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Book by Claude Dellacherie and Paul-André Meyer
Probabilities and Potential (titled Probabilités et Potentiel in the original French) is a mathematics book written by Claude Dellacherie and Paul-André
Probabilities_and_Potential
French mathematician
stochastic differential geometry and quantum probability. His most cited book is Probabilities and Potential B, written with Claude Dellacherie. The preceding
Paul-André_Meyer
French mathematician (born 1943)
potentiel. 4 vols. Hermann, Paris 1975–1992; English translation, Probabilities and Potential. North Holland, 1978–1988 Capacités et processus stochastiques
Claude_Dellacherie
Branch of mathematics concerning probability
understanding and unification of discrete and continuous probabilities, measure-theoretic treatment also allows us to work on probabilities outside R n
Probability_theory
Quantum mechanics concept
to a "box", but one which has finite potential "walls". Unlike the infinite potential well, there is a probability associated with the particle being found
Finite_potential_well
Discrete probability distribution
special case of the multinomial distribution, in that it gives the probabilities of potential outcomes of a single drawing rather than multiple drawings. Occasionally
Categorical_distribution
Theorem on changes in stochastic processes
and exp. ed.). Springer. ISBN 3-540-63929-2. Dellacherie, C.; Meyer, P.-A. (1982). "Decomposition of Supermartingales, Applications". Probabilities and
Girsanov_theorem
Model for the potential energy of a diatomic molecule
anharmonicity of real bonds and the non-zero transition probability for overtone and combination bands. The Morse potential can also be used to model other
Morse_potential
Mathematical concept
must be equal to the countable sum of the probabilities of each of these events. For example, the probability of the union of the mutually exclusive events
Probability_space
Table in statistics
conditional probability table (CPT) is defined for a set of discrete and mutually dependent random variables to display conditional probabilities of a single
Conditional_probability_table
Theorem in measure theory
measure. The probability of a "two-dimensional" event E {\displaystyle E} could then be obtained as an integral of the one-dimensional probabilities of the
Disintegration_theorem
Harmonic functions as solutions to Laplace's equation
probabilities and densities proportional to potentials. Even in the finite case, the analogue I-K[clarification needed] of the Laplacian in potential
Potential_theory
potential energy in a classical mechanical system. These probability densities are helpful in gaining insight into the correspondence principle and making
Classical_probability_density
Neuron communication by electric impulses
across a cell membrane. An action potential occurs when the membrane potential of a specific cell rapidly rises and falls. This "depolarization" (physically
Action_potential
Theory of behavioral economics
moderate probabilities or losses have small probabilities; risk-seeking behavior when losses have moderate probabilities or gains have small probabilities. Below
Prospect_theory
Behavioral model of risky decision-making
function that depends on relative payoff, and replacing cumulative probabilities with weighted cumulative probabilities. In the general case, this leads to
Cumulative_prospect_theory
Probabilities of the presence of a condition
Pre-test probability and post-test probability (alternatively spelled pretest and posttest probability) are the probabilities of the presence of a condition
Pre- and post-test probability
Pre-_and_post-test_probability
Discrete-variable probability distribution
{\displaystyle P} is a probability measure. p X ( x ) {\displaystyle p_{X}(x)} can also be simplified as p ( x ) {\displaystyle p(x)} . The probabilities associated
Probability_mass_function
Indexed set in mathematics
Paul-André Meyer (1979). Probabilities and Potential. Elsevier. ISBN 9780720407013. George Lowther (November 8, 2009). "Filtrations and Adapted Processes".
Filtration_(mathematics)
Complex number whose squared absolute value is a probability
These numerical weights are called probability amplitudes, and this relationship used to calculate probabilities from given pure quantum states (such
Probability_amplitude
Method of analysis of a patient's history and physical examination
potentially bringing the probabilities for competing candidate conditions to negligible levels. If such negligible probabilities are achieved, the clinician
Differential_diagnosis
Description of a quantum-mechanical system
Why should we assign probabilities at all to outcomes that are certain to occur in some worlds, and why should the probabilities be given by the Born
Schrödinger_equation
universality probabilities is dense in the open interval (0, 1). Universality probability was thoroughly studied and characterized by Barmpalias and Dowe in
Universality_probability
In statistics and probability theory, set of outcomes to which a probability is assigned
family of subsets. For the standard tools of probability theory, such as joint and conditional probabilities, to work, it is necessary to use a σ-algebra
Event_(probability_theory)
American mathematician (1910–2004)
developed martingale theory into a central method of probability, and pioneered probabilistic potential theory. His 1953 monograph Stochastic Processes became
Joseph_L._Doob
1968 book by Robert M. Blumenthal and Ronald K. Getoor
Markov Processes and Potential Theory is a mathematics book written by Robert McCallum Blumenthal and Ronald Getoor. It was first published in 1968 by
Markov Processes and Potential Theory
Markov_Processes_and_Potential_Theory
Discrete probability distribution
In probability theory and statistics, the Poisson distribution (/ˈpwɑːsɒn/) is a discrete probability distribution that expresses the probability of a
Poisson_distribution
Lack of quantifiable knowledge in economics
space is known but probabilities are not; unknown unknowns, to cases where the event space is unknown and, by implication, probabilities also are unknown
Knightian_uncertainty
of exposure probabilities for each unit in the analysis. First, define a diagonal matrix with a vector of treatment assignment probabilities P = diag
Spillover_(experiment)
Area, where a potential exhibits a local maximum
barrier with a non-zero probability R = | r | 2 = 1 − T . {\displaystyle R=|r|^{2}=1-T.} The transmission and reflection probabilities are in fact oscillating
Rectangular_potential_barrier
Model of an energy potential in quantum mechanics
In quantum mechanics the delta potential is a potential well mathematically described by the Dirac delta function - a generalized function. Qualitatively
Delta_potential
Analysis of potential system failures
possible to identify potential failure modes in a system and their causes and effects. For each component, the failure modes and their resulting effects
Failure mode and effects analysis
Failure_mode_and_effects_analysis
Mathematical concept
Press. pp. 356–357. ISBN 978-1-107-00800-7. Meyer, P.A. (1966). Probability and Potentials, Blaisdell Publishing Co, N. Y. (p.19, Theorem T22). De La Vallée
Uniform_integrability
Industry concept of crude oil and natural gas reserves and resources
legislative requirements and legal framework of the host Country outwith SEC regulations The probabilities associated with the 1P, 2P and 3P reserve categories
Oil and gas reserves and resource quantification
Oil_and_gas_reserves_and_resource_quantification
1924 book by Herbert Butterfield
trajectories and processes over time, but the characters in a historical novel live as real human beings do, being only aware of probabilities and potential situations
The_Historical_Novel
Statistical technique
stratified sampling. Weighting, when correctly applied, can potentially improve the efficiency and reduce the bias of unweighted estimators. One very early
Inverse_probability_weighting
Average uncertainty in variable's states
the state of the variable, considering the distribution of probabilities across all potential states. Given a discrete random variable X {\displaystyle
Entropy_(information_theory)
Severe events involving radioactive materials
empirically observed that ionizing radiation leads to higher probability of potentially developing cancer. Epidemiological studies therefore use for example
Nuclear and radiation accidents and incidents
Nuclear_and_radiation_accidents_and_incidents
French polymath (1749–1827)
Philosophical Essay on Probabilities (1902) at the Internet Archive Dale, Andrew I.; Laplace, Pierre-Simon (1995). Philosophical Essay on Probabilities. Sources in
Pierre-Simon_Laplace
species problem Unsolved problems in statistics Upper and lower probabilities Upside potential ratio – finance Urn problem Ursell function Utility maximization
List_of_statistics_articles
Value for the flow of probability in quantum mechanics
density and 4-current. In regions where a step potential or potential barrier occurs, the probability current is related to the transmission and reflection
Probability_current
Distribution of an uncertain quantity
uninformative prior. Some attempts have been made at finding a priori probabilities, i.e., probability distributions in some sense logically required by the nature
Prior_probability
Platforms for betting on events
known in advance and bounded. Academic literature has examined the meaning of prices in terms of probabilities. Justin Wolfers and Eric Zitzewitz showed
Prediction_market
Entity capable of developing into a person
In philosophy and bioethics, potential (future) person (in plural, sometimes termed potential people) has been defined as an entity which is not currently
Potential_person
Statistical measure used in survey research
able to trace back the decision and accurately calculate the exact inclusion probability. When these selection probabilities are hard to trace back, they
Design_effect
stated. That is, the participant is shown the potential outcomes for both choices as well as the probabilities of all the outcomes within each choice. Typically
Description-experience_gap
without sharp numerical probabilities. It includes both qualitative (comparative probability, partial preference orderings,...) and quantitative models (interval
SIPTA
Decision science practice and analytical framework
this approach from traditional decision theory and risk analysis, which typically assume that probabilities can be assigned to different outcomes. In contrast
Decision-making under deep uncertainty
Decision-making_under_deep_uncertainty
Overview of and topical guide to probability
science and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems. Probability and randomness
Outline_of_probability
Quantum mechanical statistic
quantum-mechanical potential, subsequently quantum potential, it was later elaborated upon by Bohm and Basil Hiley in its interpretation as an information potential which
Quantum_potential
Statistical Markov model
two types, transition probabilities and emission probabilities (also known as output probabilities). The transition probabilities control the way the hidden
Hidden_Markov_model
Technique used in the field of human reliability assessment (HRA)
account for performance-shaping factors that may influence these probabilities. The probabilities for the human reliability analysis event tree (HRAET), for
Technique for human error-rate prediction
Technique_for_human_error-rate_prediction
Center for computing asteroid and comet orbits
solutions calculate NEO close approaches to Earth, and produce assessments of NEO impact probabilities over the next century or more. CNEOS is the home
Center for Near-Earth Object Studies
Center_for_Near-Earth_Object_Studies
pairwise probabilities, and it is purely qualitative. Hamelryck and co-workers later gave a quantitative explanation for the statistical potentials, according
Statistical_potential
Ratio of the probability of an event happening versus not happening
algorithm. The odds are a ratio of probabilities; an odds ratio is a ratio of odds, that is, a ratio of ratios of probabilities. Odds-ratios are often used in
Odds
AI thought experiment
and the basilisk, a mythical creature capable of destroying enemies with its stare. LessWrong co-founder Eliezer Yudkowsky considered it a potential information
Roko's_basilisk
Measure for hazard from asteroid or comet impacts on Earth
seriousness of collision predictions, by combining probability statistics and known kinetic damage potentials into a single threat value. The Palermo scale
List of near-Earth potentially hazardous objects
List_of_near-Earth_potentially_hazardous_objects
System in quantum mechanics
quantum mechanics and scattering theory, the one-dimensional step potential is an idealized system used to model incident, reflected and transmitted matter
Step_potential
Expected value of a random variable given that certain conditions are known to occur
A. Meyer, Probability and Potentials, Blaisdell Publishing Co., 1966, page 28 Grimmett, Geoffrey; Stirzaker, David (2001). Probability and Random Processes
Conditional_expectation
Thermodynamic potential of entropy, analogous to the free energy
the subject of free probability. A free entropy is generated by a Legendre transformation of the entropy. The different potentials correspond to different
Free_entropy
consisted of 2 ANN, a policy network to predict the probabilities of potential moves by opponents, and a value network to predict the win chance of a given
Machine learning in video games
Machine_learning_in_video_games
1214/ss/1030037961. Getoor, Ronald (1980). "Review: Probabilities and potential, by C. Dellacherie and P. A. Meyer". Bull. Amer. Math. Soc. (N.S.). 2 (3):
Hunt_process
Description of physical properties at the atomic and subatomic scale
gives probabilities. Mathematically, a probability is found by taking the square of the absolute value of a complex number, known as a probability amplitude
Quantum_mechanics
Selection of data points in statistics
respondent driven sampling, allow calculation of selection probabilities and are probability sampling methods under certain conditions. The voluntary sampling
Sampling_(statistics)
Energy needed to remove an electron
Clouds, Probabilities, and Energies". chem.libretexts.org. UC Davis ChemWiki. May 23, 2019. Retrieved November 2, 2020. "Quantum numbers and orbitals-
Ionization_energy
Quantum mechanical phenomenon
with a short, narrow potential barrier, a small part of wavefunction can appear outside of the barrier representing a probability for tunnelling through
Quantum_tunnelling
Hypothetical intelligent extraterrestrial life
from earthlings, not from E.T.” The potential changes from extraterrestrial contact could vary greatly in magnitude and type, based on the extraterrestrial
Extraterrestrial_intelligence
For data monitoring in statistical quality control
real-world data, and for a number of highly non-normal probability distributions. The difference between data point, x i {\displaystyle x_{i}} , and its predecessor
Shewhart individuals control chart
Shewhart_individuals_control_chart
Cognitive modeling method
Iterate as needed and check with prototyping if possible Once complete, the calculations can then be used to determine the probability of a user remembering
Human_processor_model
magnitude, including counts of things, dimensionless quantities, and probabilities. Each number is given a name in the short scale, which is used in
Orders_of_magnitude_(numbers)
Rifle cartridge originally designed for use in the M4 carbine
energy at 700 meters that the M855 has at 500 meters. In terms of hit probability, the Blackout has an effective range of 460 meters. From a 9 in (230 mm)
.300_AAC_Blackout
Concept in economics
account of decision making under risk (when probabilities are known) and under uncertainty (when probabilities are not objectively known). Savage concluded
Expected_utility_hypothesis
Chart used in statistical quality control
binomial distribution is the basis for the p-chart and requires the following assumptions: The probability of nonconformity p is the same for each unit; Each
P-chart
Measure for hazard from asteroid or comet impacts on Earth
seriousness of collision predictions, by combining probability statistics and known kinetic damage potentials into a single threat value. The Palermo scale
Torino_scale
Computer hardware technology that uses quantum mechanics
behaves similarly to a (classical) probability vector, with one key difference: unlike probabilities, probability amplitudes are not necessarily positive
Quantum_computing
Futures studies lessons learned methods
probabilities of an element in a forecast set, and it helps to assess probabilities in view of judgements about potential interactions between those elements. The
Futures_techniques
Concept in physics
phonons ℏ Ω m {\displaystyle \hbar {\Omega }_{m}} . When the transition probabilities for all the modes are summed, the zero-phonon transitions always add
Zero-phonon line and phonon sideband
Zero-phonon_line_and_phonon_sideband
Probability that random variable X is less than or equal to x
of probabilities and address the cumulative probability for each potential range of X and Y, and here is the example: given the joint probability mass
Cumulative distribution function
Cumulative_distribution_function
Measure for evaluating probabilistic forecasts
to report probabilities equal to his personal beliefs. In addition to the simple case of a binary decision, such as assigning probabilities to 'rain'
Scoring_rule
Probabilistic problem-solving algorithm
distributions of the random states of a Markov process whose transition probabilities depend on the distributions of the current random states (see McKean–Vlasov
Monte_Carlo_method
U.S. federal statute known as Obamacare
Laiteerapong, Neda (2016). "The Affordable Care Act and Diabetes Diagnosis and Care: Exploring the Potential Impacts". Current Diabetes Reports. 16 (4): 27
Affordable_Care_Act
Gambling strategy where the amount is raised until a person wins or becomes insolvent
over all bets that could potentially occur in the series, of the expected value of a potential bet times the probability that the player will make that
Martingale_(betting_system)
Grammar model in linguistics
Each production is assigned a probability. The probability of a derivation (parse) is the product of the probabilities of the productions used in that
Probabilistic context-free grammar
Probabilistic_context-free_grammar
Type of cognitive bias
concern". While government policies in regard to potential dangers should focus on statistics and probabilities, government efforts to raise public awareness
Neglect_of_probability
Obligation on a party to prove their case
'the balance of probabilities'. In competition law cases, the standard of proof is the civil standard ("on the balance of probabilities") subject, because
Burden_of_proof_(law)
End of the human species
PMC 11866485. PMID 40018008. Rowe, Thomas; Beard, Simon (2018). "Probabilities, methodologies and the evidence base in existential risk assessments". Working
Human_extinction
Logical modeling technique
success and failure that explores responses through a single initiating event and lays a path for assessing probabilities of the outcomes and overall
Event_tree_analysis
Methodology for evaluating risks
killed) and their likelihoods of occurrence are expressed as probabilities or frequencies (i.e., the number of occurrences or the probability of occurrence
Probabilistic_risk_assessment
1986 book by Romano and Siegel
Counterexamples in Probability and Statistics is a mathematics book by Joseph P. Romano and Andrew F. Siegel. It began as Romano's senior thesis at Princeton
Counterexamples in Probability and Statistics
Counterexamples_in_Probability_and_Statistics
Mathematical concept
the probabilities in the Gibbs measure conditional on the frozen degrees of freedom. The Hammersley–Clifford theorem implies that any probability measure
Gibbs_measure
Measures the relative position of nations' and regions' peacefulness
democracy and transparency, education and material well-being. As such, it seeks to understand the relative importance of a range of potential determinants
Global_Peace_Index
Distance function defined between probability distributions
probability metric. If there exists a f {\displaystyle f} that reaches the supremum exactly, then such a function is called a Kantorovich potential for
Wasserstein_metric
as the potential reservoir. However, wells have not targeted these intervals due to current depths, there is a high probability that potential sources
Tarfaya_Basin
Human male external reproductive organ
understood but involve complex neurological and vascular factors. Potential complications include ischaemia, thrombosis, and impotence. In serious cases the condition
Human_penis
Event-related potential
stimulus would be a click and a 1 in 3 chance that the following stimulus would be a flash. The second cue type had probabilities that were the reverse of
P300_(neuroscience)
Physical law in electrochemistry
calculation of the reduction potential of a reaction (half-cell or full cell reaction) from the standard electrode potential, absolute temperature, the
Nernst_equation
Risk-listed near-Earth asteroid
reflecting its size and an estimated probability greater than 1% that it would impact Earth on 22 December 2032. The estimated impact probability peaked at 3
2024_YR4
United States power outages
damage. On October 10, SCE cut power to 13,000 customers, (and warned 175,000 of potential power cuts depending on conditions). By October 11, three days
2019 California power shutoffs
2019_California_power_shutoffs
American birth control activist and nurse (1879–1966)
concluded that by 1939 the birth control movement had lost its progressive potential, and had evolved into a racist program of population control. Davis' interpretation
Margaret_Sanger
lenient when fed and rested.) Conservatism or regressive bias: Tendency to remember high values and high likelihoods/probabilities/frequencies as lower
List_of_cognitive_biases
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