Relevant bibliographies by topics / Geometric statistics

Academic literature on the topic 'Geometric statistics'

Author: Grafiati
Published: 22 June 2024

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Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Journal articles on the topic "Geometric statistics":

1

Berry, M. V., and Pragya Shukla. "Geometric Phase Curvature Statistics." Journal of Statistical Physics 180, no. 1-6 (October 9, 2019): 297–303. http://dx.doi.org/10.1007/s10955-019-02400-6.

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Constantin, Peter. "Geometric Statistics in Turbulence." SIAM Review 36, no. 1 (March 1994): 73–98. http://dx.doi.org/10.1137/1036004.

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Drew, Donald A. "Evolution of Geometric Statistics." SIAM Journal on Applied Mathematics 50, no. 3 (June 1990): 649–66. http://dx.doi.org/10.1137/0150038.

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Grady, D. E., and M. E. Kipp. "Geometric statistics and dynamic fragmentation." Journal of Applied Physics 58, no. 3 (August 1985): 1210–22. http://dx.doi.org/10.1063/1.336139.

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Timonin, P. N. "Statistics of geometric clusters in Potts model: statistical mechanics approach." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2240 (August 2020): 20200215. http://dx.doi.org/10.1098/rspa.2020.0215.

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The percolation of Potts spins with equal values in Potts model on graphs (networks) is considered. The general method for finding the Potts clusters' size distributions is developed. It allows full description of percolation transition when a giant cluster of equal-valued Potts spins appears. The method is applied to the short-ranged q-state ferromagnetic Potts model on the Bethe lattices with the arbitrary coordination number z . The analytical results for the field-temperature percolation phase diagram of geometric spin clusters and their size distribution are obtained. The last appears to be proportional to that of the classical non-correlated bond percolation with the bond probability, which depends on temperature and Potts model parameters.
6

Trofimov, V. K. "Encoding geometric sources with unknown statistics." Herald of the Siberian State University of Telecommunications and Informatics, no. 2 (June 18, 2021): 79–87. http://dx.doi.org/10.55648/1998-6920-2021-15-2-79-87.

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Universal encoding method of an arbitrary set of sources without memory generating letters of an infinite alphabet is proposed. The probabilities of the input alphabet letter appearance are a geometric progression. The proposed method is weakly universal for the set of all geometric sources. If the denominator of the geometric progression exceeds δ, δ > 0, the proposed encoding is universal. Redundancy estimates are obtained for an arbitrary subset of geometric sources.
7

Anevski, Dragi, Christopher Genovese, Geurt Jongbloed, and Wolfgang Polonik. "Statistics for Shape and Geometric Features." Oberwolfach Reports 13, no. 3 (2016): 1821–74. http://dx.doi.org/10.4171/owr/2016/32.

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Feragen, Aasa, Thomas Hotz, Stephan Huckemann, and Ezra Miller. "Statistics for Data with Geometric Structure." Oberwolfach Reports 15, no. 1 (January 4, 2019): 125–86. http://dx.doi.org/10.4171/owr/2018/3.

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9

ANASTOPOULOS, CHARIS. "SPIN-STATISTICS THEOREM AND GEOMETRIC QUANTIZATION." International Journal of Modern Physics A 19, no. 05 (February 20, 2004): 655–76. http://dx.doi.org/10.1142/s0217751x04017860.

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We study the relation of the spin-statistics theorem to the geometric structures on phase space, which are introduced in quantization procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the nonrelativistic domain (in fact for any symmetry group including internal symmetries) by requiring that the exchange can be implemented smoothly by a class of symmetry transformations that project in the phase space of the joint system system. We discuss the interpretation of this requirement, stressing the fact that any distinction of identical particles comes solely from the choice of coordinates — the exchange then arises from suitable change of coordinate system. We then examine our construction in the geometric and the coherent-state-path-integral quantization schemes. In the appendix we apply our results to exotic systems exhibiting continuous "spin" and "fractional statistics." This gives novel and unusual forms of the spin-statistics relation.
10

Dettmann, C. P., O. Georgiou, and G. Knight. "Spectral statistics of random geometric graphs." EPL (Europhysics Letters) 118, no. 1 (April 1, 2017): 18003. http://dx.doi.org/10.1209/0295-5075/118/18003.

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Journal articles Dissertations / Theses Books

Dissertations / Theses on the topic "Geometric statistics":

1

Saive, Yannick. "DirCNN: Rotation Invariant Geometric Deep Learning." Thesis, KTH, Matematisk statistik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-252573.

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Recently geometric deep learning introduced a new way for machine learning algorithms to tackle point cloud data in its raw form. Pioneers like PointNet and many architectures building on top of its success realize the importance of invariance to initial data transformations. These include shifting, scaling and rotating the point cloud in 3D space. Similarly to our desire for image classifying machine learning models to classify an upside down dog as a dog, we wish geometric deep learning models to succeed on transformed data. As such, many models employ an initial data transform in their models which is learned as part of a neural network, to transform the point cloud into a global canonical space. I see weaknesses in this approach as they are not guaranteed to perform completely invariant to input data transformations, but rather approximately. To combat this I propose to use local deterministic transformations which do not need to be learned. The novelty layer of this project builds upon Edge Convolutions and is thus dubbed DirEdgeConv, with the directional invariance in mind. This layer is slightly altered to introduce another layer by the name of DirSplineConv. These layers are assembled in a variety of models which are then benchmarked against the same tasks as its predecessor to invite a fair comparison. The results are not quite as good as state of the art results, however are still respectable. It is also my belief that the results can be improved by improving the learning rate and its scheduling. Another experiment in which ablation is performed on the novel layers shows that the layers  main concept indeed improves the overall results.
Nyligen har ämnet geometrisk deep learning presenterat ett nytt sätt för maskininlärningsalgoritmer att arbeta med punktmolnsdata i dess råa form.Banbrytande arkitekturer som PointNet och många andra som byggt på dennes framgång framhåller vikten av invarians under inledande datatransformationer. Sådana transformationer inkluderar skiftning, skalning och rotation av punktmoln i ett tredimensionellt rum. Precis som vi önskar att klassifierande maskininlärningsalgoritmer lyckas identifiera en uppochnedvänd hund som en hund vill vi att våra geometriska deep learning-modeller framgångsrikt ska kunna hantera transformerade punktmoln. Därför använder många modeller en inledande datatransformation som tränas som en del av ett neuralt nätverk för att transformera punktmoln till ett globalt kanoniskt rum. Jag ser tillkortakommanden i detta tillgångavägssätt eftersom invariansen är inte fullständigt garanterad, den är snarare approximativ. För att motverka detta föreslår jag en lokal deterministisk transformation som inte måste läras från datan. Det nya lagret i det här projektet bygger på Edge Convolutions och döps därför till DirEdgeConv, namnet tar den riktningsmässiga invariansen i åtanke. Lagret ändras en aning för att introducera ett nytt lager vid namn DirSplineConv. Dessa lager sätts ihop i olika modeller som sedan jämförs med sina efterföljare på samma uppgifter för att ge en rättvis grund för att jämföra dem. Resultaten är inte lika bra som toppmoderna resultat men de är ändå tillfredsställande. Jag tror även resultaten kan förbättas genom att förbättra inlärningshastigheten och dess schemaläggning. I ett experiment där ablation genomförs på de nya lagren ser vi att lagrens huvudkoncept förbättrar resultaten överlag.
2

Ho, Pak-kei. "Parametric and non-parametric inference for Geometric Process." Click to view the E-thesis via HKUTO, 2005. http://sunzi.lib.hku.hk/hkuto/record/B31483859.

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Ho, Pak-kei, and 何柏基. "Parametric and non-parametric inference for Geometric Process." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B31483859.

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4

Keil, Mitchel J. "Automatic generation of interference-free geometric models of spatial mechanisms." Diss., This resource online, 1990. http://scholar.lib.vt.edu/theses/available/etd-08252008-162631/.

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5

Suttmiller, Alexander Gage. "Streamline Feature Detection: Geometric and Statistical Evaluation of Streamline Properties." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1315967677.

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Saha, Abhijoy. "A Geometric Framework for Modeling and Inference using the Nonparametric Fisher–Rao metric." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1562679374833421.

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7

Chu, Chi-Yang. "Applied Nonparametric Density and Regression Estimation with Discrete Data| Plug-In Bandwidth Selection and Non-Geometric Kernel Functions." Thesis, The University of Alabama, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10262364.

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Bandwidth selection plays an important role in kernel density estimation. Least-squares cross-validation and plug-in methods are commonly used as bandwidth selectors for the continuous data setting. The former is a data-driven approach and the latter requires a priori assumptions about the unknown distribution of the data. A benefit from the plug-in method is its relatively quick computation and hence it is often used for preliminary analysis. However, we find that much less is known about the plug-in method in the discrete data setting and this motivates us to propose a plug-in bandwidth selector. A related issue is undersmoothing in kernel density estimation. Least-squares cross-validation is a popular bandwidth selector, but in many applied situations, it tends to select a relatively small bandwidth, or undersmooths. The literature suggests several methods to solve this problem, but most of them are the modifications of extant error criterions for continuous variables. Here we discuss this problem in the discrete data setting and propose non-geometric discrete kernel functions as a possible solution. This issue also occurs in kernel regression estimation. Our proposed bandwidth selector and kernel functions perform well in simulated and real data.

8

Carriere, Mathieu. "On Metric and Statistical Properties of Topological Descriptors for geometric Data." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS433/document.

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Dans le cadre de l'apprentissage automatique, l'utilisation de représentations alternatives, ou descripteurs, pour les données est un problème fondamental permettant d'améliorer sensiblement les résultats des algorithmes. Parmi eux, les descripteurs topologiques calculent et encodent l'information de nature topologique contenue dans les données géométriques. Ils ont pour avantage de bénéficier de nombreuses bonnes propriétés issues de la topologie, et désirables en pratique, comme par exemple leur invariance aux déformations continues des données. En revanche, la structure et les opérations nécessaires à de nombreuses méthodes d'apprentissage, comme les moyennes ou les produits scalaires, sont souvent absents de l'espace de ces descripteurs. Dans cette thèse, nous étudions en détail les propriétés métriques et statistiques des descripteurs topologiques les plus fréquents, à savoir les diagrammes de persistance et Mapper. En particulier, nous montrons que le Mapper, qui est empiriquement un descripteur instable, peut être stabilisé avec une métrique appropriée, que l'on utilise ensuite pour calculer des régions de confiance et pour régler automatiquement ses paramètres. En ce qui concerne les diagrammes de persistance, nous montrons que des produits scalaires peuvent être utilisés via des méthodes à noyaux, en définissant deux noyaux, ou plongements, dans des espaces de Hilbert en dimension finie et infinie
In the context of supervised Machine Learning, finding alternate representations, or descriptors, for data is of primary interest since it can greatly enhance the performance of algorithms. Among them, topological descriptors focus on and encode the topological information contained in geometric data. One advantage of using these descriptors is that they enjoy many good and desireable properties, due to their topological nature. For instance, they are invariant to continuous deformations of data. However, the main drawback of these descriptors is that they often lack the structure and operations required by most Machine Learning algorithms, such as a means or scalar products. In this thesis, we study the metric and statistical properties of the most common topological descriptors, the persistence diagrams and the Mappers. In particular, we show that the Mapper, which is empirically instable, can be stabilized with an appropriate metric, that we use later on to conpute confidence regions and automatic tuning of its parameters. Concerning persistence diagrams, we show that scalar products can be defined with kernel methods by defining two kernels, or embeddings, into finite and infinite dimensional Hilbert spaces
9

Pedersen, Morten Akhøj. "Méthodes riemanniennes et sous-riemanniennes pour la réduction de dimension." Electronic Thesis or Diss., Université Côte d'Azur, 2023. http://www.theses.fr/2023COAZ4087.

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Nous proposons dans cette thèse de nouvelles méthodes de réduction de dimension fondées sur la géométrie différentielle. Il s'agit de trouver une représentation d'un ensemble d'observations dans un espace de dimension inférieure à l'espace d'origine des données. Les méthodes de réduction de dimension constituent la pierre angulaire des statistiques et ont donc un très large éventail d'applications. Dans les statistiques euclidiennes ordinaires, les données appartiennent à un espace vectoriel et l'espace de dimension inférieure peut être un sous-espace linéaire ou une sous-variété non linéaire approximant les observations. L'étude de telles variétés lisses, la géométrie différentielle, joue naturellement un rôle important dans ce dernier cas. Lorsque l'espace des données est lui-même une variété, l'espace approximant de dimension réduite est naturellement une sous-variété de la variété initiale. Les méthodes d'analyse de ce type de données relèvent du domaine des statistiques géométriques. Les statistiques géométriques pour des observations appartenant à une variété riemannienne sont le point de départ de cette thèse, mais une partie de notre travail apporte une contribution même dans le cas de données appartenant à l'espace euclidien, mathbb{R}^d.Les formes, dans notre cas des courbes ou des surfaces discrètes ou continues, sont un exemple important de données à valeurs dans les variétés. En biologie évolutive, les chercheurs s'intéressent aux raisons et aux implications des différences morphologiques entre les espèces. Cette application motive la première contribution principale de la thèse. Nous généralisons une méthode de réduction de dimension utilisée en biologie évolutive, l'analyse en composantes principales phylogénétiques (P-PCA), pour travailler sur des données à valeur dans une variété riemannienne - afin qu'elle puisse être appliquée à des données de forme. P-PCA est une version de PCA pour des observations qui sont les feuilles d'un arbre phylogénétique. D'un point de vue statistique, la propriété importante de ces données est que les observations ne sont pas indépendantes. Nous définissons et estimons des moyennes et des covariances intrinsèquement pondérées sur une variété qui prennent en compte cette dépendance des observations. Nous définissons ensuite l'ACP phylogénétique sur une variété comme la décomposition propre de la covariance pondérée dans l'espace tangent de la moyenne pondérée. Nous montrons que l'estimateur de moyenne actuellement utilisé en biologie évolutive pour étudier la morphologie correspond à ne prendre qu'une seule étape de notre algorithme de descente de gradient riemannien pour la moyenne intrinsèque, lorsque les observations sont représentées dans l'espace des formes de Kendall.Notre deuxième contribution principale est une méthode non paramétrique de réduction de dimension fondée sur une classe très flexible de sous-variétés qui est novatrice même dans le cas de données euclidiennes. Grâce à une PCA locale, nous construisons tout d'abord un sous-fibré du fibré tangent sur la variété des données que nous appelons le sous-fibré principal. Cette distribution (au sens géométrique) induit une structure sous riemannienne. Nous montrons que les géodésiques sous-riemanniennes correspondantes restent proches de l'ensemble des observations et que l'ensemble des géodésiques partant d'un point donné génèrent localement une sous-variété qui est radialement alignée avec le sous-fibré principal, même lorsqu'il est non intégrables, ce qui apparait lorsque les données sont bruitées. Notre méthode démontre que la géométrie sous-riemannienne est le cadre naturel pour traiter de tels problèmes. Des expériences numériques illustrent la puissance de notre cadre en montrant que nous pouvons réaliser des reconstructions d'une extension importante, même en présence de niveaux de bruit assez élevés
In this thesis, we propose new methods for dimension reduction based on differential geometry, that is, finding a representation of a set of observations in a space of lower dimension than the original data space. Methods for dimension reduction form a cornerstone of statistics, and thus have a very wide range of applications. For instance, a lower dimensional representation of a data set allows visualization and is often necessary for subsequent statistical analyses. In ordinary Euclidean statistics, the data belong to a vector space and the lower dimensional space might be a linear subspace or a non-linear submanifold approximating the observations. The study of such smooth manifolds, differential geometry, naturally plays an important role in this last case, or when the data space is itself a known manifold. Methods for analysing this type of data form the field of geometric statistics. In this setting, the approximating space found by dimension reduction is naturally a submanifold of the given manifold. The starting point of this thesis is geometric statistics for observations belonging to a known Riemannian manifold, but parts of our work form a contribution even in the case of data belonging to Euclidean space, mathbb{R}^d.An important example of manifold valued data is shapes, in our case discrete or continuous curves or surfaces. In evolutionary biology, researchers are interested in studying reasons for and implications of morphological differences between species. Shape is one way to formalize morphology. This application motivates the first main contribution of the thesis. We generalize a dimension reduction method used in evolutionary biology, phylogenetic principal component analysis (P-PCA), to work for data on a Riemannian manifold - so that it can be applied to shape data. P-PCA is a version of PCA for observations that are assumed to be leaf nodes of a phylogenetic tree. From a statistical point of view, the important property of such data is that the observations (leaf node values) are not necessarily independent. We define and estimate intrinsic weighted means and covariances on a manifold which takes the dependency of the observations into account. We then define phylogenetic PCA on a manifold to be the eigendecomposition of the weighted covariance in the tangent space of the weighted mean. We show that the mean estimator that is currently used in evolutionary biology for studying morphology corresponds to taking only a single step of our Riemannian gradient descent algorithm for the intrinsic mean, when the observations are represented in Kendall's shape space. Our second main contribution is a non-parametric method for dimension reduction that can be used for approximating a set of observations based on a very flexible class of submanifolds. This method is novel even in the case of Euclidean data. The method works by constructing a subbundle of the tangent bundle on the data manifold via local PCA. We call this subbundle the principal subbundle. We then observe that this subbundle induces a sub-Riemannian structure and we show that the resulting sub-Riemannian geodesics with respect to this structure stay close to the set of observations. Moreover, we show that sub-Riemannian geodesics starting from a given point locally generate a submanifold which is radially aligned with the estimated subbundle, even for non-integrable subbundles. Non-integrability is likely to occur when the subbundle is estimated from noisy data, and our method demonstrates that sub-Riemannian geometry is a natural framework for dealing which such problems. Numerical experiments illustrate the power of our framework by showing that we can achieve impressively large range reconstructions even in the presence of quite high levels of noise
I denne afhandling præsenteres nye metoder til dimensionsreduktion, baseret p˚adifferential geometri. Det vil sige metoder til at finde en repræsentation af et datasæti et rum af lavere dimension end det opringelige rum. S˚adanne metoder spiller enhelt central rolle i statistik, og har et meget bredt anvendelsesomr˚ade. En laveredimensionalrepræsentation af et datasæt tillader visualisering og er ofte nødvendigtfor efterfølgende statistisk analyse. I traditionel, Euklidisk statistik ligger observationernei et vektor rum, og det lavere-dimensionale rum kan være et lineært underrumeller en ikke-lineær undermangfoldighed som approksimerer observationerne.Studiet af s˚adanne glatte mangfoldigheder, differential geometri, spiller en vigtig rollei sidstnævnte tilfælde, eller hvis rummet hvori observationerne ligger i sig selv er enmangfoldighed. Metoder til at analysere observationer p˚a en mangfoldighed udgørfeltet geometrisk statistik. I denne kontekst er det approksimerende rum, fundetvia dimensionsreduktion, naturligt en submangfoldighed af den givne mangfoldighed.Udgangspunktet for denne afhandling er geometrisk statistik for observationer p˚a ena priori kendt Riemannsk mangfoldighed, men dele af vores arbejde udgør et bidragselv i tilfældet med observationer i Euklidisk rum, Rd.Et vigtigt eksempel p˚a data p˚a en mangfoldighed er former, i vores tilfældediskrete kurver eller overflader. I evolutionsbiologi er forskere interesseret i at studeregrunde til og implikationer af morfologiske forskelle mellem arter. Former er ´en m˚adeat formalisere morfologi p˚a. Denne anvendelse motiverer det første hovedbidrag idenne afhandling. We generaliserer en metode til dimensionsreduktion brugt i evolutionsbiologi,phylogenetisk principal component analysis (P-PCA), til at virke for datap˚a en Riemannsk mangfoldighed - s˚a den kan anvendes til observationer af former. PPCAer en version af PCA for observationer som antages at være de yderste knuder iet phylogenetisk træ. Fra et statistisk synspunkt er den vigtige egenskab ved s˚adanneobservationer at de ikke nødvendigvis er uafhængige. We definerer og estimerer intrinsiskevægtede middelværdier og kovarianser p˚a en mangfoldighed, som tager højde fors˚adanne observationers afhængighed. Vi definerer derefter phylogenetisk PCA p˚a enmangfoldighed som egendekomposition af den vægtede kovarians i tanget-rummet tilden vægtede middelværdi. Vi viser at estimatoren af middelværdien som pt. bruges ievolutionsbiologi til at studere morfologi svarer til at tage kun et enkelt skridt af voresRiemannske gradient descent algoritme for den intrinsiske middelværdi, n˚ar formernerepræsenteres i Kendall´s form-mangfoldighed.Vores andet hovedbidrag er en ikke-parametrisk metode til dimensionsreduktionsom kan bruges til at approksimere et data sæt baseret p˚a en meget flexibel klasse afsubmangfoldigheder. Denne metode er ny ogs˚a i tilfældet med Euklidisk data. Metodenvirker ved at konstruere et under-bundt af tangentbundet p˚a datamangfoldighedenM via lokale PCA´er. Vi kalder dette underbundt principal underbundtet. Viobserverer at dette underbundt inducerer en sub-Riemannsk struktur p˚a M og vi viserat sub-Riemannske geodæter fra et givent punkt lokalt genererer en submangfoldighedsom radialt flugter med det estimerede subbundt, selv for ikke-integrable subbundter.Ved støjfyldt data forekommer ikke-integrabilitet med stor sandsynlighed, og voresmetode demonstrerer at sub-Riemannsk geometri er en naturlig tilgang til at h˚andteredette. Numeriske eksperimenter illustrerer styrkerne ved metoden ved at vise at denopn˚ar rekonstruktioner over store afstande, selv under høje niveauer af støj
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Neeser, Rudolph. "A Comparison of Statistical and Geometric Reconstruction Techniques: Guidelines for Correcting Fossil Hominin Crania." Thesis, University of Cape Town, 2007. http://pubs.cs.uct.ac.za/archive/00000413/.

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The study of human evolution centres, to a large extent, around the study of fossil morphology, including the comparison and interpretation of these remains within the context of what is known about morphological variation within living species. However, many fossils suffer from environmentally caused damage (taphonomic distortion) which hinders any such interpretation: fossil material may be broken and fragmented while the weight and motion of overlaying sediments can cause their plastic distortion. To date, a number of studies have focused on the reconstruction of such taphonomically damaged specimens. These studies have used myriad approaches to reconstruction, including thin plate spline methods, mirroring, and regression-based approaches. The efficacy of these techniques remains to be demonstrated, and it is not clear how different parameters (e.g., sample sizes, landmark density, etc.) might effect their accuracy. In order to partly address this issue, this thesis examines three techniques used in the virtual reconstruction of fossil remains by statistical or geometrical means: mean substitution, thin plate spline warping (TPS), and multiple linear regression. These methods are compared by reconstructing the same sample of individuals using each technique. Samples drawn from Homo sapiens, Pan troglodytes, Gorilla gorilla, and various hominin fossils are reconstructed by iteratively removing then estimating the landmarks. The testing determines the methods' behaviour in relation to the extant of landmark loss (i.e., amount of damage), reference sample sizes (this being the data used to guide the reconstructions), and the species of the population from which the reference samples are drawn (which may be different to the species of the damaged fossil). Given a large enough reference sample, the regression-based method is shown to produce the most accurate reconstructions. Various parameters effect this: when using small reference samples drawn from a population of the same species as the damaged specimen, thin plate splines is the better method, but only as long as there is little damage. As the damage becomes severe (missing 30% of the landmarks, or more), mean substitution should be used instead: thin plate splines are shown to have a rapid error growth in relation to the amount of damage. When the species of the damaged specimen is unknown, or it is the only known individual of its species, the smallest reconstruction errors are obtained with a regression-based approach using a large reference sample drawn from a living species. Testing shows that reference sample size (combined with the use of multiple linear regression) is more important than morphological similarity between the reference individuals and the damaged specimen. The main contribution of this work are recommendations to the researcher on which of the three methods to use, based on the amount of damage, number of reference individuals, and species of the reference individuals.
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Books on the topic "Geometric statistics":

1

Gibilisco, Paolo, Eva Riccomagno, Maria Piera Rogantin, and Henry P. Wynn, eds. Algebraic and Geometric Methods in Statistics. Cambridge: Cambridge University Press, 2009. http://dx.doi.org/10.1017/cbo9780511642401.

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Calin, Ovidiu, and Constantin Udrişte. Geometric Modeling in Probability and Statistics. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-07779-6.

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Gibilisco, Paolo. Algebraic and geometric methods in statistics. Cambridge: Cambridge University Press, 2010.

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Roux, Brigitte Le. Combinatorial Inference in Geometric Data Analysis. Boca Raton, Florida, USA: Chapman and Hall/CRC, Taylor & Francis Group, 2019.

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Kiêu, Kiên. Three lectures on systematic geometric sampling. Aarhus [Denmark]: Dept. of Theoretical Statistics, 1997.

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V, Buldygin V., and Kharazishvili A. B, eds. Geometric aspects of probability theory and mathematical statistics. Dordrecht: Kluwer Academic, 2000.

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Buldygin, V. V., and A. B. Kharazishvili. Geometric Aspects of Probability Theory and Mathematical Statistics. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-017-1687-1.

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NATO Advanced Study on Propagation of Correlations in Constrained Systems (1990 Cargèse, France). Correlations and connectivity: Geometric aspects of physics, chemistry, and biology. Dordrecht: Kluwer Academic Publishers, 1990.

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Kanatani, Kenʼichi. Statistical optimization for geometric computation: Theory and practice. Amsterdam: Elsevier, 1996.

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Fang, Kʻai-tʻai. Number-theoretic methods in statistics. London: Chapman & Hall, 1994.

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Book chapters on the topic "Geometric statistics":

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Marshall, Albert W., Ingram Olkin, and Barry C. Arnold. "Geometric Inequalities." In Springer Series in Statistics, 269–96. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-0-387-68276-1_8.

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Kühnel, Line, Tom Fletcher, Sarang Joshi, and Stefan Sommer. "Latent Space Geometric Statistics." In Pattern Recognition. ICPR International Workshops and Challenges, 163–78. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-68780-9_16.

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Saville, David J., and Graham R. Wood. "The Geometric Tool Kit." In Springer Texts in Statistics, 10–38. New York, NY: Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4612-0971-3_2.

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Dorst, Leo, and Steven De Keninck. "Physical Geometry by Plane-Based Geometric Algebra." In Springer Proceedings in Mathematics & Statistics, 43–76. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-55985-3_2.

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Leung, Kit-Nam. "Arithmetic and Geometric Processes." In Springer Handbook of Engineering Statistics, 931–55. London: Springer London, 2006. http://dx.doi.org/10.1007/978-1-84628-288-1_49.

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Hitzer, Eckhard, and Dietmar Hildenbrand. "Introduction to Geometric Algebra." In Springer Proceedings in Mathematics & Statistics, 1–41. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-55985-3_1.

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Scheaffer, Richard L., Ann Watkins, Mrudulla Gnanadesikan, and Jeffrey A. Witmer. "Waiting for Reggie Jackson: The Geometric Distribution." In Activity-Based Statistics, 79–81. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4757-3843-8_17.

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Chang, Ted. "Tangent Space Approximation in Geometric Statistics." In Springer Handbook of Engineering Statistics, 1059–73. London: Springer London, 2023. http://dx.doi.org/10.1007/978-1-4471-7503-2_53.

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Kosambi, D. D. "The Geometric Method in Mathematical Statistics." In D.D. Kosambi, 131–39. New Delhi: Springer India, 2016. http://dx.doi.org/10.1007/978-81-322-3676-4_17.

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Abramov, Viktor, and Jaan Vajakas. "Geometric Approach to Ghost Fields." In Springer Proceedings in Mathematics & Statistics, 475–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-55361-5_27.

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Conference papers on the topic "Geometric statistics":

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CAI, JUN, and JOSÉ GARRIDO. "ASYMPTOTIC FORMS AND BOUNDS FOR TAILS OF CONVOLUTIONS OF COMPOUND GEOMETRIC DISTRIBUTIONS, WITH APPLICATIONS." In Proceedings of Statistics 2001 Canada: The 4th Conference in Applied Statistics. PUBLISHED BY IMPERIAL COLLEGE PRESS AND DISTRIBUTED BY WORLD SCIENTIFIC PUBLISHING CO., 2002. http://dx.doi.org/10.1142/9781860949531_0010.

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Sudsuk, Areeya, and Winai Bodhisuwan. "The Topp-Leone geometric distribution." In 2016 12th International Conference on Mathematics, Statistics, and Their Application (ICMSA). IEEE, 2016. http://dx.doi.org/10.1109/icmsa.2016.7954319.

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Li, Lee Siaw, and Maman A. Djauhari. "Monitoring autocorrelated process: A geometric Brownian motion process approach." In INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND STATISTICS 2013 (ICMSS2013): Proceedings of the International Conference on Mathematical Sciences and Statistics 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4823976.

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Sagadavan, Revathi, and Maman A. Djauhari. "Autocorrelated multivariate process control: A geometric Brownian motion approach." In INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND STATISTICS 2013 (ICMSS2013): Proceedings of the International Conference on Mathematical Sciences and Statistics 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4823979.

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Lei, Li, and LongTing Wang. "Geometric and topological structures of complex numbers." In International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), edited by Ke Chen, Nan Lin, Romeo Meštrović, Teresa A. Oliveira, Fengjie Cen, and Hong-Ming Yin. SPIE, 2022. http://dx.doi.org/10.1117/12.2628101.

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Ting, Dai. "Statistics Properties of Geometric Brown Motion under Haar Wavelet." In 2009 First International Conference on Information Science and Engineering. IEEE, 2009. http://dx.doi.org/10.1109/icise.2009.1090.

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Fletcher, P. Thomas, Suresh Venkatasubramanian, and Sarang Joshi. "Robust statistics on Riemannian manifolds via the geometric median." In 2008 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2008. http://dx.doi.org/10.1109/cvpr.2008.4587747.

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Kurfess, Thomas R., and David L. Banks. "Statistical Verification of Conformance to Geometric Tolerance." In ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/detc1994-0065.

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Abstract Modern coordinate measurement machines have provided industry with new tools for inspecting complex parts. This paper develops statistical procedures that complement these inspection methods, and it ties the conformance problem into the hypothesis testing formalism of conventional statistics. Also, the paper suggests strategies for efficient sampling of the part surface, and an implementation of the usual decision-theoretic formulation of the tradeoff between false acceptance and false rejection of part geometries. These ideas are illustrated through the analysis of real and simulated data for perfect and imperfect cylinders.
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Kuchkarova, Dilarom, Bafo Khaitov, and Bakhtiyor Ismatov. "Geometric modeling of the fore camera’s surface of pumping stations." In 2021 ASIA-PACIFIC CONFERENCE ON APPLIED MATHEMATICS AND STATISTICS. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0090264.

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Chen, Shuonan, Ziting Huang, Yuchen Lai, and Xingyi Lu. "Simulation of geometric Brownian motion in stock price." In International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), edited by Ke Chen, Nan Lin, Romeo Meštrović, Teresa A. Oliveira, Fengjie Cen, and Hong-Ming Yin. SPIE, 2022. http://dx.doi.org/10.1117/12.2628052.

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Reports on the topic "Geometric statistics":

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Singer, D. A., and R. Kouda. Application of geometric probability and Bayesian statistics to the search for mineral deposits. Natural Resources Canada/ESS/Scientific and Technical Publishing Services, 1990. http://dx.doi.org/10.4095/128119.

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Thompson, David C., Joseph Maurice Rojas, and Philippe Pierre Pebay. Computational algebraic geometry for statistical modeling FY09Q2 progress. Office of Scientific and Technical Information (OSTI), March 2009. http://dx.doi.org/10.2172/984161.

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Willsky, Alan S. Multiresolution, Geometric, and Learning Methods in Statistical Image Processing, Object Recognition, and Sensor Fusion. Fort Belvoir, VA: Defense Technical Information Center, July 2004. http://dx.doi.org/10.21236/ada425745.

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Wilson, D., Matthew Kamrath, Caitlin Haedrich, Daniel Breton, and Carl Hart. Urban noise distributions and the influence of geometric spreading on skewness. Engineer Research and Development Center (U.S.), November 2021. http://dx.doi.org/10.21079/11681/42483.

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Statistical distributions of urban noise levels are influenced by many complex phenomena, including spatial and temporal variations in the source level, multisource mixtures, propagation losses, and random fading from multipath reflections. This article provides a broad perspective on the varying impacts of these phenomena. Distributions incorporating random fading and averaging (e.g., gamma and noncentral Erlang) tend to be negatively skewed on logarithmic (decibel) axes but can be positively skewed if the fading process is strongly modulated by source power variations (e.g., compound gamma). In contrast, distributions incorporating randomly positioned sources and explicit geometric spreading [e.g., exponentially modified Gaussian (EMG)] tend to be positively skewed with exponential tails on logarithmic axes. To evaluate the suitability of the various distributions, one-third octave band sound-level data were measured at 37 locations in the North End of Boston, MA. Based on the Kullback-Leibler divergence as calculated across all of the locations and frequencies, the EMG provides the most consistently good agreement with the data, which were generally positively skewed. The compound gamma also fits the data well and even outperforms the EMG for the small minority of cases exhibiting negative skew. The lognormal provides a suitable fit in cases in which particular non-traffic noise sources dominate.
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Rockmore, Daniel. Dynamic Information Networks: Geometry, Topology and Statistical Learning for the Articulation of Structure. Fort Belvoir, VA: Defense Technical Information Center, June 2015. http://dx.doi.org/10.21236/ada624183.

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Perdigão, Rui A. P., and Julia Hall. Spatiotemporal Causality and Predictability Beyond Recurrence Collapse in Complex Coevolutionary Systems. Meteoceanics, November 2020. http://dx.doi.org/10.46337/201111.

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Causality and Predictability of Complex Systems pose fundamental challenges even under well-defined structural stochastic-dynamic conditions where the laws of motion and system symmetries are known. However, the edifice of complexity can be profoundly transformed by structural-functional coevolution and non-recurrent elusive mechanisms changing the very same invariants of motion that had been taken for granted. This leads to recurrence collapse and memory loss, precluding the ability of traditional stochastic-dynamic and information-theoretic metrics to provide reliable information about the non-recurrent emergence of fundamental new properties absent from the a priori kinematic geometric and statistical features. Unveiling causal mechanisms and eliciting system dynamic predictability under such challenging conditions is not only a fundamental problem in mathematical and statistical physics, but also one of critical importance to dynamic modelling, risk assessment and decision support e.g. regarding non-recurrent critical transitions and extreme events. In order to address these challenges, generalized metrics in non-ergodic information physics are hereby introduced for unveiling elusive dynamics, causality and predictability of complex dynamical systems undergoing far-from-equilibrium structural-functional coevolution. With these methodological developments at hand, hidden dynamic information is hereby brought out and explicitly quantified even beyond post-critical regime collapse, long after statistical information is lost. The added causal insights and operational predictive value are further highlighted by evaluating the new information metrics among statistically independent variables, where traditional techniques therefore find no information links. Notwithstanding the factorability of the distributions associated to the aforementioned independent variables, synergistic and redundant information are found to emerge from microphysical, event-scale codependencies in far-from-equilibrium nonlinear statistical mechanics. The findings are illustrated to shed light onto fundamental causal mechanisms and unveil elusive dynamic predictability of non-recurrent critical transitions and extreme events across multiscale hydro-climatic problems.
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Thompson, Beavers, and Han. L51544 Criteria to Stop Active Pit Growth. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), January 1987. http://dx.doi.org/10.55274/r0010282.

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The purpose of this research program was to determine the requirement to stop active pitting and compare that to the requirement to stop general corrosion and prevent pit initiation. This report examines the cathodic protection requirement to stop active pitting in buried natural gas transmission lines and compare it to the cathodic protection requirement to stop general corrosion and further prevent pit initiation. During the two-year period of this research program, two different pit geometries were examined: (1) a small diameter pit of 10 mils in diameter and approximately 10 mils deep which had less than five mils of active pit growth prior to cathodic polarization, and (2) large diameter pits of 1/2-inch in diameter which had approximately 50 mils of pit growth prior to cathodic polarization. Statistical analyses were used to determine whether pit growth continued during the cathodic polarization portion of the experiment or whether the active pit growth was stopped.
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Zevotek, Robin, and Steve Kerber. Fire Service Summary Report: Study of the Effectiveness of Fire Service Positive Pressure Ventilation During Fire Attack in Single Family Homes Incorporating Modern Construction Practices. UL Firefighter Safety Research Institute, May 2016. http://dx.doi.org/10.54206/102376/ncck4947.

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There is a continued tragic loss of firefighter and civilian lives, as shown by fire statistics. One significant contributing factor is the lack of understanding of fire behavior in residential structures resulting from the use of ventilation as a firefighter practice on the fire ground. The changing dynamics of residential fires as a result of the changes in home construction materials, contents, size and geometry over the past 30 years compounds our lack of understanding of the effects of ventilation on fire behavior. Positive Pressure Ventilation (PPV) fans were introduced as a technology to increase firefighter safety by controlling the ventilation. However, adequate scientific data is not available for PPV to be used without increasing the risk to firefighters. This fire research report details the experimental data from cold flow experiments, fuel load characterization experiments and full scale fire experiments. During the project it was identified that the positive pressure attack (PPA) and positive pressure ventilation (PPV) were often used interchangeably. For the purpose of this report they have been defined as PPA for when the fan is utilized prior to fire control and PPV for when the fan is used post fire control. The information from the full scale tests was reviewed with assistance from our technical panel of fire service experts to develop tactical considerations for the use of PPV fans in residential single family structures.
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Zevotek, Robin, and Steve Kerber. Study of the Effectiveness of Fire Service Positive Pressure Ventilation During Fire Attack in Single Family Homes Incorporating Modern Construction Practices. UL Firefighter Safety Research Institute, May 2016. http://dx.doi.org/10.54206/102376/gsph6169.

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There is a continued tragic loss of firefighter and civilian lives, as shown by fire statistics. One significant contributing factor is the lack of understanding of fire behavior in residential structures resulting from the use of ventilation as a firefighter practice on the fire ground. The changing dynamics of residential fires as a result of the changes in home construction materials, contents, size and geometry over the past 30 years compounds our lack of understanding of the effects of ventilation on fire behavior. Positive Pressure Ventilation (PPV) fans were introduced as a technology to increase firefighter safety by controlling the ventilation. However, adequate scientific data is not available for PPV to be used without increasing the risk to firefighters. This fire research report details the experimental data from cold flow experiments, fuel load characterization experiments and full scale fire experiments. During the project it was identified that the positive pressure attack (PPA) and positive pressure ventilation (PPV) were often used interchangeably. For the purpose of this report they have been defined as PPA for when the fan is utilized prior to fire control and PPV for when the fan is used post fire control. The information from the full scale tests was reviewed with assistance from our technical panel of fire service experts to develop tactical considerations for the use of PPV fans in residential single family structures.
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Kerber, Steve. Fire Service Summary: Study of the Effectiveness of Fire Service Vertical Ventilation and Suppression Tactics in Single Family Homes. UL Firefighter Safety Research Institute, June 2013. http://dx.doi.org/10.54206/102376/roua2913.

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There is a continued tragic loss of firefighter and civilian lives, as shown by fire statistics. One significant contributing factor is the lack of understanding of fire behavior in residential structures resulting from the use of ventilation as a firefighter practice on the fire ground. The changing dynamics of residential fires as a result of the changes in home construction materials, contents, size and geometry over the past 30 years compounds our lack of understanding of the effects of ventilation on fire behavior (Kerber S. , 2012). If used properly, ventilation improves visibility and reduces the chance of flashover or back draft. If a fire is not properly ventilated, it could result in an anticipated flashover, greatly reducing firefighter safety (Kerber S. , 2012). This fire research project developed empirical data from full-scale house fire experiments to examine vertical ventilation, suppression techniques and the resulting fire behavior. The purpose of this study was to improve firefighter knowledge of the effects of vertical ventilation and the impact of different suppression techniques. The experimental results may be used to develop tactical considerations outlining firefighting ventilation and suppression practices to reduce firefighter death and injury. This fire research project will further work from previous DHS AFG sponsored research (EMW-2008-FP-01774), which studied the impact of horizontal ventilation through doors and windows (Kerber S. , 2010).

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