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9th episode of the 6th season of Star Trek: Deep Space Nine
"Statistical Probabilities" is the 133rd episode of the syndicated American science fiction television series Star Trek: Deep Space Nine, the ninth episode
Statistical_Probabilities
Interpretation of probability
probability was defined in terms of the principle of indifference, based on the natural symmetry of a problem, so, for example, the probabilities of
Frequentist_probability
American film by Vanessa Caswill
Caswill and written by Katie Lovejoy, based upon the 2011 novel The Statistical Probability of Love at First Sight by Jennifer E. Smith. It stars Haley Lu
Love at First Sight (2023 film)
Love_at_First_Sight_(2023_film)
Type of mathematical model
A statistical model represents, often in considerably idealized form, the data-generating process. When referring specifically to probabilities, the
Statistical_model
Interpretation of probability
to different probability judgments, these agents' probabilities are "personal" (but amenable to objective study). Personal probabilities are problematic
Bayesian_probability
Conditional probability used in Bayesian statistics
see also class-membership probabilities. While statistical classification methods by definition generate posterior probabilities, Machine Learners usually
Posterior_probability
Mathematical function for the probability a given outcome occurs in an experiment
In probability theory and statistics, a probability distribution describes how probabilities are assigned to the possible results of a random phenomenon—more
Probability_distribution
Distance between two statistical objects
In statistics, probability theory, and information theory, a statistical distance quantifies the distance between two statistical objects, which can be
Statistical_distance
Method of statistical inference
A statistical hypothesis test is a method of statistical inference used to decide whether the data provide sufficient evidence to reject a particular hypothesis
Statistical_hypothesis_test
Probability of an event occurring, given that another event has already occurred
the two probabilities can lead to various errors of reasoning, which is commonly seen through base rate fallacies. While conditional probabilities can provide
Conditional_probability
Concept in inferential statistics
In statistical hypothesis testing, a result has statistical significance when a result at least as extreme would be very infrequent if the null hypothesis
Statistical_significance
Study of collection and analysis of data
or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups
Statistics
Selection of data points in statistics
individuals from within a statistical population to estimate characteristics of the whole population. The subset, called a statistical sample (or sample, for
Sampling_(statistics)
Term in statistical hypothesis testing
concrete, a typical statistical test would be based on a test statistic t calculated from the sampled data, which has a particular probability distribution under
Power_(statistics)
Number measuring the chance an event occurs
theoretical probability (in contrast to empirical probability, dealing with probabilities in the context of real experiments). The probability is a number
Probability
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
Process of using data analysis for predicting population data from sample data
probabilities (i.e. probabilities conditional on the observed data), compared to the marginal (but conditioned on unknown parameters) probabilities used
Statistical_inference
Description of continuous random distribution
p_{n}} are the probabilities associated with these values. This substantially unifies the treatment of discrete and continuous probability distributions
Probability_density_function
Physics of many interacting particles
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic
Statistical_mechanics
Probability theory for low quality data
upper probabilities, or interval probabilities belief functions possibility and necessity measures lower and upper previsions comparative probability orderings
Imprecise_probability
Categorization of data using statistics
classification – Problem in machine learning and statistical classification Class membership probabilities – Machine learning problemPages displaying short
Statistical_classification
Branch of mathematics concerning probability
unification of discrete and continuous probabilities, measure-theoretic treatment also allows us to work on probabilities outside R n {\displaystyle \mathbb
Probability_theory
Type of statistical inference
approach allows probabilities to be associated with unknown parameters, where these probabilities can sometimes have a frequency probability interpretation
Frequentist_inference
Statistical property quantifying how much a collection of data is spread out
distribution is stretched or squeezed. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range
Statistical_dispersion
score statistic The result of applying a statistical algorithm to a data set. It can also be described as an observable random variable. statistical dispersion
Glossary of probability and statistics
Glossary_of_probability_and_statistics
distribution, a discrete distribution important in statistical physics which describes the probabilities of the various discrete energy levels of a system
List of probability distributions
List_of_probability_distributions
Complete set of items that share at least one property in common
all possible hands in a game of poker). In statistical inference, the population is modelled by a probability distribution with unknown parameters. By analyzing
Statistical_population
Statistical probability Statistical process control Statistical proof Statistical randomness Statistical range – see range (statistics) Statistical regularity
List_of_statistics_articles
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
Theory of statistics
make statistical inferences and decisions, much of statistical theory consists of mathematical statistics, and is closely linked to probability theory
Statistical_theory
Generalized learning mechanism
etc.) to word boundaries other than the statistical probabilities. Within a word, the transitional probability of two syllable pairs was 1.0: in the word
Statistical learning in language acquisition
Statistical_learning_in_language_acquisition
Mathematical rule for inverting probabilities
marginal probabilities. Bayes' theorem may be derived from the relation between joint and conditional probabilities. The joint probability of the events
Bayes'_theorem
Statistic quantifying the association between two events
the cell probabilities, and conversely, the cell probabilities can be recovered given knowledge of the odds ratio and the marginal probabilities P(X = 1) = p11 + p10
Odds_ratio
When the occurrence of one event does not affect the likelihood of another
conditional independence) if and only if their joint probability equals the product of their probabilities: A ∩ B ≠ ∅ {\displaystyle A\cap B\neq \emptyset
Independence (probability theory)
Independence_(probability_theory)
Philosophical interpretation of the axioms of probability
"physical" and "evidential" probabilities. Physical probabilities, which are also called objective or frequency probabilities, are associated with random
Probability_interpretations
Type of average of a collection of numbers
Meeting of the American Statistical Association, Colorado State University. pp. 68–69. Medhi, Jyotiprasad (1992). Statistical Methods: An Introductory
Arithmetic_mean
Method of statistical inference
/ˈbeɪʒən/ BAY-zhən) is a method of statistical inference in which Bayes' theorem is used to calculate a probability of a hypothesis, given prior evidence
Bayesian_inference
Kth smallest value in a statistical sample
order statistic of a statistical sample is equal to its kth-smallest value. Given a sample of size n {\displaystyle n} , the kth order statistic is denoted
Order_statistic
Quantity that indexes a parametrized family of probability distributions
and variance can generally still be regarded as statistical parameters of the population, and statistical procedures can still attempt to make inferences
Statistical_parameter
Method of quality control
Statistical process control (SPC) or statistical quality control (SQC) is the application of statistical methods to monitor and control the quality of
Statistical_process_control
Measure of statistical dispersion
Interdecile range – Statistical measure Midhinge Probable error – Measure of statistical dispersion Robust measures of scale – Statistical indicators of the
Interquartile_range
Statistical test comparing two probability distributions
of Statistical Software. 39 (11): 1–18. doi:10.18637/jss.v039.i11. Moscovich A, Nadler B (2017). "Fast calculation of boundary crossing probabilities for
Kolmogorov–Smirnov_test
Apparent lack of pattern or predictability in events
the probability of decay in a given time. Thus, quantum mechanics does not specify the outcome of individual experiments, but only the probabilities. Hidden
Randomness
Type of statistics
A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features from a collection of information
Descriptive_statistics
Non-parametric method for testing whether samples originate from the same distribution
is required to compute exact probabilities for the Kruskal–Wallis test. Existing software only provides exact probabilities for sample sizes of less than
Kruskal–Wallis_test
Class of statistical models
predicts a probability of making a yes/no choice (a Bernoulli variable) is even less suitable as a linear-response model, since probabilities are bounded
Generalized_linear_model
Theory and paradigm of statistics
form of a prior distribution. Bayesian statistical methods use Bayes' theorem to compute and update probabilities after obtaining new data. Bayes' theorem
Bayesian_statistics
Statistical hypothesis test
the test statistic approximates a chi-squared distribution more and more closely as sample sizes increase. In the 19th century, statistical analytical
Chi-squared_test
Statistic measuring inter-rater agreement for categorical items
prevalence (are the codes equiprobable or do their probabilities vary) and bias (are the marginal probabilities for the two observers similar or different).
Cohen's_kappa
Statistical model for a binary dependent variable
the probabilities that the corresponding y k {\displaystyle y_{k}} will equal one, and 1 − p k {\displaystyle 1-p_{k}} are the probabilities that
Logistic_regression
Concept in probability theory
} This is the largest absolute difference between the probabilities that the two probability distributions assign to the same event. The total variation
Total variation distance of probability measures
Total_variation_distance_of_probability_measures
Random process independent of past history
system are called transitions. The probabilities associated with various state changes are called transition probabilities. The process is characterized by
Markov_chain
Middle quantile of a data set or probability distribution
Statistical property Central tendency – Statistical value representing the center or average of a distribution Concentration of measure – Statistical
Median
specific examples taken from the parallel texts, or may calculate statistical probabilities to select a preferred option out of all possible translations
Comparison of different machine translation approaches
Comparison_of_different_machine_translation_approaches
Range to estimate an unknown parameter
variables. Let X {\displaystyle X} be a random sample from a probability distribution with statistical parameter ( θ , φ ) {\displaystyle (\theta ,\varphi )}
Confidence_interval
Function related to statistics and probability theory
independence in probability: the probabilities of two independent events happening, given a model, is the product of the probabilities. This is particularly
Likelihood_function
Distribution function associated with the empirical measure of a sample
the Dvoretzky–Kiefer–Wolfowitz inequality provides bound on the tail probabilities of n ‖ F ^ n − F ‖ ∞ {\textstyle {\sqrt {n}}\left\|{\widehat
Empirical distribution function
Empirical_distribution_function
Type of numerical analysis
also used in probabilistic classification to calibrate the predicted probabilities of supervised machine learning models. Isotonic regression for the simply
Isotonic_regression
Function of the observed sample results
metascience. In 2016, the American Statistical Association (ASA) made a formal statement that "p-values do not measure the probability that the studied hypothesis
P-value
Statistical relationship
In statistics, correlation is a type of statistical relationship between two random variables or bivariate data. It usually refers to the extent to which
Correlation
Concept in statistical estimation theory
In statistical estimation theory, the coverage probability, or coverage for short, is the probability that a confidence interval or confidence region will
Coverage_probability
Test statistic
153: Pan's procedure for the tail probabilities of the Durbin-Watson statistic". Journal of the Royal Statistical Society, Series C. 29 (2): 224–227
Durbin–Watson_statistic
Method of logical reasoning
non-random and the sample size is very small. Statistical generalizations are also called statistical projections and sample projections. An anecdotal
Inductive_reasoning
1814 essay by Pierre-Simon Laplace on probability theory and its applications
Philosophical Essay on Probabilities at Wikisource "A Philosophical Essay on Probabilities". Project Gutenberg. "A philosophical essay on probabilities (1902 English
A Philosophical Essay on Probabilities
A_Philosophical_Essay_on_Probabilities
Measure of the shape of a function
(2). American Statistical Association: 111–119. doi:10.2307/2684482. JSTOR 2684482. Feller, W. (1957-1971). An introduction to probability theory and its
Moment_(mathematics)
Single measure of some attribute of a sample
statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes
Statistic
American actor (b. 1949)
"Sharing Cher" 1997–1998 Star Trek: Deep Space Nine Episodes: "Statistical Probabilities", "It's Only a Paper Moon" 1997–1999 Star Trek: Voyager 4 episodes
Anson_Williams
Estimate of an unobservable underlying probability density function
Self-Consistent Method for Density Estimation, Journal of the Royal Statistical Society Series B: Statistical Methodology, Volume 73, Issue 3, June 2011, Pages 407–422
Density_estimation
Variable representing a random phenomenon
over which probabilities can be defined. Normally, a particular such sigma-algebra is used, the Borel σ-algebra, which allows for probabilities to be defined
Random_variable
Probability distribution of energy states of a system
states with lower energy will always have a higher probability of being occupied. The ratio of probabilities of two states is known as the Boltzmann factor
Boltzmann_distribution
Class of statistics in estimation theory
In statistical theory, a U-statistic is a class of statistics defined as the average over the application of a given function applied to all tuples of
U-statistic
Branch of statistics
application of probability theory and other mathematical concepts to statistics, as opposed to techniques for collecting statistical data. Specific mathematical
Mathematical_statistics
Concept in statistics
derivation of the result. It is a bit loose with the calculation of the probabilities. Let m , M {\displaystyle m,M} denote respectively the min and max of
Range_(statistics)
Measure of variation in statistics
having equal probabilities, the values have different probabilities, let x1 have probability p1, x2 have probability p2, ..., xN have probability pN . In this
Standard_deviation
Statistical interpretation with many tests
many statistical tests are performed on the same dataset. Each test has its own chance of a Type I error (false positive), so the overall probability of
Multiple_comparisons_problem
American academic (1922–1998)
in St. Louis. He wrote extensively on statistical mechanics and on foundations of probability and statistical inference, initiating in 1957 the maximum
Edwin_Thompson_Jaynes
Numeric quantity representing the center of a collection of numbers
denoted μ {\displaystyle \mu } or μ x {\displaystyle \mu _{x}} . Outside probability and statistics, a wide range of other notions of mean are often used
Mean
Type of statistics
even if the underlying distributional assumptions are incorrect. Robust statistical methods have been developed for many common problems, such as estimating
Robust_statistics
Probability distribution
plays a role in a number of widely used statistical analyses, including Student's t-test for assessing the statistical significance of the difference between
Student's_t-distribution
Performance metric in football and hockey
is a statistical metric in association football that assigns a probability that each shot will result in a goal. By summing these probabilities, xG is
Expected_goals
Discrete probability distribution
(1913). "On the use of the theory of probabilities in statistics relating to society". Journal of the Royal Statistical Society. 76 (2): 165–193. doi:10.2307/2340091
Poisson_distribution
Evaluates how likely it is that any difference between data sets arose by chance
chi-squared test or Pearson's χ 2 {\displaystyle \chi ^{2}} test is a statistical test applied to sets of categorical data to evaluate how likely it is
Pearson's_chi-squared_test
Estimator for quality of a statistical model
foundations of statistics and is also widely used for statistical inference. Suppose that we have a statistical model of some data. Let k be the number of estimated
Akaike_information_criterion
Number of occurrences in an experiment or study
graphically or in tabular form. They may be used as estimators of empirical probabilities or cumulative distribution functions, for instance. The relative frequency
Frequency_(statistics)
Value that appears most often in a set of data
that is most likely to be sampled. Like the statistical mean and median, the mode is a summary statistic about the central tendency of a random variable
Mode_(statistics)
Measure of total value one, generalizing probability distributions
that the probability assigned to the union of two disjoint (mutually exclusive) events by the measure should be the sum of the probabilities of the events;
Probability_measure
Statistical hypothesis test
An F-test is a statistical test that compares variances. It is used to determine if the variances of two samples, or if the ratios of variances among
F-test
Simultaneous observation and analysis of more than one outcome variable
multivariate statistical theory throughout his career, particularly in the mid-20th century. One of his key works is the book titled "Advanced Statistical Methods
Multivariate_statistics
10th episode of the 6th season of Star Trek: Deep Space Nine
Masterson as Leeta Iggy Pop as Yelgrun Episode chronology ← Previous "Statistical Probabilities" Next → "Waltz" Star Trek: Deep Space Nine season 6 List of episodes
The_Magnificent_Ferengi
Table that displays the frequency of variables
associated. The odds ratio has a simple expression in terms of probabilities; given the joint probability distribution: B = 1 B = 0 A = 1 p 11 p 10 A = 0 p 01 p
Contingency_table
Model for generating observable data in probability and statistics
degree of statistical modelling. Terminology is inconsistent, but three major types can be distinguished: A generative model is a statistical model of
Generative_model
entirely to probability. Huygens presented systematic solutions to gambling problems and introduced formulas that could calculate probabilities of different
History_of_probability
Experiment methodology
concepts such as statistical significance and the null hypothesis, which are used in statistical hypothesis testing. Modern statistical methods for assessing
A/B_testing
Statistical method for handling multiple comparisons
of the probability distribution curve. For example, in a set of data where all null hypotheses are true, 50% of results will yield probabilities between
False_discovery_rate
Logarithm of probabilities, useful for calculations
interval. Since the probabilities of independent events multiply, and logarithms convert multiplication to addition, log probabilities of independent events
Log_probability
Approximation method in statistics
chi-squared statistic, based on the minimized value of the residual sum of squares (objective function), S. The denominator, n − m, is the statistical degrees
Least_squares
Set of statistical processes for estimating the relationships among variables
In statistical modeling, regression analysis is a statistical method for estimating the relationship between a dependent variable (often called the outcome
Regression_analysis
(published 1663) – Cardano's Liber de ludo aleae attempts to calculate probabilities of dice throws. He demonstrates the efficacy of defining odds as the
Timeline of probability and statistics
Timeline_of_probability_and_statistics
Failure analysis system used in safety engineering and reliability engineering
labeled with actual numbers for failure probabilities, computer programs can calculate failure probabilities from fault trees. When a specific event is
Fault_tree_analysis
Overview of and topical guide to statistics
programming List of statistical packages List of academic statistical associations List of national and international statistical services List of statistics
Outline_of_statistics
STATISTICAL PROBABILITIES
STATISTICAL PROBABILITIES
STATISTICAL PROBABILITIES
STATISTICAL PROBABILITIES
Boy/Male
Scottish
From Mesniers.
Girl/Female
Australian, German, Turkish
Golden
Girl/Female
Tamil
Moment
Girl/Female
Muslim/Islamic
Successful
Boy/Male
Arabic, Australian, French, Indonesian, Malaysian, Muslim
Lion; Good Man
Surname or Lastname
English
English : variant spelling of Paget.
Girl/Female
Gujarati, Hindu, Indian, Kannada, Telugu
Light Climate; Goddess Lakshmi
Girl/Female
Indian
World Famous
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
A River
Female
Russian
(Юлиана) Russian form of Roman Latin Juliana, YULIANA means "descended from Jupiter (Jove)."
STATISTICAL PROBABILITIES
STATISTICAL PROBABILITIES
STATISTICAL PROBABILITIES
STATISTICAL PROBABILITIES
STATISTICAL PROBABILITIES
n.
Classified facts respecting the condition of the people in a state, their health, their longevity, domestic economy, arts, property, and political strength, their resources, the state of the country, etc., or respecting any particular class or interest; especially, those facts which can be stated in numbers, or in tables of numbers, or in any tabular and classified arrangement.
n.
The act of forming into a table or tables; as, the tabulation of statistics.
n.
A book or table, containing a calendar of days, and months, to which astronomical data and various statistics are often added, such as the times of the rising and setting of the sun and moon, eclipses, hours of full tide, stated festivals of churches, terms of courts, etc.
n.
A book published yearly; any annual report or summary of the statistics or facts of a year, designed to be used as a reference book; as, the Congregational Yearbook.
n.
An account, or formal report, of an action performed, of a duty discharged, of facts or statistics, and the like; as, election returns; a return of the amount of goods produced or sold; especially, in the plural, a set of tabulated statistics prepared for general information.
adv.
In the way of statistics.
a.
Alt. of Statistical
pl.
of Probability
a.
Of or pertaining to statistics; as, statistical knowledge, statistical tabulation.
a.
Hence: Not admitting of any doubt, condition, qualification, or discretion; not dependent on circumstances or probabilities; not speculative; compelling assent or obedience; peremptory; indisputable; decisive; as, positive instructions; positive truth; positive proof.
n.
One versed in statistics; one who collects and classifies facts for statistics.
n.
See Statistics, 2.
n.
An official registration of the number of the people, the value of their estates, and other general statistics of a country.
a.
Arranged in a schedule; as, tabular statistics.
n.
The science which has to do with the collection and classification of certain facts respecting the condition of the people in a state.
n.
Vital statistics.
n.
The branch of mathematics which studies methods for the calculation of probabilities.
n.
A statistician.