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Decision that leads to the best outcome in decision theory
An optimal decision is a decision that leads to at least as good a known or expected outcome as all other available decision options. It is an important
Optimal_decision
Hypothesis in neuroscience
backward Kolmogorov equations. Optimal decision problems (usually formulated as partially observable Markov decision processes) are treated within active
Free_energy_principle
Mathematical model for sequential decision making under uncertainty
above is called an optimal policy and is usually denoted π ∗ {\displaystyle \pi ^{*}} . A particular MDP may have multiple distinct optimal policies. Because
Markov_decision_process
Branch of applied probability theory
Normative decision theory is concerned with identification of optimal decisions where optimality is often determined by considering an ideal decision maker
Decision_theory
Experimental design that is optimal with respect to some statistical criterion
same precision as an optimal design. In practical terms, optimal experiments can reduce the costs of experimentation. The optimality of a design depends
Optimal_experimental_design
Necessary condition for optimality associated with dynamic programming
Optimality condition in optimal control theory Markov decision process – Mathematical model for sequential decision making under uncertainty Optimal control
Bellman_equation
Behavioral ecology model
explained by the optimal foraging theory. In each case, there are costs, benefits, and limitations that ultimately determine the optimal decision rule that the
Optimal_foraging_theory
Decision support tool
to generate such optimal trees have been devised, such as ID3/4/5, CLS, ASSISTANT, and CART. Among decision support tools, decision trees (and influence
Decision_tree
Process to choose a course of action
found that rats and humans can optimally accumulate incoming sensory evidence, to make statistically optimal decisions. Another study found that lesions
Decision-making
Machine learning algorithm
algorithm where locally optimal decisions are made at each node. Such algorithms cannot guarantee to return the globally optimal decision tree. To reduce the
Decision_tree_learning
Measure of value difference between best possible decision and made decision
actual decision made and what would have been the optimal decision in hindsight. Unlike traditional models that consider regret as merely a post-decision emotional
Regret_(decision_theory)
Mathematical relation assigning a probability event to a cost
choose the optimal action under the actual observed data to obtain a uniformly optimal one, whereas choosing the actual frequentist optimal decision rule as
Loss_function
Empirical law on the variance of species in a habitat
Binns, MR; Bostonian, NJ (1990). "Robustness in empirically based binomial decision rules for integrated pest management". J Econ Entomol. 83 (2): 420–442
Taylor's_law
Algorithms to decode messages
metric for hard decision Viterbi decoders. The squared Euclidean distance is used as a metric for soft decision decoders. Optimal decision decoding algorithm
Decoding_methods
Mathematical problem involving optimal stopping theory
scenario involving optimal stopping theory that is studied extensively in the fields of applied probability, statistics, and decision theory. It is also
Secretary_problem
Bet sizing formula for long-term growth
finding the optimal set S o {\displaystyle S^{o}} of outcomes on which it is reasonable to bet and it gives explicit formula for finding the optimal fractions
Kelly_criterion
Discipline covering formal decision making
Prescriptive decision-making research focuses on how to make "optimal" decisions (based on the axioms of rationality), while descriptive decision-making research
Decision_analysis
Graphical representation of the distribution of numerical data
the minimum number of bins required for an asymptotically optimal histogram, where optimality is measured by the integrated mean squared error. The bound
Histogram
Unit of information
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Data
Middle quantile of a data set or probability distribution
pp. 43. ISBN 978-0-521-13250-3. DeGroot, Morris H. (1970). Optimal Statistical Decisions. McGraw-Hill Book Co., New York-London-Sydney. p. 232. ISBN 9780471680291
Median
Probabilistic problem-solving algorithm
"Estimation and nonlinear optimal control: Particle resolution in filtering and estimation". Studies on: Filtering, optimal control, and maximum likelihood
Monte_Carlo_method
Trading of favors by legislative members
regardless, individuals will always choose the option they value most. Decisions reach an optimum only when they are unanimous, when votes are not coerced and everyone
Logrolling
Generalization of a Markov decision process
exact solution to a POMDP yields the optimal action for each possible belief over the world states. The optimal action maximizes the expected reward (or
Partially observable Markov decision process
Partially_observable_Markov_decision_process
Least-weight tree connecting graph vertices
is optimal - no algorithm can do better than the optimal decision tree. Thus, this algorithm has the peculiar property that it is provably optimal although
Minimum_spanning_tree
Experimental design framework
experimental design is to a certain extent based on the theory for making optimal decisions under uncertainty. The aim when designing an experiment is to maximize
Bayesian_experimental_design
Type of statistical measure over subsets of a dataset
by updating an indexable skiplist. Statistically, the moving average is optimal for recovering the underlying trend of the time series when the fluctuations
Moving_average
Process of using data analysis for predicting population data from sample data
formulated by Fraser has close links to decision theory and Bayesian statistics and can provide optimal frequentist decision rules if they exist. See Universal
Statistical_inference
Mathematical concept
f(x^{*})} ) is called Pareto optimal if there does not exist another solution that dominates it. The set of Pareto optimal outcomes, denoted X ∗ {\displaystyle
Multi-objective_optimization
expectation is met. Contrast alternative hypothesis. opinion poll optimal decision optimal design outlier p-value pairwise independence A set of random variables
Glossary of probability and statistics
Glossary_of_probability_and_statistics
Statistical measure of association
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Cramér's_V
Weakly optimal allocation of resources
identify a single "best" (optimal) outcome. Instead, it only identifies a set of outcomes that might be considered optimal, by at least one person. Formally
Pareto_efficiency
Concept in decision-making
exploitation opportunity. Finding the optimal balance between these two strategies is a crucial challenge in many decision-making problems whose goal is to
Exploration–exploitation dilemma
Exploration–exploitation_dilemma
Concept in machine learning
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Double_descent
Range to estimate an unknown parameter
/ 2 ) {\displaystyle (\theta -1/2,\theta +1/2)} distribution. Then the optimal 50% confidence procedure for θ {\displaystyle \theta } is X ¯ ± { | X 1
Confidence_interval
Function of the observed sample results
revised with further experimentation. In contrast, decision procedures require a clear-cut decision, yielding an irreversible action, and the procedure
P-value
Making of satisfactory, not optimal, decisions
moment rather than an optimal solution. Therefore, humans do not undertake a full cost-benefit analysis to determine the optimal decision, but rather, choose
Bounded_rationality
Problem of allocation of money by consumers in order to most benefit themselves
so does the decision of the consumer. Consumer can modify their decisions due to a change of preference over time (for example in an optimal choice of consumption
Utility_maximization_problem
Statistical measure of how far values spread from their average
factor that performs better than the corrected sample variance, though the optimal scale factor depends on the excess kurtosis of the population (see Mean
Variance
Subset of decision science
likely to make an optimal decision. But if people do not share all of their information, the group may make a sub-optimal decision. Stasser and Titus
Group_decision-making
1970s paradigm shift in economic thought, named for American economist Robert Lucas
structure of an econometric model consists of optimal decision rules of economic agents, and that optimal decision rules vary systematically with changes in
Lucas_critique
Statistical measure of variability
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Median_absolute_deviation
Study of health and disease within a population
prevent diseases. It is a cornerstone of public health, and shapes policy decisions and evidence-based practice by identifying risk factors for disease and
Epidemiology
Measure of linear correlation
Retrieved 22 August 2020. Moriya, N. (2008). "Noise-related multivariate optimal joint-analysis in longitudinal stochastic processes". In Yang, Fengshan
Pearson correlation coefficient
Pearson_correlation_coefficient
Heuristic search algorithm for evaluating game trees
tree search (MCTS) is a heuristic tree search algorithm for some kinds of decision processes, most notably those employed in software that plays board games
Monte_Carlo_tree_search
Study of collection and analysis of data
generally concerned with the use of data in the context of uncertainty and decision-making in the face of uncertainty. Statistics is indexed at 62, a subclass
Statistics
Interpretation of probability
Princeton University Press. DeGroot, Morris (2004) [1970]. Optimal Statistical Decisions. Wiley Classics Library. Wiley. ISBN 0-471-68029-X.. Hacking
Bayesian_probability
Experiment methodology
companies now use the "designed experiment" approach to making marketing decisions, with the expectation that relevant sample results can improve positive
A/B_testing
Method of data analysis
linearly related as: q = α p {\displaystyle q=\alpha p} . To find the optimal linear relationship, we minimize the total squared reconstruction error:
Principal_component_analysis
Measure of statistical dispersion
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Interquartile_range
Statistic measuring inter-rater agreement for categorical items
14/16 or 0.875. The disagreement is due to quantity because allocation is optimal. κ is 0.01. The disagreement proportion is 2/16 or 0.125. The disagreement
Cohen's_kappa
Time at which a random variable stops exhibiting a behavior of interest
and which will almost always lead to a decision to stop at some finite time. Stopping times occur in decision theory, and the optional stopping theorem
Stopping_time
Measure of variation in statistics
Retrieved 30 September 2014. Kessy, A.; Lewin, A.; Strimmer, K. (2018). "Optimal whitening and decorrelation". The American Statistician. 72 (4): 309–314
Standard_deviation
Statistical considerations on how many observations to make
sub-sample sizes). Selecting these nh optimally can be done in various ways, using (for example) Neyman's optimal allocation. There are many reasons to
Sample_size_determination
Statistical modeling method
_{i}(y_{i}-{\vec {\beta }}\,\cdot \,{\vec {x_{i}}})^{2}} . As shown below the same optimal parameter that minimizes L ( D , β → ) {\displaystyle L(D,{\vec {\beta
Linear_regression
Scientific procedure performed to validate a hypothesis
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Experiment
Numerical measure of a statistical relationship between variables
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Correlation_coefficient
Statistical test comparing two probability distributions
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Kolmogorov–Smirnov_test
Set of statistical processes for estimating the relationships among variables
distinguished between two inhomogeneous sets of data and might have thought of an optimal solution in terms of bias, though not in terms of effectiveness." He previously
Regression_analysis
Nonparametric measure of rank correlation
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Number taken as representative of a list of numbers
(2009). "The Generalized Hybrid Averaging Operator and its Application in Decision Making". Journal of Quantitative Methods for Economics and Business Administration
Average
Method to measure individual sensitivity
decision is made when sufficient evidence has accumulated favoring one alternative over the other. — Bogacz et al., The Physics of Optimal Decision Making
Two-alternative_forced_choice
Design of tasks
first English-language publication on an optimal design for regression models in 1876. A pioneering optimal design for polynomial regression was suggested
Design_of_experiments
Statistical relationship
function. This density is both a Bayesian posterior density and an exact optimal confidence distribution density. The information given by a correlation
Correlation
Statistic which divides a data set into 100 parts and analyzes it as a percentage
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Percentile
Test of normality in frequentist statistics
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Shapiro–Wilk_test
Measure of the joint variability
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Covariance
Fundamental theorem in probability theory and statistics
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Central_limit_theorem
Type of "good" decision rule in Bayesian statistics
Statistical Decision Theory and Bayesian Analysis (2nd ed.). Springer-Verlag. ISBN 0-387-96098-8. DeGroot, Morris (2004) [1st. pub. 1970]. Optimal Statistical
Admissible_decision_rule
Fourth standardized moment in statistics
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Kurtosis
Class of statistical models
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Generalized_linear_model
Data visualization
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Box_plot
Type of numerical analysis
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Isotonic_regression
Statistical methods for comparing samples
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Two-proportion_Z-test
decisive advantage for finding the optimal limiting value. A simple suboptimal rule, which performs almost as well as the optimal rule within the class of memoryless
Robbins'_problem
Method of estimating the parameters of a statistical model
University Press. ISBN 978-0-521-83971-6. DeGroot, M. (1970). Optimal Statistical Decisions. McGraw-Hill. ISBN 0-07-016242-5. Sorenson, Harold W. (1980)
Maximum a posteriori estimation
Maximum_a_posteriori_estimation
Method of statistical inference
Adrian F. M. (1994). Bayesian Theory. Wiley. DeGroot, Morris H., Optimal Statistical Decisions. Wiley Classics Library. 2004. (Originally published (1970)
Bayesian_inference
Method of plotting numeric data
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Violin_plot
Theory and technique of psychological measurement
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Psychometrics
Type of chart
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Bar_chart
Generates a forecast of future values of a time series
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Exponential_smoothing
Diagnostic plot of binary classifier ability
probability on the x-axis. ROC analysis provides tools to select possibly optimal models and to discard suboptimal ones independently from (and prior to
Receiver operating characteristic
Receiver_operating_characteristic
Statistical model for a binary dependent variable
processing. Disaster planners and engineers rely on these models to predict decisions taken by householders or building occupants in small-scale and large-scales
Logistic_regression
Circular statistical graph of proportionality
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Pie_chart
Psychological illusion about the future
much they will change in the future, but in doing so jeopardize their optimal decision making. The reason for the illusion has not been studied, although
End-of-history_illusion
Theory of pathological and excessive empathy
According to Saad, suicidal empathy is the inability to implement optimal decisions when one is psychologically conditioned to prioritize empathy or displays
Suicidal_empathy
Method of statistical inference
number of other approaches to reaching a decision based on data are available via decision theory and optimal decisions, some of which have desirable properties
Statistical_hypothesis_test
Plot using the dispersal of scattered dots to show the relationship between variables
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Scatter_plot
Value that appears most often in a set of data
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Mode_(statistics)
Non-probabilistic decision-making model
worst-case outcomes – the optimal decision is one with the least bad outcome. It is one of the most important models in robust decision making in general and
Wald's_maximin_model
Measure of the asymmetry of random variables
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Skewness
Complete set of items that share at least one property in common
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Statistical_population
Statistical sampling technique
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Latin_hypercube_sampling
Apparent lack of pattern or predictability in events
other with another goat), the player must decide to either keep their decision, or to switch and select the other door. Intuitively, one might think the
Randomness
Statistical hypothesis test
of freedom, the error in this approximation would not affect practical decisions. This conclusion caused some controversy in practical applications and
Chi-squared_test
Statistical test
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Z-test
Estimator for quality of a statistical model
is not asymptotically optimal under the assumption. Yang additionally shows that the rate at which AIC converges to the optimum is, in a certain sense
Akaike_information_criterion
Collection of statistical models
to the significance level (α). The ANOVA F-test is known to be nearly optimal in the sense of minimizing false negative errors for a fixed rate of false
Analysis_of_variance
Statistical hypothesis test
statistic might not follow a t distribution, while the dependent t-test is sub-optimal as it discards the unpaired data. Most two-sample t-tests are robust to
Student's_t-test
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics
Coefficient_of_variation
Concept in inferential statistics
271–316. ISBN 978-1-4129-0546-6. Borror, Connie M. (2009). "Statistical decision making". The Certified Quality Engineer Handbook (3rd ed.). Milwaukee,
Statistical_significance
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