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Probability theory for low quality data
Imprecise probability generalizes probability theory to allow for partial probability specifications, and is applicable when information is scarce, vague
Imprecise_probability
Mathematical framework to model epistemic uncertainty
understood connections to other frameworks such as probability, possibility and imprecise probability theories. Introduced by Arthur P. Dempster in the
Dempster–Shafer_theory
Society for Imprecise Probability: Theories and Applications (SIPTA) was created in February 2002, with the aim of promoting the research on Imprecise probability
SIPTA
Mathematical theory for handling uncertainty
This allows one to study possibility theory using the tools of imprecise probabilities. We call generalized possibility every function satisfying Axiom
Possibility_theory
Applications of logic under uncertainty
Bayesian inference, Bayesian network, Bayesian probability Cox's theorem Fréchet inequalities Imprecise probability Non-monotonic logic Possibility theory Probabilistic
Probabilistic_logic
Mathematical method of risk analysis
probabilities without dependence assumptions. Bounding probabilities has continued to the present day (e.g., Walley's theory of imprecise probability
Probability_bounds_analysis
Concept in probability
(2007). Imprecise probability methods for sensitivity analysis in engineering. Proceedings of the 5th International Symposium on Imprecise Probability: Theories
Probability_box
Written work by John Maynard Keynes
the subsequent development of 'modern Bayesian probability', and the notion of imprecise probabilities is now well established in statistics, with a wide
A_Treatise_on_Probability
of the central limit theorem Image denoising Importance sampling Imprecise probability Impulse response Imputation (statistics) Incidence (epidemiology)
List_of_statistics_articles
Probabilistic graphical models based on imprecise probability
based on imprecise probability. Credal networks can be regarded as an extension of Bayesian networks, where credal sets replace probability mass functions
Credal_network
British computer scientist
Society for Imprecise Probability (SIPTA) in 2019, he was invited to deliver a talk on "Game-theoretic foundations for imprecise probabilities" in Belgium
Vladimir_Vovk
Subset of artificial intelligence
understood connections to other frameworks such as probability, possibility and imprecise probability theories. These theoretical frameworks can be thought
Machine_learning
Subadditive or superadditive integral
In imprecise probability theory, the Choquet integral is also used to calculate the lower expectation induced by a 2-monotone lower probability, or the
Choquet_integral
Representations of imprecise probability
Upper and lower probabilities are representations of imprecise probability. Whereas probability theory uses a single number, the probability, to describe
Upper_and_lower_probabilities
Bayesian nonparametric model of probability distributions
Moreover, a-posteriori, it assigns zero probability to any set that does not include the observations. The imprecise Dirichlet process has been proposed to
Imprecise_Dirichlet_process
(2007). Imprecise probability methods for sensitivity analysis in engineering. Proceedings of the 5th International Symposium on Imprecise Probability: Theories
Applications of p-boxes and probability bounds analysis
Applications_of_p-boxes_and_probability_bounds_analysis
System for reasoning about vagueness
based on imprecise and non-numerical information. Fuzzy models or fuzzy sets are mathematical means of representing vagueness and imprecise information
Fuzzy_logic
Sport statistic representing player's contribution
derive, or imprecise. With the aid of Retrosheet, however, win probability added has become substantially easier to calculate. The win probability for a specific
Win_probability_added
org/nlab/show/category-theoretic+approaches+to+probability+theory https://golem.ph.utexas.edu/category/2024/07/imprecise_probabilities_toward.html#more https://ncatlab
Categorical_probability
Type of sensitivity analysis
introduction to the imprecise Dirichlet model for multinomial data. Tutorial for the Third International Symposium on Imprecise Probabilities and Their Applications
Robust_Bayesian_analysis
Paradox in decision theory
probabilities. The agent then tries to satisfice the expected utility and maximize the robustness against uncertainty in the imprecise probabilities.
Ellsberg_paradox
Terms used to convey the likelihood of an event occurring
Words of estimative probability (WEP or WEPs) are terms used by intelligence analysts in the production of analytic reports to convey the likelihood of
Words of estimative probability
Words_of_estimative_probability
Set of probability measures
[citation needed] Imprecise probability Dempster–Shafer theory Probability box Robust Bayes analysis Upper and lower probabilities Levi, Isaac (1980)
Credal_set
Iterative decision analytic framework
emerged from the literatures on scenario planning, robust control, imprecise probability, and info-gap decision theory and methods. An early review of many
Robust_decision-making
Professor of civil engineering (born 1968)
theories of probability to civil engineering and environmental systems, including random set theory, the theory of imprecise probability and info-gap
Jim_Hall_(civil_engineer)
American computer scientist
specializes in formal epistemology. Much of his work has focused on imprecise probability. He is currently Professor of Philosophy and Computer Science at
Gregory_Wheeler
a results of such calculations we will get so called imprecise probability. Imprecise probability is understood in a very wide sense. It is used as a generic
Interval_finite_element
American philosopher (1930–2018)
Sanders Peirce. Levi was known for his work in belief revision and imprecise probability. Levi, Isaac (1973) [1967]. Gambling with truth: an essay on induction
Isaac_Levi
Bayesian probability Bayesian programming Bayesianism Checking if a coin is fair Conjugate prior Factor graph Good–Turing frequency estimation Imprecise probability
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Statistical principle for robust inference
confidence. Proceedings of the Eighth International Symposium on Imprecise Probability: Theory and Applications. https://isipta13.sipta.org/proceedings/013
False_confidence_theorem
Selection of data points in statistics
the sample design, particularly in stratified sampling. Results from probability theory and statistical theory are employed to guide the practice. In
Sampling_(statistics)
Polish–American economist and mathematician (1917–2008)
"Information Processing under Imprecise Risk with the Hurwicz criterion" (PDF). International Symposium on Imprecise Probability: Theories and Applications
Leonid_Hurwicz
Dutch mathematician and physicist (1629–1695)
S2CID 163762875. Vovk, V.; Shafer, G. (2014). "Game-theoretic probability". Introduction to Imprecise Probabilities. John Wiley & Sons, Ltd. pp. 114–134. doi:10.1002/9781118763117
Christiaan_Huygens
Natural hazard involving ground movement
rainfall in Manizales City (Colombia) using multinomial probability and imprecise probabilities. Modelación no paramétrica de lluvias para la ciudad de
Landslide
Principle in Bayesian statistics
The principle of maximum entropy states that, among all probability distributions consistent with a given set of constraints (such as normalization or
Principle_of_maximum_entropy
(X)-\mathrm {Cov} (X,D)\mathrm {Var} (D)^{-1}\mathrm {Cov} (D,X).} Imprecise probability Bayes Linear Methods Goldstein, M. (1981) Revising Previsions: a
Bayes_linear_statistics
Measures of observational error
measurements averaged. Further, the central limit theorem shows that the probability distribution of the averaged measurements will be closer to a normal
Accuracy_and_precision
Mathematical concept
terminology developed in calculus courses; this section is necessarily imprecise as well as inexact, and the reader should refer to the formal clarifications
Convergence_of_measures
finite-state machines. Fuzzy logic Probabilistic logic Plausible reasoning Imprecise probability C. J. van Rijsbergen (1986), A non-classical logic for information
Uncertain_inference
American computer scientist
Verlag, 2014, pp. 163–193. M. Beer, S. Ferson, and V. Kreinovich, "Imprecise probabilities in engineering analyses", Mechanical Systems and Signal Processing
Vladik_Kreinovich
German atmospheric physicist and climatologist
Held, H.; Dawson, R.; Kriegler, E.; Schellnhuber, H. J. (2009). "Imprecise probability assessment of tipping points in the climate system". PNAS. 106 (13):
Hans_Joachim_Schellnhuber
fallacy, decision-point fallacy) – improperly rejecting a claim for being imprecise. Correlative-based fallacies Suppressed correlative – a correlative is
List_of_fallacies
Diagnostic plot of binary classifier ability
area under the probability distribution from − ∞ {\displaystyle -\infty } to the discrimination threshold) of the detection probability in the y-axis versus
Receiver operating characteristic
Receiver_operating_characteristic
Study of collection and analysis of data
any one-to-one (injective) transformation. Ordinal measurements have imprecise differences between consecutive values, but have a meaningful order to
Statistics
Probability distribution
In probability and statistics, the Dirichlet distribution (after Peter Gustav Lejeune Dirichlet), often denoted Dir ( α ) {\displaystyle \operatorname
Dirichlet_distribution
mathematical evidence theories such as Dempster-Shafer Theory, imprecise probability theories, etc. may be used for certain system models having epistemic
Time-utility_function
French mathematician
process" Didier Dubois, Henri Prade (2004) "Interval-valued Fuzzy Sets, Possibility Theory and Imprecise Probability" Didier Dubois, Henri Prade v t e
Didier_Dubois_(mathematician)
Dirichlet process Dependent Dirichlet process Hierarchical Dirichlet process Imprecise Dirichlet process Dirichlet ring (number theory) Dirichlet series (analytic
List of things named after Peter Gustav Lejeune Dirichlet
List_of_things_named_after_Peter_Gustav_Lejeune_Dirichlet
Scottish mathematician and theologian
the time. Several later mathematicians complained about his imprecise use of probability and the unsupported derivation of his formula. Stephen Stigler
John_Craig_(mathematician)
Overall strategy utilized to carry out research
valid answers to research questions while weak designs yield unreliable, imprecise or irrelevant answers. Incorporated in the design of a research study
Research_design
Discrete probability distribution
probability distribution that describes the possible results of a random variable that can take on one of K possible categories, with the probability
Categorical_distribution
Feature of some statistical distributions
numbers of occurrences of events with various probabilities, etc. The term is often used loosely, with an imprecise definition, but precise definitions are
Long_tail
Medical procedure
test is its reproducibility when it is repeated on the same sample. An imprecise test yields widely varying results on repeated measurement. Precision
Medical_test
Taxonomy of statistical data elements
and permit any one-to-one transformation. Ordinal measurements have imprecise differences between consecutive values, but have a meaningful order to
Statistical_data_type
Italian mathematician (born 1935)
of Probability in Statistical Physics. Transport Theory and Statistical Physics. (2000) The Role of Coherence in Eliciting and Handling Imprecise Probabilities
Romano_Scozzafava
Misuse of data analysis
variable. Conventional tests of statistical significance are based on the probability that a particular result would arise if chance alone were at work, and
Data_dredging
Machine learning paradigm
for a subset of the training data. The remaining data is unlabeled or imprecisely labeled. Active learning: Instead of assuming that all of the training
Supervised_learning
Subdivisions of geological time
between the Manicouagan Impact and palynomorph turnover, and even then the probability of synchronicity is only about 34%. Lucas, Spencer G (1998-11-01). "Global
Triassic land vertebrate faunachrons
Triassic_land_vertebrate_faunachrons
Family of stochastic processes
realizations are probability distributions. In other words, a Dirichlet process is a probability distribution whose range is itself a set of probability distributions
Dirichlet_process
Estimation method
applies an approximation to the known function rather than to the imprecisely-known probability distribution. He suggested that a better approach would be to
Unscented_transform
Statistics and machine learning technique
seeks to solve this problem. It involves training only the fast (but imprecise) algorithms in the bucket, and then using the performance of these algorithms
Ensemble_learning
encoders imprecise, specific algorithms can be used to provide exponentially accurate approximations for the value of beta, despite the imprecise results
Beta_encoder
Paradigm for the design, analysis, and scoring of tests
error of measurement. All tests, questionnaires, and inventories are imprecise tools; we can never know a person's true score, but rather only have an
Item_response_theory
variables. The relationships between variables (possibly uncertain or imprecise) are represented by the functions called valuations. The two basic operations
Valuation-based_system
Algorithm that estimates unknowns from a series of measurements over time
accurate than those based on a single measurement, by estimating a joint probability distribution over the variables for each time-step. The filter is constructed
Kalman_filter
Theory of sexual orientation
the more older brothers a male has from the same mother, the greater probability he will have a homosexual orientation. It was identified by Ray Blanchard
Fraternal birth order and male sexual orientation
Fraternal_birth_order_and_male_sexual_orientation
Paradigm in machine learning
for a subset of the training data. The remaining data is unlabeled or imprecisely labeled. Intuitively, it can be seen as an exam and labeled data as sample
Weak_supervision
Formal information theory restatement of Occam's Razor
makes it possible to usefully compare, say, a model with many parameters imprecisely stated against a model with fewer parameters more accurately stated.
Minimum_message_length
Sorting method in information retrieval
is obvious: IR systems deal with natural language, and this is too far imprecise to enable a system to state with certainty which document will be relevant
Ranking (information retrieval)
Ranking_(information_retrieval)
Measure of the degree to which software possesses some property
Some argue that the definition of many measurement methodologies are imprecise, and consequently it is often unclear how tools for computing them arrive
Software_metric
American mathematician and philosopher (born 1960)
(2009), and Intelligent Design Uncensored (2010). He has postulated that probability theory can be used to prove both specified complexity and irreducible
William_A._Dembski
Type of statistical analysis
evidently violated. The term "nonparametric statistics" has been defined imprecisely in the following two ways, among others: The first meaning of nonparametric
Nonparametric_statistics
Mathematical models of strategic interactions
rigorous mathematical analysis of game theory might help formalize the more imprecise philosophical discussions. However, this expectation was only materialized
Game_theory
Method used for calculating creditworthiness
expert opinions which makes it more adapted to cases with insufficient and imprecise hard data, as well as for modeling risks that are not fully understood
Credit_analysis
Ralf Dittmann; Wolfgang Lehner. "Error-Aware Density-Based Clustering of Imprecise Measurement Values". Seventh IEEE International Conference on Data Mining
Uncertain_data
not rely on precise definitions, rather they seemed to make hundreds of imprecise assumptions, correcting them when necessary using their entire body of
History of artificial intelligence
History_of_artificial_intelligence
Scoring systems are used in hospital intensive care units
from this score, but these methods are not too well defined and rather imprecise. APACHE III is an updated version. SAPS II was designed to provide a predicted
Medical_scoring
English polymath (1642–1727)
the two decades preceding 1684". It has been argued that Newton had an imprecise or limited understanding of limits. However, the mathematician Bruce Pourciau
Isaac_Newton
Deciding between multiple options
Intuitive Recognition-based Combination Recognizing that "type" is an imprecise term, an alternate way to classify types of choices is to look at outcomes
Choice
Coefficient of rate of a chemical reaction
collision theory, and transition state theory, respectively, although the imprecise notion of ΔE, the energy needed to overcome the activation barrier, has
Reaction_rate_constant
2014 aircraft disappearance
also supported the underwater search area, although this method is very imprecise over long periods. On 17 January 2017, the three countries jointly announced
Malaysia_Airlines_Flight_370
similarly to humans. The first system is the approximate number system, an imprecise system used for estimations of quantities. This system is distinguished
Number_sense_in_animals
Quantity in solid state thermodynamics
that at thermodynamic equilibrium this energy level would have a 50% probability of being occupied at any given time. The position of the Fermi level
Fermi_level
Varying application boundaries
being fixed once and for all. That means the idea is somewhat vague or imprecise. Yet it is not unclear or meaningless. It has a definite meaning, which
Fuzzy_concept
Founder of Islam (c. 570–632)
the Islamic corroboration system. The appellation is generally deemed imprecise, as the text neither established a state nor enacted Quranic statutes
Muhammad
Sets whose elements have degrees of membership
used in a wide range of domains in which information is incomplete or imprecise, such as bioinformatics. A fuzzy set is a pair ( U , m ) {\displaystyle
Fuzzy_set
Relativistic wave equation in quantum mechanics
t}}=-{\frac {1}{2m}}\nabla ^{2}\varphi .} This procedure is rather technically imprecise, and does not easily generalize to include interactions. It also does
Klein–Gordon_equation
American financial services company
of any risk measure can be wrong by a considerable margin. If from the imprecise estimate we cannot get a good understanding what the true value could
RiskMetrics
Sexual attraction to prepubescent children
them. Researchers state that the above uses of the term pedophilia are imprecise or suggest that they are best avoided. Writing in Mayo Clinic Proceedings
Pedophilia
Principle in quantum information theory
1103/RevModPhys.76.93. ISSN 0034-6861. S2CID 7481797. Hall, Michael J.W. (1987). "Imprecise measurements and non-locality in quantum mechanics". Physics Letters A
No-communication_theorem
Measurement of the direction from which a received signal was transmitted
the now-outdated Loran C have radio direction finding methods that are imprecise for today's needs. Radio direction finding networks also no longer exist
Direction_finding
Quantitative analysis of law
Jurimetrics is the application of quantitative methods, especially probability and statistics, to law. In the United States, the journal Jurimetrics is
Jurimetrics
Physiological quantity
in current practice has been questioned by some, as it is a relatively imprecise and non-specific test compared to other available diagnostic tests. Current
Erythrocyte sedimentation rate
Erythrocyte_sedimentation_rate
Converting classical mechanics to quantum mechanics
statement is not unique since it can be argued that the mathematically imprecise notation of Dirac, even still today, can elucidate the equivalence. Just
First_quantization
Branch of mathematics
definition of continuity in terms of infinitesimals, and a (somewhat imprecise) prototype of an (ε, δ)-definition of limit in the definition of differentiation
Calculus
Book series published by Encyclopædia Britannica
criticisms discount the importance of books solely because of generic, imprecise, and possibly irrelevant characteristics of the books' authors rather
Great Books of the Western World
Great_Books_of_the_Western_World
Attribution of human traits to non-human entities
humans; the options are either to leverage an emotional, imprecise human metaphor, or to reject imprecise metaphor and make use of more precise, domain-specific
Anthropomorphism
Software testing technique that tests programs with random inputs
only as precise as the specification and specifications are typically imprecise. It compares poorly with other techniques to find bugs (e.g. static program
Random_testing
Computer system simulating intelligence
storing information and processing it in a goal-oriented way, even if it is imprecise and lacks certainty. SC is based on the model of the human brain with
Computational_intelligence
Statistical estimator
{\displaystyle x\in {\mathcal {X}}} related through the conditional probability distribution P ( x ∣ θ ) {\displaystyle P(x\mid \theta )\,\!} . The goal
Minimax_estimator
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