove that the two-dimensional harmonic crystal with a weak local pinning to a wall has finite variance and exponentially decaying correlations, regardless how weak the pinning is. The proof is based on an improved pressure estimate and an application of reflection positivity.","PeriodicalId":416422,"journal":{"name":"Ims Lecture Notes Monograph Series","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124550815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 15
From A to Z: asymptotic expansions by van Zwet 从A到Z: van Zwet渐近展开式
Ims Lecture Notes Monograph Series Pub Date : 1900-01-01 DOI: 10.1214/LNMS/1215090060
W. Albers
{"title":"From A to Z: asymptotic expansions by van Zwet","authors":"W. Albers","doi":"10.1214/LNMS/1215090060","DOIUrl":"https://doi.org/10.1214/LNMS/1215090060","url":null,"abstract":"Refinements of first order asymptotic results are reviewed, with a number of Ph.D. projects supervised by van Zwet serving as stepping stones. Berry-Esseen bounds and Edgeworth expansions are discussed for R-, L- and U-statistics. After these special classes, the question about a general second order theory for asymptotically normal statistics is addressed. As a final topic, empirical Edgeworth expansions are considered","PeriodicalId":416422,"journal":{"name":"Ims Lecture Notes Monograph Series","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133430451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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