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Notion in intelligent design
A universal probability bound is a probabilistic threshold whose existence is asserted by William A. Dembski and is used by him in his works promoting
Universal_probability_bound
Topics referred to by the same term
The universal probability is the algorithmic probability of a universal prefix-free Turing machine, used to define a universal prior distribution. Universal
Universal probability (disambiguation)
Universal_probability_(disambiguation)
Creationist argument by William Dembski
present in a specified event whose probability did not exceed 1 in 10150, which he calls the universal probability bound. In that context, "specified" meant
Specified_complexity
Mathematical method of assigning a prior probability to a given observation
machines, and the universal prior is a probability distribution over the set of finite binary strings calculated from a probability distribution over
Algorithmic_probability
Technique for selecting hash functions
upper bound of ϵ < 1 {\displaystyle \epsilon <1} on the collision probability, we say that we have ϵ {\displaystyle \epsilon } -almost universality. So
Universal_hashing
Fallacious argument against abiogenesis of chance
arguments invoking the junkyard tornado analogy also invoke the universal probability bound, which claims that highly improbable events do not occur. It
Junkyard_tornado
1999 book by William Dembski
necessity; the latter two rule out chance. Combined with his universal probability bound of 10−150, he claims that this criterion is completely accurate
Intelligent_Design_(book)
Type of prefix code
decreasing probability and then sending the index of the intended message. Universal codes are generally not used for precisely known probability distributions
Universal code (data compression)
Universal_code_(data_compression)
Topics referred to by the same term
Union bound estimate, a probability theory bound Union of Bookmakers Employees United Bank of Egypt, a bank co-owned by Banque du Caire Universal Basic
UBE
Interpretation of probability
Bayesian probability (/ˈbeɪziən/ BAY-zee-ən or /ˈbeɪʒən/ BAY-zhən) is an interpretation of the concept of probability, in which, instead of frequency or
Bayesian_probability
Measure of algorithmic complexity
Algorithmic Probability became associated with Solomonoff, who focused on prediction using his invention of the universal prior probability distribution
Kolmogorov_complexity
American inventor of algorithmic probability and artificial intelligence researcher
mathematician who invented algorithmic probability, his General Theory of Inductive Inference (also known as Universal Inductive Inference), and was a founder
Ray_Solomonoff
Mathematical inequality explaining concentration of random variables
insight. Another almost universal example of a secondary random variable is the law of large numbers of classical probability theory which states that
Concentration_inequality
Mathematical theory
This posterior probability is derived from Bayes' rule and some universal prior, that is, a prior that assigns a positive probability to any computable
Solomonoff's theory of inductive inference
Solomonoff's_theory_of_inductive_inference
2006 book by Michael Shermer
William Dembski proposed this new conservation law and defined a universal probability bound that he claims is 500 bits of information. It has not been generally
Why_Darwin_Matters
communication, the Slepian–Wolf coding, also known as the Slepian–Wolf bound, is a result in distributed source coding discovered by David Slepian and
Slepian–Wolf_coding
mathematical study of permutations and permutation patterns, a superpattern or universal permutation is a permutation that contains all of the patterns of a given
Superpattern
Determining the probability of future events based on past events
Inductive probability attempts to give the probability of future events based on past events. It is the basis for inductive reasoning, and gives the mathematical
Inductive_probability
Lossless data compression scheme
and P {\displaystyle P} is the probability of the source symbol. An entropy coding attempts to approach this lower bound. Two of the most common entropy
Entropy_coding
Average uncertainty in variable's states
describe the state of the variable, considering the distribution of probabilities across all potential states. Given a discrete random variable X {\displaystyle
Entropy_(information_theory)
Subfield of information theory and computer science
software, the probability of occurrence of any data structure is of the order of the shortest program that generates it when running on a universal machine
Algorithmic information theory
Algorithmic_information_theory
Probability distribution in number theory
around 1800, and Rodion Kuzmin, who gave a bound on the rate of convergence in 1929. It is given by the probability mass function p ( k ) = − log 2 ( 1 −
Gauss–Kuzmin_distribution
Zeta-like functions approximate arbitrary holomorphic functions
values of t that satisfy inequality (1). An effective universality theorem places an upper bound on the smallest such t. For example, in 2003, Garunkštis
Zeta_function_universality
Basic circuit in quantum computing
{\displaystyle v_{1}} are the complex probability amplitudes of the qubit. These values determine the probability of measuring a 0 or a 1, when measuring
Quantum_logic_gate
Computational complexity class of problems
take a majority vote to achieve any desired probability of correctness less than 1, using the Chernoff bound. The complexity class is unchanged by allowing
BQP
Principle in Bayesian statistics
respects the universal "constraint" that the sum of the probabilities is one. Under this constraint, the maximum entropy discrete probability distribution
Principle_of_maximum_entropy
Variation of the minimax algorithm
search is a variant described in Universal Artificial Intelligence: Sequential Decisions Based on Algorithmic Probability (2005) by Tom Everitt and Marcus
Expectiminimax
Theorem in probability theory
In probability theory, the central limit theorem states that, under certain circumstances, the probability distribution of the scaled mean of a random
Berry–Esseen_theorem
Statistical function that defines the quantiles of a probability distribution
In probability and statistics, the quantile function of a probability distribution is the inverse of its cumulative distribution function. That is, the
Quantile_function
Family of hash functions
The first definition along these lines was universal hashing, which guarantees a low collision probability for any two designated keys. More generally
K-independent_hashing
1994 video game
the universal cosmic destroyer Giygas. EarthBound had a lengthy development period that spanned five years. Its returning staff from EarthBound Beginnings
EarthBound
Probabilistic graphical representation of causal relationships
as naïve Bayes networks, or by restrictions on the conditional probabilities. The bounded variance algorithm developed by Dagum and Luby was the first provable
Bayesian_network
Diagram that shows all possible logical relations between a collection of sets
elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science. A Venn diagram
Venn_diagram
Israeli computer scientist
sub-optimal universal coding schemes for voice coding. I. Sadeh, "Bounds on Data Compression Ratio with a given Error Probability," Probability in the Engineering
Ilan_Sadeh
O(n^{c/\log {\log {n}}})} discrepancy, for some universal constant c, with high probability (i.e. with probability 1-1/poly(n), where the exponent of the polynomial
Geometric_discrepancy
Lemma in cryptography
must also bound information held in a quantum system. Hayashi analyzed the exponential decreasing rate of leaked information for universal random privacy
Leftover_hash_lemma
Method of logical reasoning
supported not with deductive certainty, but at best with some degree of probability. Unlike deductive reasoning (such as mathematical induction), where the
Inductive_reasoning
Function used in computer cryptography
probability 3/4 (because the probability that an arbitrary p is odd is 1/2, and likewise for q, so if they're chosen independently, the probability that
One-way_function
Fundamental theorem in probability theory and statistics
In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample
Central_limit_theorem
In probability theory, a rule for assigning epistemic probabilities
principle of insufficient reason) is a rule for assigning epistemic probabilities. The principle of indifference states that in the absence of any relevant
Principle_of_indifference
Method of statistical inference
Solomonoff's universal prior probability of any prefix p of a computable sequence x is the sum of the probabilities of all programs (for a universal computer)
Bayesian_inference
Universal encoding scheme for positive integers
code is a universal code encoding positive integers developed by Peter Elias. It is used most commonly when coding integers whose upper bound cannot be
Elias_gamma_coding
Calculation of complex statistical distributions
is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution, one can construct a Markov chain whose
Markov_chain_Monte_Carlo
Mathematical methods used in Bayesian inference and machine learning
the posterior probability of the unobserved variables, in order to do statistical inference over these variables. To derive a lower bound for the marginal
Variational_Bayesian_methods
Mathematical proposition
network with N {\displaystyle N} nodes, where each edge is included with probability p {\displaystyle p} , it is unlikely for the graph to contain a Hamiltonian
Kahn–Kalai_conjecture
Counting technique in combinatorics
as the sieve formula. As finite probabilities are computed as counts relative to the cardinality of the probability space, the formulas for the principle
Inclusion–exclusion_principle
Multiple states under one central authority, usually created by conquest
every concerned case. Hence, "when the system's borders are rigid, the probability of hegemony is high". The circumscription theory was stressed in the
Empire
Number associated with self-avoiding walks
the critical probability threshold for percolation), it is nonetheless an important quantity that appears in conjectures for universal laws. Furthermore
Connective_constant
Binary sequence
sequence Gregory Chaitin Stochastics Monte Carlo method K-trivial set Universality probability Statistical randomness Li, Ming; Vitányi, P. M. (2019). "1.9 Randomness"
Algorithmically random sequence
Algorithmically_random_sequence
Rule for calculating an estimate of a given quantity based on observed data
of estimates converge in probability to the quantity being estimated as the index (usually the sample size) grows without bound. In other words, increasing
Estimator
Christian theological doctrine
retains solid (objective) probability. In estimating the degree which is required and which suffices for solid probability, moralists lay down the general
Catholic_probabilism
End of the human species
William of Ockham, and Gerolamo Cardano expanded the study of logic and probability and began wondering if abstract worlds existed, including a world without
Human_extinction
Branch of probability theory
In probability theory, the theory of large deviations concerns the asymptotic behaviour of remote tails of sequences of probability distributions. While
Large_deviations_theory
Computational statistics technique
the unconditional acceptance probability is higher the less that ratio varies, since M {\displaystyle M} is the upper bound for the likelihood ratio f (
Rejection_sampling
Problem in computer science
V(x)=U(h(x))} . An optimal machine is a universal machine that achieves the Kolmogorov complexity invariance bound, i.e. for every machine V, there exists
Halting_problem
Notion of boundary associated with a group
boundary can be characterized as a universal boundary space for harmonic analysis on the group, in the sense that bounded harmonic functions can be represented
Furstenberg_boundary
Ability of a computing system to simulate Turing machines
physical resources, so they are only linear bounded automaton complete. In contrast, the abstraction of a universal computer is defined as a device with a
Turing_completeness
a random k-dimensional subspace satisfies the above inequality with probability very close to 1. The proof gives the sharp dependence on k: N ( k , ε
Dvoretzky's_theorem
Collection of models with the same renormalization group flow limit
In statistical mechanics, an universality class is a set of mathematical models which share a scale-invariant limit under renormalization group flow. While
Universality_class
Classification algorithm in statistics
classification, the Bayes classifier is the classifier having the smallest probability of misclassification of all classes using the same set of features. Suppose
Bayes_classifier
System for reasoning about vagueness
lack of a probability theory for jointly modelling uncertainty and vagueness. Bart Kosko claims in Fuzziness vs. Probability that probability theory is
Fuzzy_logic
Eighteenth letter of the Greek alphabet
with bounded quantifiers beginning with existential quantifiers, alternating n − 1 {\displaystyle n-1} times between existential and universal quantifiers
Sigma
Concept in information theory
out that Heisenberg's uncertainty principle can be expressed as a lower bound on the sum of these entropies. This is stronger than the usual statement
Entropic_uncertainty
Generalization of conditional expectation
the notion of conditional expectation in classical probability. The space of essentially bounded measurable functions on a σ {\displaystyle \sigma }
Non-commutative conditional expectation
Non-commutative_conditional_expectation
Algorithm that employs a degree of randomness as part of its logic or procedure
an amount of time that can be bounded by a function the input size and its parameter k, but allows a small probability of error. Observe that any Las
Randomized_algorithm
Mathematical framework to model epistemic uncertainty
given hypothesis or a more specific one, thus forming a lower bound on its probability. Belief (usually denoted Bel) measures the strength of the evidence
Dempster–Shafer_theory
Principle in theoretical physics
2015. Bekenstein, Jacob D. (January 1981). "Universal upper bound on the entropy-to-energy ratio for bounded systems". Physical Review D. 23 (215): 287–298
Holographic_principle
Method for determining the origin of a packet on the Internet
encoding this. They state that this approach essentially reduces the probability of collision to (1/(211)m). For further details see Song and Perrig.
IP_traceback
Finds likely sequence of hidden states
\left|{S}\right|^{2})} . If it is known which state transitions have non-zero probability, an improved bound can be found by iterating over only those r {\displaystyle r}
Viterbi_algorithm
field E. 4. In probability theory, denotes a conditional probability. For example, P ( A / B ) {\displaystyle P(A/B)} denotes the probability of A, given
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Type of statistical analysis
points, have distribution P f {\displaystyle \mathbb {P} _{f}} . A universal lower bound on estimation for a hypothesis class H {\displaystyle {\mathcal
Nonparametric_statistics
Variable used for specification
parametric family, i.e. as an indexed family of functions. Examples from probability theory are given further below. In a section on frequently misused words
Parameter
Hypothesis about sapient life and the universe
the anthropic principle essentially just says that the conditional probability of finding yourself in a universe compatible with your existence is always
Anthropic_principle
Locally compact topological group with an invariant averaging operation
compact topological group G carrying a kind of averaging operation on bounded functions that is invariant under translation by group elements. The original
Amenable_group
Universal hash family used for message authentication in cryptography
and its derivatives against forgery follows from its bounded difference probability as a universal hash family: If m 1 {\displaystyle m_{1}} and m 2 {\displaystyle
Poly1305
Branch of statistics
of the quantity q ( θ ) {\displaystyle q(\theta )} is bounded from below by the universal bound V a r θ [ T ( X ) ] ≥ ∇ q ( θ ) I ( θ ) − 1 ∇ q ( θ )
Parametric_statistics
Quantum error correction schemes can suppress the logical error rate arbitrarily low
circuit on n qubits and containing p(n) gates may be simulated with probability of error at most ε using O ( log c ( p ( n ) / ε ) p ( n ) ) {\displaystyle
Threshold_theorem
Theorem in probability
The Khintchine inequality, is a result in probability also frequently used in analysis bounding the expectation a weighted sum of Rademacher random variables
Khintchine_inequality
Mathematical description of quantum state
interpretation of quantum mechanics, the Born rule, relating transition probabilities to inner products. The Schrödinger equation determines how wave functions
Wave_function
Quantum ergodicity states, roughly, that in the high-energy limit, the probability distributions associated to energy eigenstates of a quantized ergodic
Quantum_ergodicity
Generalization of the concept from statistical mechanics
The partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the
Partition function (mathematics)
Partition_function_(mathematics)
Functional relationship between two quantities
obey the treasured paradigm of statistical completeness. Especially probability bounds, the suspected cause of typical bending and/or flattening phenomena
Power_law
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
Method of deriving conclusions
many three-valued systems. Some many-valued logics take the form of probability logics, which make it possible to reason from uncertain information to
Rule_of_inference
Hash functions computed by exclusive or
the probability that those keys are mapped to those values is 1/mk. 2-independent hashing schemes are automatically universal, and any universal hashing
Tabulation_hashing
Question of whether inductive reasoning leads to definitive knowledge
induction helps to establish the grounds for probability, as he writes in A Treatise of Human Nature that "probability is founded on the presumption of a resemblance
Problem_of_induction
Theory of probability
In the theory of probability, the Glivenko–Cantelli theorem (sometimes referred to as the fundamental theorem of statistics), named after Valery Ivanovich
Glivenko–Cantelli_theorem
Short story by Jorge Luis Borges
majority of the books in this universe are pure gibberish, the laws of probability dictate that the library also must contain, somewhere, every coherent
The_Library_of_Babel
Mapping arbitrary data to fixed-size values
that is, any key will map to any particular slot with probability 1/m, a characteristic of universal hash functions. While Knuth worries about adversarial
Hash_function
Computer hardware technology that uses quantum mechanics
machine with an error probability of at most 1/3. As a class of probabilistic problems, BQP is the quantum counterpart to BPP ("bounded error, probabilistic
Quantum_computing
Process of copying a quantum state with no modification of the original
photons of any polarization with equally likely probability. This symmetry ensures the universality of the machine. When input states are restricted
Quantum_cloning
Everywhere except a set of measure zero
of measure zero. In probability theory, the terms almost surely, almost certain and almost always refer to events with probability 1 not necessarily including
Almost_everywhere
Concept in topology
extension, β X {\displaystyle \beta X} is characterized by a universal property: every bounded continuous function on X extends uniquely to a continuous
Stone–Čech_compactification
Statistical concept
null is true, then the probability that a product of e-values will ever become larger than 1 / α {\displaystyle 1/\alpha } is bounded by α {\displaystyle
E-values
Possibility of something bad happening
assessment. In particular, because of bounded rationality, the risk of extreme events is discounted because the probability is too low to evaluate intuitively
Risk
Foundational principle in quantum physics
}{2}}.~} In particular, the above Kennard bound is saturated for the ground state n=0, for which the probability density is just the normal distribution
Uncertainty_principle
Australian and American mathematician (born 1975)
László; Yau, Horng-Tzer; Yin, Jun (2012). "Bulk universality for generalized Wigner matrices". Probability Theory and Related Fields. 154 (1–2): 341–407
Terence_Tao
Algorithm to be run on quantum computers
BQP (bounded-error quantum polynomial time) is the set of decision problems solvable by a quantum computer in polynomial time with error probability of
Quantum_algorithm
Deep learning method
mathematical theory behind these methods. In modern probability theory based on measure theory, a probability space also needs to be equipped with a σ-algebra
Generative adversarial network
Generative_adversarial_network
entails that all incomes are at least the lower bound xm, which is positive. At this income the probability density suddenly jumps up from zero and then
Pareto_index
UNIVERSAL PROBABILITY-BOUND
UNIVERSAL PROBABILITY-BOUND
Boy/Male
Hindu
Universal
Boy/Male
Hindu, Indian, Sanskrit, Telugu
Universal
Girl/Female
Greek
Universal.
Girl/Female
Indian
Universal
Boy/Male
Hindu
Universal
Girl/Female
Arabic
Universal
Girl/Female
Tamil
Sarvika | ஸரà¯à®µà®¿à®•à®¾
Universal
Sarvika | ஸரà¯à®µà®¿à®•à®¾
Boy/Male
Slavic
Universal.
Boy/Male
Tamil
Universal
Girl/Female
Greek
Universal.
Boy/Male
Tamil
Vishavam | வீஷாவாம
Universal
Vishavam | வீஷாவாம
Girl/Female
Tamil
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Indian, Punjabi, Sikh
Universal
Girl/Female
Greek
Universal.
Girl/Female
Swedish American Teutonic English German
Universal.
Girl/Female
Arabic, Muslim
Universal
Boy/Male
Indian, Sanskrit
Universal
Girl/Female
Hindu, Indian
Universal
Girl/Female
Greek
Universal.
Girl/Female
Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Tamil, Telugu
Universal
UNIVERSAL PROBABILITY-BOUND
UNIVERSAL PROBABILITY-BOUND
UNIVERSAL PROBABILITY-BOUND
UNIVERSAL PROBABILITY-BOUND
UNIVERSAL PROBABILITY-BOUND
UNIVERSAL PROBABILITY-BOUND
UNIVERSAL PROBABILITY-BOUND