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Books on the topic 'Probabilistic representation'

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Published: 4 June 2021
Last updated: 1 June 2024

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1

Aven, Terje. Uncertainty in risk assessment: The representation and treatment of uncertainties by probabilistic and non-probabilistic methods. Chichester, West Sussex, United Kingdom: Wiley, 2014.

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2

Fisseler, Jens. Learning and modeling with probabilistic conditional logic. Heidelberg: Ios Press, 2010.

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3

Felsberg, Michael. Probabilistic and Biologically Inspired Feature Representations. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-031-01822-0.

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4

Aven, Terje, Enrico Zio, Piero Baraldi, and Roger Flage. Uncertainty in Risk Assessment: The Representation and Treatment of Uncertainties by Probabilistic and Non-Probabilistic Methods. Wiley & Sons, Limited, John, 2014.

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5

Aven, Terje, Enrico Zio, Piero Baraldi, and Roger Flage. Uncertainty in Risk Assessment: The Representation and Treatment of Uncertainties by Probabilistic and Non-Probabilistic Methods. Wiley & Sons, Incorporated, John, 2013.

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6

Uncertainty in Risk Assessment: The Representation and Treatment of Uncertainties by Probabilistic and Non-Probabilistic Methods. Wiley & Sons, Incorporated, John, 2013.

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7

Aven, Terje, Enrico Zio, Piero Baraldi, and Roger Flage. Uncertainty in Risk Assessment: The Representation and Treatment of Uncertainties by Probabilistic and Non-Probabilistic Methods. Wiley & Sons, Incorporated, John, 2013.

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8

Baulieu, Laurent, John Iliopoulos, and Roland Sénéor. Functional Integrals and Probabilistic Amplitudes. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198788393.003.0008.

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Functional integrals and probabilistic amplitudes. Brief historical notes. The reconstruction of quantum mechanics from path integrals. The Feynman formulation. Definition and properties of the coherent states and the Bargmann representation.
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9

Classification and Probabilistic Representation of the Positive Solutions of a Semilinear Elliptic Equation. American Mathematical Society (AMS), 2004.

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10

Hancox, J., and J. Boardman. The Impact of an Alternative Representation of the Atmosphere on the Predictions of the Probabilistic Consequence Code CONDOR (Reports). AEA Technology Plc, 1992.

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11

Medioni, Gerard, Michael Felsberg, and Sven Dickinson. Probabilistic and Biologically Inspired Feature Representations. Morgan & Claypool Publishers, 2018.

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12

Felsberg, Michael. Probabilistic and Biologically Inspired Feature Representations. Springer International Publishing AG, 2018.

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13

Felsberg, Michael. Probabilistic and Biologically Inspired Feature Representations. Morgan & Claypool Publishers, 2018.

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14

Felsberg, Michael. Probabilistic and Biologically Inspired Feature Representations. Morgan & Claypool Publishers, 2018.

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15

Grenander, Ulf, and Michael I. Miller. Pattern Theory. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198505709.001.0001.

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Pattern Theory provides a comprehensive and accessible overview of the modern challenges in signal, data, and pattern analysis in speech recognition, computational linguistics, image analysis and computer vision. Aimed at graduate students in biomedical engineering, mathematics, computer science, and electrical engineering with a good background in mathematics and probability, the text includes numerous exercises and an extensive bibliography. Additional resources including extended proofs, selected solutions and examples are available on a companion website. The book commences with a short overview of pattern theory and the basics of statistics and estimation theory. Chapters 3-6 discuss the role of representation of patterns via condition structure. Chapters 7 and 8 examine the second central component of pattern theory: groups of geometric transformation applied to the representation of geometric objects. Chapter 9 moves into probabilistic structures in the continuum, studying random processes and random fields indexed over subsets of Rn. Chapters 10 and 11 continue with transformations and patterns indexed over the continuum. Chapters 12-14 extend from the pure representations of shapes to the Bayes estimation of shapes and their parametric representation. Chapters 15 and 16 study the estimation of infinite dimensional shape in the newly emergent field of Computational Anatomy. Finally, Chapters 17 and 18 look at inference, exploring random sampling approaches for estimation of model order and parametric representing of shapes.
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16

Foundations of Measurement: Geometrical, Threshold, and Probabilistic Representations (Foundations of Measurement). Academic Pr, 1989.

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17

Tversky, Amos, Patrick Suppes, David H. Krantz, and R. Duncan Luce. Foundations of Measurement Volume II: Geometrical, Threshold, and Probabilistic Representations (Foundations of Measurement). Dover Publications, 2006.

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18

National Aeronautics and Space Administration (NASA) Staff. Demonstration of Probabilistic Sensitivity Analyses Tools on the Structural Response of a Representative Inflatable Space Structure. Independently Published, 2019.

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19

Heunen, Chris, and Jamie Vicary. Categories for Quantum Theory. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198739623.001.0001.

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Monoidal category theory serves as a powerful framework for describing logical aspects of quantum theory, giving an abstract language for parallel and sequential composition and a conceptual way to understand many high-level quantum phenomena. Here, we lay the foundations for this categorical quantum mechanics, with an emphasis on the graphical calculus that makes computation intuitive. We describe superposition and entanglement using biproducts and dual objects, and show how quantum teleportation can be studied abstractly using these structures. We investigate monoids, Frobenius structures and Hopf algebras, showing how they can be used to model classical information and complementary observables. We describe the CP construction, a categorical tool to describe probabilistic quantum systems. The last chapter introduces higher categories, surface diagrams and 2-Hilbert spaces, and shows how the language of duality in monoidal 2-categories can be used to reason about quantum protocols, including quantum teleportation and dense coding. Previous knowledge of linear algebra, quantum information or category theory would give an ideal background for studying this text, but it is not assumed, with essential background material given in a self-contained introductory chapter. Throughout the text, we point out links with many other areas, such as representation theory, topology, quantum algebra, knot theory and probability theory, and present nonstandard models including sets and relations. All results are stated rigorously and full proofs are given as far as possible, making this book an invaluable reference for modern techniques in quantum logic, with much of the material not available in any other textbook.
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20

Austerweil, Joseph L., Samuel J. Gershman, and Thomas L. Griffiths. Structure and Flexibility in Bayesian Models of Cognition. Edited by Jerome R. Busemeyer, Zheng Wang, James T. Townsend, and Ami Eidels. Oxford University Press, 2015. http://dx.doi.org/10.1093/oxfordhb/9780199957996.013.9.

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Probability theory forms a natural framework for explaining the impressive success of people at solving many difficult inductive problems, such as learning words and categories, inferring the relevant features of objects, and identifying functional relationships. Probabilistic models of cognition use Bayes’s rule to identify probable structures or representations that could have generated a set of observations, whether the observations are sensory input or the output of other psychological processes. In this chapter we address an important question that arises within this framework: How do people infer representations that are complex enough to faithfully encode the world but not so complex that they “overfit” noise in the data? We discuss nonparametric Bayesian models as a potential answer to this question. To do so, first we present the mathematical background necessary to understand nonparametric Bayesian models. We then delve into nonparametric Bayesian models for three types of hidden structure: clusters, features, and functions. Finally, we conclude with a summary and discussion of open questions for future research.
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21

Williams, J. Robert G. Probability and Nonclassical Logic. Edited by Alan Hájek and Christopher Hitchcock. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199607617.013.12.

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This chapter presents axioms for comparative conditional probability relations. The axioms presented here are more general than usual. Each comparative relation is a weak partial order on pairs of sentences but need not be a complete order relation. The axioms for these comparative relations are probabilistically sound for the broad class of conditional probability functions known as Popper functions. Furthermore, these axioms are probabilistically complete. Arguably, the notion of comparative conditional probability provides a foundation for Bayesian confirmation theory. Bayesian confirmation functions are overly precise probabilistic representations of the more fundamental logic of comparative support. The most important features of evidential support are captured by comparative relationships among argument strengths, realized by the comparative support relations and their logic.
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22

Borodin, Alexei, and Leonid Petrov. Integrable probability: stochastic vertex models and symmetric functions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0002.

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This chapter presents the study of a homogeneous stochastic higher spin six-vertex model in a quadrant. For this model concise integral representations for multipoint q-moments of the height function and for the q-correlation functions are derived. At least in the case of the step initial condition, these formulas degenerate in appropriate limits to many known formulas of such type for integrable probabilistic systems in the (1+1)d KPZ universality class, including the stochastic six-vertex model, ASEP, various q-TASEPs, and associated zero-range processes. The arguments are largely based on properties of a family of symmetric rational functions that can be defined as partition functions of the higher spin six-vertex model for suitable domains; they generalize classical Hall–Littlewood and Schur polynomials. A key role is played by Cauchy-like summation identities for these functions, which are obtained as a direct corollary of the Yang–Baxter equation for the higher spin six-vertex model.
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23

Mason, Peggy. Perceiving the World. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780190237493.003.0014.

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As exemplified by sensory illusions, perception is interpretative rather than faithfully representational of the changes in the world. All perceptual pathways involve stimulus transduction, transmission, and modulation before sensory events are coded by the nervous system. The set of stimuli that humans respond to are a subset of the stimuli that elicit reactions across the animal kingdom. The brain processes visual, auditory, mechanical, and vestibular stimuli by breaking stimuli into their sinusoidal components for neuronal processing. The probabilistic response of sensory receptors to stimulation within a receptive field is described. A fundamental property of sensory perception is responsiveness to a wide range of stimulus intensities over several orders of magnitude. Yet, at any one time, the response to a stimulus is proportional to the background level of stimulation. The concept of labeled line sensory transmission is described, and the reality of multimodal integration is revealed through examples.
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24

Oaksford, Mike, and Nick Chater. Causal Models and Conditional Reasoning. Edited by Michael R. Waldmann. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199399550.013.5.

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There are deep intuitions that the meaning of conditional statements relate to probabilistic law-like dependencies. In this chapter it is argued that these intuitions can be captured by representing conditionals in causal Bayes nets (CBNs) and that this conjecture is theoretically productive. This proposal is borne out in a variety of results. First, causal considerations can provide a unified account of abstract and causal conditional reasoning. Second, a recent model (Fernbach & Erb, 2013) can be extended to the explicit causal conditional reasoning paradigm (Byrne, 1989), making some novel predictions on the way. Third, when embedded in the broader cognitive system involved in reasoning, causal model theory can provide a novel explanation for apparent violations of the Markov condition in causal conditional reasoning (Ali et al, 2011). Alternative explanations are also considered (see, Rehder, 2014a) with respect to this evidence. While further work is required, the chapter concludes that the conjecture that conditional reasoning is underpinned by representations and processes similar to CBNs is indeed a productive line of research.
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25

Dresher, B. Elan, and Harry van der Hulst, eds. The Oxford History of Phonology. Oxford University Press, 2022. http://dx.doi.org/10.1093/oso/9780198796800.001.0001.

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This volume is an up-to-date history of phonology from the earliest known examples of phonological thinking through the rise of phonology as a field in the 20th century and up to the present time. The volume is divided into five parts. Part I, Early insights in phonology, begins with writing systems and has chapters devoted to the great ancient and medieval intellectual traditions of phonological thought that form the foundation of later thinking and continue to enrich phonological theory. Part II, The founders of phonology, describes the important schools and individuals of the late nineteenth and early twentieth centuries who shaped phonology as an organized scientific field. Part III takes up Mid-twentieth-century developments in phonology in the Soviet Union, Northern and Western Europe, and North America; it continues with precursors to generative grammar, and culminates in a chapter on Chomsky & Halle’s The Sound Pattern of English (SPE). Part IV, Phonology after SPE, shows how phonological theorists responded to SPE with respect to derivations, representations, and phonology-morphology interaction. Theories discussed include Dependency Phonology, Government Phonology, Constraint-and-Repair theories, and Optimality Theory. This part ends with a chapter on the study of variation. Part V, New methods and approaches, has chapters on phonetic explanation, corpora and phonological analysis, probabilistic phonology, computational modelling, models of phonological learning, and the evolution of phonology. This exploration of the history of phonology from various viewpoints provides new perspectives on where phonology has been and throws light on where it is going.
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