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Not-for-profit foundation for study and research in the mathematical sciences
The Applied Probability Trust is a UK-based non-profit foundation for study and research in the mathematical sciences, founded in 1964 and based in the
Applied_Probability_Trust
Application of probability theory
Applied probability is the application of probability theory to statistical problems and other scientific and engineering domains. Much research involving
Applied_probability
Queue model
Steady-State Solution of the M/K2/m Queue". Advances in Applied Probability. 12 (3). Applied Probability Trust: 799–823. doi:10.2307/1426432. JSTOR 1426432. S2CID 124883099
M/G/k_queue
Student laurel
the Senior Wranglers?" (PDF). Mathematical Spectrum. 29 (1). Applied Probability Trust. Retrieved 25 September 2008. Andrew Forsyth (1935) Old Tripos
Wrangler (University of Cambridge)
Wrangler_(University_of_Cambridge)
Iran Trust Ancient Monuments Society Anglo-Norman Text Society Anthropological Society of London Applied Microbiology International Applied Probability Trust
List of learned societies in the United Kingdom
List_of_learned_societies_in_the_United_Kingdom
Aspect of mathematical queueing theory
Solution of Finite Capacity M/D/1 Queues". Journal of Applied Probability. 37 (4). Applied Probability Trust: 1092–1098. doi:10.1239/jap/1014843086. JSTOR 3215497
M/D/1_queue
Form of written communication for math
Language of Geometry", in A Mathematical Spectrum Miscellany, Applied Probability Trust. Lawrence. A. Chang (1983) Handbook for spoken mathematics The
Language_of_mathematics
Topics referred to by the same term
photo transfer process (APT process), a process used in animation Applied Probability Trust, a UK-based non-profit-making foundation for study and research
Apt
Theory in actuarial science and applied probability
In actuarial science and applied probability, ruin theory (sometimes risk theory or collective risk theory) uses mathematical models to describe an insurer's
Ruin_theory
Matrix describing continuous-time Markov chains
Times in Finite Markov Processes" (PDF). Journal of Applied Probability. 26 (4). Applied Probability Trust: 744–756. doi:10.2307/3214379. JSTOR 3214379. S2CID 54623773
Transition-rate_matrix
Part of mathematical queueing theory
Transient Characteristics of M/M/∞ Queues". Journal of Applied Probability. 33 (2). Applied Probability Trust: 490–506. doi:10.2307/3215073. ISSN 0021-9002. JSTOR 3215073
M/M/∞_queue
Directed graph where each vertex pair has one arc
Excursion and Its Various Applications", Advances in Applied Probability, 23 (3), Applied Probability Trust: 557–585, doi:10.2307/1427622, JSTOR 1427622. Thomassen
Tournament_(graph_theory)
Branch of probability theory
Erhan (1969). "Markov Renewal Theory". Advances in Applied Probability. 1 (2). Applied Probability Trust: 123–187. doi:10.2307/1426216. JSTOR 1426216. Lawrence
Renewal_theory
Mathematical model in queueing theory
Versatile Markovian Point Process". Journal of Applied Probability. 16 (4). Applied Probability Trust: 764–779. doi:10.2307/3213143. JSTOR 3213143. S2CID 123525892
Markovian_arrival_process
Stochastic epidemic model
Collective Reed-Frost Epidemic Processes". Advances in Applied Probability. 22 (2). Applied Probability Trust: 269–294. doi:10.2307/1427536. ISSN 0001-8678. JSTOR 1427536
Reed–Frost_model
Public university in Sheffield, South Yorkshire, England
recipients include Sheffield Galleries and Museums Trust, Sheffield Industrial Museums Trust and Ken Hawley Trust. In 1987 the university became one of the twelve
University_of_Sheffield
Theorem of queueing theory about instantaneous behavior at arrival times
(1969). "Markov Population Processes". Journal of Applied Probability. 6 (1). Applied Probability Trust: 1–18. doi:10.2307/3212273. JSTOR 3212273. Mitrani
Arrival_theorem
German mathematician (1931–1998)
Stoyan: Obituary: Klaus Matthes. In: Journal of Applied Probability. 36(4)/1999. Applied Probability Trust, pp. 1255–1257, ISSN 0021-9002 Short biography
Klaus_Matthes
Method of analysis in probability theory
Algorithm for Quasi-Birth-Death Processes". Journal of Applied Probability. 30 (3). Applied Probability Trust: 650–674. JSTOR 3214773. Pérez, J. F.; Van Houdt
Matrix_geometric_method
Approximating Ordinary Differential Processes". Journal of Applied Probability. 8 (2). Applied Probability Trust: 344–356. JSTOR 3211904. Bramson, M. (1999). "A
Fluid_limit
Non-Negative Markovian Increments". Journal of Applied Probability. 23 (1). Applied Probability Trust: 71–88. doi:10.2307/3214117. JSTOR 3214117. S2CID 222275620
Generalized_renewal_process
Absolutely continuous distribution with rational Laplace–Stieltjes transform
"On matrix exponential distributions". Advances in Applied Probability. 39. Applied Probability Trust: 271–292. doi:10.1239/aap/1175266478. Fackrell, M
Matrix-exponential distribution
Matrix-exponential_distribution
Mathematics concept
Proof of Lorden's Renewal Inequality". Advances in Applied Probability. 18 (4). Applied Probability Trust: 1015–1016. doi:10.2307/1427260. JSTOR 1427260.
Lorden's_inequality
British mathematician
finitely many elements of bounded height. In 1952, he moved to the Town Trust Chair of Pure Mathematics at Sheffield University. He remained at Sheffield
Douglas_Northcott
Mathematician (1912–1999)
Essays in statistical science: papers in honour of P.A.P. Moran. Applied Probability Trust. ISBN 978-0-902016-01-9. Vincze, István; Erdös, Paul (1958). "Über
István_Vincze_(mathematician)
Term in psychology and sociology
psychology of trust, or in particulars of empirical data collection. Formal metrics tend to have a strong foundations in algebra, probability or logic. There
Trust_metric
Swedish mathematician and statistician (born 1941)
Jagers: a collegial perspective". Advances in Applied Probability. 50A: 3–9 – via Applied Probability Trust. "Individual - ISI". Individual Members. Archived
Peter_Jagers
Australian statistician
Methuen. Hannan, E.J. (1965). Group Representations and Applied Probability. Applied Probability Trust. Hannan, E.J. (1970). Multiple Time Series. Wiley. Hannan
Edward_J._Hannan
application to selective predation". Journal of Applied Probability. Vol. 13, no. 4. Applied Probability Trust. pp. 795–797. doi:10.2307/3212535. JSTOR 3212535
Wallenius' noncentral hypergeometric distribution
Wallenius'_noncentral_hypergeometric_distribution
Statistician
supervision of Richard L. Smith. After four years at the department of Probability and Statistics at Sheffield, Tawn joined Lancaster University in 1992
Jonathan_Tawn
British mathematician
from A Mathematical Spectrum Miscellany: selections from Mathematical Spectrum, 1967–1994, Applied Probability Trust, 2000, p. 3, ISBN 9780902016057
Hazel_Perfect
Generation of trusted authorities or user trust through cryptography
a lower level of probability that these collaborations will be successful. Trust is a particular level of the subjective probability with which an agent
Computational_trust
Model-free reinforcement learning algorithm
deep RL when the policy network is very large. The predecessor to PPO, Trust Region Policy Optimization (TRPO), was published in 2015. It addressed the
Proximal_policy_optimization
Applications of logic under uncertainty
belief fusion in Dempster–Shafer theory. Source trust and epistemic uncertainty about the probabilities they provide, such as defined in subjective logic
Probabilistic_logic
Probabilistic theory of knowledge
Bayes' work in the field of probability theory. It is based on the idea that beliefs can be interpreted as subjective probabilities. As such, they are subject
Bayesian_epistemology
American computer scientist and engineer
networks, data-driven decision-making in man-machine systems, and applied probability and queueing theory. In 2009, he was designated a Fellow of the Institute
Gustavo_de_Veciana
Lebanese-American author (born 1960)
risk analyst, and aphorist. His work concerns problems of randomness, probability, complexity, and uncertainty. Taleb wrote Incerto, a five-volume work
Nassim_Nicholas_Taleb
Estimated potential loss for an investment under a given set of conditions
It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day
Value_at_risk
Data structure for approximate set membership
counting Bloom filter variant); the more items added, the larger the probability of false positives. Bloom proposed the technique for applications where
Bloom_filter
Greek mathematician and information theorist
College, Cambridge. His research interests are in information theory, probability and statistics, including their applications in data compression, bioinformatics
Ioannis_Kontoyiannis
Resource problem in machine learning
In probability theory and machine learning, the multi-armed bandit problem (sometimes called the K- or N-armed bandit problem) is named from imagining
Multi-armed_bandit
Assumption of and reliance on the honesty of another party
Castelfranchi, C.; Falcone, R. (2000). "Trust is much more than subjective probability: Mental components and sources of trust". Proceedings of the 33rd Annual
Trust_(social_science)
Concepts from statistical hypothesis testing
statistical hypothesis tests have a probability of making type I and type II errors. The type I error rate is the probability of rejecting the null hypothesis
Type_I_and_type_II_errors
Logic error due to ignoring the base rate
a false positive. The confusion of the posterior probability of infection with the prior probability of receiving a false positive is a natural error
Base_rate_fallacy
Argonne Helen Byrne, British applied mathematician and mathematical biologist María Emilia Caballero, Mexican probability theorist Angelina Cabras (1898–1993)
List_of_women_in_mathematics
Cambridge University master's course
the Mayhew Prize for applied mathematics, the Tyson Medal for mathematics and astronomy, the Bartlett Prize for applied probability, the Wishart Prize for
Part III of the Mathematical Tripos
Part_III_of_the_Mathematical_Tripos
Theorem of convex functions
as a probability distribution, and the summations are replaced by integrals. Let ( Ω , A , μ ) {\displaystyle (\Omega ,A,\mu )} be a probability space
Jensen's_inequality
Mathematics problem
The 100 prisoners problem is a mathematical problem in probability theory and combinatorics. In this problem, 100 numbered prisoners must find their own
100_prisoners_problem
Possibility of something bad happening
Conjecture: Evidence and Probability Before Pascal, Baltimore: Johns Hopkins University Press. John Handmer; Paul James (2005). "Trust Us and Be Scared: The
Risk
Class of reinforcement learning algorithm
model-free algorithm is an algorithm which does not estimate the transition probability distribution (and the reward function) associated with the Markov decision
Model-free (reinforcement learning)
Model-free_(reinforcement_learning)
Observed inability to reproduce scientific studies
significance, the probability of replication increases with power, and prior probability for H 1 {\displaystyle H_{1}} . If the prior probability for H 1 {\displaystyle
Replication_crisis
Pattern-recognition performance metrics
perform. A no-skill classifier is defined by the property that the joint probability P ( C = P , C ^ = P ) = P ( C = P ) P ( C ^ = P ) {\displaystyle \mathbb
Precision_and_recall
Random process of binary (boolean) random variables
In probability and statistics, a Bernoulli process (named after Jacob Bernoulli) is a finite or infinite sequence of binary random variables, so it is
Bernoulli_process
1890 U.S. anti-monopoly law
first to hold that the law applied to labor unions. Chesapeake & Ohio Fuel Co. v. United States (1902), in which the trust was dissolved Northern Securities
Sherman_Antitrust_Act
Series of language models developed by Google AI
with a [MASK] token with probability 80%, replaced with a random word token with probability 10%, not replaced with probability 10%. The reason not all
BERT_(language_model)
SI derived unit of absorbed dose of ionizing radiation
defined as the probability of cancer induction and genetic damage. The gray measures the total absorbed energy of radiation, but the probability of stochastic
Gray_(unit)
Experimental tool
where participants were randomly paired with one another to increase the probability that the outcome would be dependent on the actions of the trustee selected
Dictator_game
Austrian mathematician and theoretical physicist (1844–1906)
The Man Who Trusted Atoms. Oxford University Press. ISBN 978-0-19-850154-1. Darrigol, Olivier (2018). Atoms, Mechanics, and Probability: Ludwig Boltzmann's
Ludwig_Boltzmann
Trusts law case
Bartlett v Barclays Bank Trust Co Ltd (No. 2) [1980] 1 Ch 515 in an English trusts law case. In it Brightman J gave a comprehensive discussion of the
Bartlett v Barclays Bank Trust Co Ltd
Bartlett_v_Barclays_Bank_Trust_Co_Ltd
Branch of economics
The revelation principle as applied to auctions is that the marginal buyer payoff or "buyer surplus" is P(v), the probability of being the winner. In every
Auction_theory
Sub-discipline of systems engineering that emphasizes dependability
equipment to function without failure. Reliability is defined as the probability that a product, system, or service will perform its intended function
Reliability_engineering
Obligation on a party to prove their case
any difference to the standard of proof to be applied in determining the facts. The inherent probabilities are simply something to be taken into account
Burden_of_proof_(law)
French polymath (1749–1827)
Sir Isaac Newton's work. In statistics, the Bayesian interpretation of probability was developed mainly by Laplace. Laplace formulated Laplace's equation
Pierre-Simon_Laplace
Statistical geneticist
University of Oxford, and the CEO of Genomics PLC. He is a specialist in applied probability and has made contributions to coalescent theory. His research group
Peter_Donnelly
Mathematical models of strategic interactions
believes that Player 2 wants to date her under a probability of 1/2 and get away from her under a probability of 1/2 (this evaluation comes from Player 1's
Game_theory
Mathematical framework to model epistemic uncertainty
subjective probability. Belief functions base degrees of belief (or confidence, or trust) for one question on the subjective probabilities for a related
Dempster–Shafer_theory
Standard example in game theory
cooperation probabilities: P = { P c c , P c d , P d c , P d d } {\displaystyle P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}} , where Pcd is the probability that X will
Prisoner's_dilemma
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
Proving validity without revealing other data
guessing. Since the probability that Peggy would have randomly succeeded at identifying each switch/non-switch is 50%, the probability of having randomly
Zero-knowledge_proof
Generalization of the Riemann integral
forms of statistical theorems that apply to discrete and continuous probability. The Riemann–Stieltjes integral of a real-valued function f {\displaystyle
Riemann–Stieltjes_integral
Analyst of business risk and uncertainty
measure and mitigate risks have their origins in 17th-century studies of probability and annuities. Actuaries in the 21st century require analytical skills
Actuary
Authenticated encryption mode
achieving a success probability of approximately n⋅2−t. The complement, 1 − n⋅2−t, bounds the adversary's failure probability for arbitrarily large
Galois/Counter_Mode
Class of reinforcement learning algorithms
argument the state of the environment s {\displaystyle s} and produces a probability distribution π θ ( ⋅ ∣ s ) {\displaystyle \pi _{\theta }(\cdot \mid s)}
Policy_gradient_method
English mathematician and philosopher (1815–1864)
general method in probabilities, focusing on determining the consequent probability of events logically connected to given probabilities. Boole's work was
George_Boole
Branch of applied mathematics
related with the more mathematical ergodic theory and some parts of probability theory. There are increasing interactions between combinatorics and physics
Mathematical_physics
Stimulus that reinforces the cessation of a behavior
occurs when a response produces a stimulus and that response decreases in probability in the future in similar circumstances. Example: A mother yells at a
Punishment_(psychology)
Settlement without third party involvement
failure probability approaches zero as the network's size, density, or credit capacity increases. Specifically, for star networks, failure probability is Θ(1/c);
Collaborative_finance
English mathematician (born 1950)
mathematician known for his work on the mathematics of random systems arising in probability theory and statistical mechanics, especially percolation theory and the
Geoffrey_Grimmett
Forecasters whose results are more accurate than average
effective than listening to political pundits. Superforecasters estimate a probability of an occurrence, and review the estimate when circumstances contributing
Superforecaster
Type of cryptographic attack
attack that exploits the mathematics behind the birthday problem in probability theory. This attack can be used to abuse communication between two or
Birthday_attack
Mapping arbitrary data to fixed-size values
applied. One is the strict avalanche criterion: whenever a single input bit is complemented, each of the output bits changes with a 50% probability.
Hash_function
Hash function phenomenon
specific birthday, but the probability of finding a set of any two people with matching birthdays increases the probability greatly. Bad actors can use
Hash_collision
AI that generates content
into a fixed latent representation, VAEs model the latent space as a probability distribution, allowing for smooth sampling and interpolation between
Generative_AI
Algorithm that generates an approximation of a random number sequence
number generators. They are summarized here: K1 – There should be a high probability that generated sequences of random numbers are different from each other
Pseudorandom_number_generator
German-English clergyman (1805–1898)
new Orphan House ... Now I am able to meet all of the expenses. In all probability, I will even have several hundred pounds more than I need. The Lord not
George_Müller
Indian theoretical physicist (1894–1974)
Heisenberg's uncertainty principle will be significant. Thus he stressed the probability of finding particles in the phase space, each state having volume h3
Satyendra_Nath_Bose
Algorithm used by Google Search to rank web pages
Kleinberg in their original papers. The PageRank algorithm outputs a probability distribution used to represent the likelihood that a person randomly
PageRank
Russian mathematician
university courses in analytical mathematics, differential equations, and probability theory, he was also active in preparing syllabi and teaching manuals
Viktor_Bunyakovsky
Collective perception of a group of people
effects of averaging subjective probability estimates between and within judges". Journal of Experimental Psychology: Applied. 6 (2): 130–147. CiteSeerX 10
Wisdom_of_the_crowd
Subjective attitude that something is true
probabilities. For example, the law of total probability might be applied to predict a subjective probability value. Wyer found that this model produces
Belief
Statistics applied to risk in insurance and other financial products
series of rigorous professional examinations focused in fields such as probability and predictive analysis. According to the U.S. News & World Report, their
Actuarial_science
Type of machine learning model
primarily stems from token bias—that is, the model assigns a higher a priori probability to specific answer tokens (such as "A") when generating responses. As
Large_language_model
for outstanding contributions to statistics, or to probability, in either theoretical or applied work Chile National Prize for Exact Sciences Ministry
List_of_mathematics_awards
British mathematician (1944–1970)
phenomena", Stochastic methods and their applications, Journal of Applied Probability, 41A: 333–346, doi:10.1239/jap/1082552209, JSTOR 3215987, MR 2057584
Rollo_Davidson
Social science studying goods and services
analysis can be applied throughout society, including business, finance, cybersecurity, health care, engineering and government. It is also applied to such diverse
Economics
Law maintaining market competition
regulation are United States antitrust law, named after the trust busting of monopolistic trusts, and European Union competition law. National and regional
Competition_law
Rule of logical inference
modus tollens, is one of the standard patterns of inference that can be applied to derive chains of conclusions that lead to the desired goal. The form
Modus_ponens
investments. By contrast, GBI optimizes an investment mix to minimize the probability of failing to achieve a minimum wealth level within a set period of time
Goal-based_investing
Solution concept of a non-cooperative game
strategies, where players choose a probability distribution over possible pure strategies (which might put 100% of the probability on one pure strategy; such
Nash_equilibrium
Practitioner of engineering
Mechanical engineering cuts across most disciplines since its core essence is applied physics. Engineers also may specialize in one industry, such as motor vehicles
Engineer
APPLIED PROBABILITY-TRUST
APPLIED PROBABILITY-TRUST
Boy/Male
Arabic, Muslim
Eternal; Everlasting; An Epithet Applied to Allah
Girl/Female
African, German, Swahili
Apple
Boy/Male
Biblical
Proud; quarrelsome (applied to Egypt).
Girl/Female
Arabic
Spotted; Dappled
Girl/Female
Muslim
Apple
Girl/Female
Indian
Apple
Surname or Lastname
English
English : variant of Appling.
Boy/Male
Biblical
Proud; quarrelsome (applied to Egypt).
Boy/Male
Indian, Sanskrit
Shining; Dappled Horse
Surname or Lastname
English
English : variant of Apley.
Girl/Female
Biblical
Supplying, supplied.
Biblical
supplying; supplied
Surname or Lastname
English
English : from Middle English appel ‘apple’ (Old English æppel), acquired as a surname in any of various senses: a topographic name for someone living by an apple orchard; an occupational name for a grower or seller of apples; or a nickname for someone supposed to resemble an apple in some way, e.g. in having bright red cheeks. The economic importance in medieval northern Europe of apples, as a fruit that could be grown in a cold climate and would keep for use throughout the winter, is hard to appreciate in these days of rapid transportation and year-round availability of fruits of all kind.Americanized form of Appel or Apfel.
Boy/Male
Buddhist, Indian, Sanskrit
Term of Respect Applied to a Buddhist Mendicant
Surname or Lastname
English
English : patronymic from Abel, which was a popular Middle English personal name. Compare Aplin.
Girl/Female
Muslim
Apple
Biblical
proud; quarrelsome (applied to Egypt)
Boy/Male
Indian, Sanskrit
Dappled Leaves
Girl/Female
Indian
Apple
Girl/Female
Muslim/Islamic
Apple
APPLIED PROBABILITY-TRUST
APPLIED PROBABILITY-TRUST
Boy/Male
Tamil
Samarchit | ஸமாஂரà¯à®šà®¿à®¤
Worshipped
Boy/Male
Indian, Punjabi, Sikh
Honourable; Modest
Boy/Male
Bengali, Indian
Not Greedy
Girl/Female
Muslim
Of ambergris
Boy/Male
English
Dusty place; brave soldier.
Boy/Male
English Scottish
Valley island. Derived from a surname and place name. Famous bearer: British actor Denholm Elliott.
Boy/Male
British, English
Place Name in Britain
Girl/Female
English
Modern feminine of John and Jon.
Surname or Lastname
English
English : variant of Waldie.German : habitational name for someone from any of several places in Pomerania and Brandenburg called Waldow.Cornelius Waldo was living in Ipswich, MA, in 1647. Samuel Waldo (1695–1759) was born in Boston and became a land speculator in ME.
Female
Finnish
Finnish form of Greek Eva, EEVA means "life."
APPLIED PROBABILITY-TRUST
APPLIED PROBABILITY-TRUST
APPLIED PROBABILITY-TRUST
APPLIED PROBABILITY-TRUST
APPLIED PROBABILITY-TRUST
n.
Probability.
adv.
In all probability; probably.
n.
Probability; likelihood.
n.
Likelihood of the occurrence of any event in the doctrine of chances, or the ratio of the number of favorable chances to the whole number of chances, favorable and unfavorable. See 1st Chance, n., 5.
n.
The quality or state of being probable; appearance of reality or truth; reasonable ground of presumption; likelihood.
pl.
of Improbability
n.
The doctrine of the probabilists.
n.
One who maintains that certainty is impossible, and that probability alone is to govern our faith and actions.
pl.
of Probability
n.
Likelihood; probability.
n.
Any fruit or other vegetable production resembling, or supposed to resemble, the apple; as, apple of love, or love apple (a tomato), balsam apple, egg apple, oak apple.
n.
One who maintains that a man may do that which has a probability of being right, or which is inculcated by teachers of authority, although other opinions may seem to him still more probable.
n.
Appearance of truth or reality; probability; verisimilitude.
n.
Probability.
adv.
By presumption, or supposition grounded or probability; presumably.
n.
Probability; verisimilitude.
n.
He who, or that which, applies.
n.
That which is or appears probable; anything that has the appearance of reality or truth.
v. i.
To grow like an apple; to bear apples.
superl.
Having probability; affording probability; probable; likely.