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Form of global sensitivity analysis
Variance-based sensitivity analysis (often referred to as the Sobol’ method or Sobol’ indices, after Ilya M. Sobol’) is a form of global sensitivity analysis
Variance-based sensitivity analysis
Variance-based_sensitivity_analysis
Study of uncertainty in the output of a mathematical model or system
cases, variance-based measures are more appropriate. Multiple or functional outputs: Generally introduced for single-output codes, sensitivity analysis extends
Sensitivity_analysis
by uniform distributions without variable interactions, variance based sensitivity analysis quantifies the contribution of the optimization variables
OptiSLang
Concept in mathematical modelling
populations: "'Explained variance' explains nothing."[page needed] Analysis of variance Variance reduction Variance-based sensitivity analysis Kent, J. T. (1983)
Explained_variation
Statistical measure of how far values spread from their average
In probability theory and statistics, variance is a measure of dispersion, meaning it is a measure of how far a set of numbers are spread out from their
Variance
Collection of statistical models
Analysis of variance (ANOVA) is a family of statistical methods used to compare the means of two or more groups by analyzing variance. Specifically, ANOVA
Analysis_of_variance
Italian researcher (born 1953)
global sensitivity analysis and total sensitivity indices, helping to popularize the variance-based sensitivity analysis work of the Russian mathematician
Andrea_Saltelli
Procedure for comparing multivariate sample means
In statistics, multivariate analysis of variance (MANOVA) is a procedure for comparing multivariate sample means. As a multivariate procedure, it is used
Multivariate analysis of variance
Multivariate_analysis_of_variance
Method of data analysis
orthogonal coordinate system that optimally describes variance in a single dataset. Robust and L1-norm-based variants of standard PCA have also been proposed
Principal_component_analysis
amplitude sensitivity testing (FAST) is a variance-based global sensitivity analysis method. The sensitivity value is defined based on conditional variances which
Fourier amplitude sensitivity testing
Fourier_amplitude_sensitivity_testing
Book published in 2007
Global Sensitivity Analysis. The Primer by Andrea Saltelli and other practitioners is an introduction to sensitivity analysis of model output, a discipline
Global Sensitivity Analysis. The Primer
Global_Sensitivity_Analysis._The_Primer
British statistician and geneticist (1919–2000)
Kempthorne is the founder of the "Iowa school" of experimental design and analysis of variance. Kempthorne and many of his former doctoral students have often emphasized
Oscar_Kempthorne
Non-parametric method for testing whether samples originate from the same distribution
parametric equivalent of the Kruskal–Wallis test is the one-way analysis of variance (ANOVA). A significant Kruskal–Wallis test indicates that at least
Kruskal–Wallis_test
Extension to cover cases with multiple dependent variables
Discriminant function analysis ANCOVA MANOVA [1] Statsoft Textbook, ANOVA/MANOVA. [2] French, A. et al., 2010. Multivariate analysis of variance (MANOVA). [3]
Multivariate analysis of covariance
Multivariate_analysis_of_covariance
Study of kind and quantity of error
inherent sensitivity of the function to small perturbations in its input and is independent of the implementation used to solve the problem. The analysis of
Error_analysis_(mathematics)
Mathematical analysis technique
Experimental uncertainty analysis is a technique that analyses a derived quantity, based on the uncertainties in the experimentally measured quantities
Experimental uncertainty analysis
Experimental_uncertainty_analysis
Property of a model
outputs (underfitting). The variance is an error from sensitivity to small fluctuations in the training set. High variance may result from an algorithm
Bias–variance_tradeoff
Statistical method that summarizes and/or integrates data from multiple sources
As such, this statistical approach involves extracting effect sizes and variance measures from various studies. By combining these effect sizes the statistical
Meta-analysis
Statistical analyses that were not specified before the data were seen
an analysis of variance (ANOVA). An ANOVA does not identify the group(s); for that, a post hoc analysis is required. Because each post hoc analysis is
Post_hoc_analysis
Screening method
of inputs, where the costs of estimating other sensitivity analysis measures such as the variance-based measures is not affordable. Like all screening
Elementary_effects_method
Statistical property
of heteroscedasticity is a major concern in regression analysis and the analysis of variance, as it invalidates statistical tests of significance which
Homoscedasticity and heteroscedasticity
Homoscedasticity_and_heteroscedasticity
Statistical hypothesis test
and nonparametric alternatives, see Lumley, et al. (2002). One-way analysis of variance (ANOVA) generalizes the two-sample t-test when the data belong to
Student's_t-test
Statistical model validation technique
result from this variation. The variance of F* can be large. For this reason, if two statistical procedures are compared based on the results of cross-validation
Cross-validation_(statistics)
introductory text for analysis of variance (one-way, multi-way, factorial, split-plot, and unbalanced designs). Also analysis of co-variance, multiple and partial
List of publications in statistics
List_of_publications_in_statistics
Mathematical framework for investment risk
Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of financial assets such that the expected
Modern_portfolio_theory
Statistical method
variance, with successive factoring continuing until there is no further meaningful variance left. The factor model must then be rotated for analysis
Factor_analysis
Analysis in applied statistics
F.; Cariboni, J.; Saltelli, A. (2003). "Sensitivity analysis: the Morris method versus the variance based measures" (PDF). Morris, M.D. (1991). "Factorial
Morris_method
Measure of the joint variability
component analysis to reduce feature dimensionality in data preprocessing. The principal components are the dimensions that explain the most variance in the
Covariance
Statistical indicators in signal processing
pure sine wave. Since the calculation of the Hjorth parameters is based on variance, the computational cost of this method is sufficiently low, which
Hjorth_parameters
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
distribution) are considered low-variance, while those with CV > 1 (such as a hyper-exponential distribution) are considered high-variance[citation needed]. Some
Coefficient_of_variation
Quantity in a statistical analysis
have to be taken into account. An alternative estimator used in a sensitivity analysis might assume that people, who were not followed for their vital status
Estimand
Branch of statistics
This is an inherent property of variance testing. Determining multicollinearity is useful in sensitivity analysis because the elimination of highly
Causal_inference
Measure of linear correlation
{\displaystyle r_{xy}} by substituting estimates of the covariances and variances based on a sample into the formula above. Given paired data { ( x 1 , y 1
Pearson correlation coefficient
Pearson_correlation_coefficient
Linear regression model with a single explanatory variable
mean β and variance σ 2 / ∑ i ( x i − x ¯ ) 2 , {\textstyle \sigma ^{2}\left/\sum _{i}(x_{i}-{\bar {x}})^{2}\right.,} where σ2 is the variance of the error
Simple_linear_regression
Concept in statistical analysis
Bivariate analysis is one of the simplest forms of quantitative (statistical) analysis. It involves the analysis of two variables (often denoted as X, Y)
Bivariate_analysis
Russian mathematician (1926–2025)
to sensitivity analysis include the development of the variance-based sensitivity indices which bear his name (Sobol' indices ) and Derivative-based Global
Ilya_M._Sobol'
Grouping a set of objects by similarity
Cluster analysis, or clustering, is a data analysis technique aimed at partitioning a set of objects into groups such that objects within the same group
Cluster_analysis
British polymath (1890–1962)
of data from crop experiments since the 1840s, and developed the analysis of variance (ANOVA). He established his reputation there in the following years
Ronald_Fisher
Branch of statistics
reliability analysis or reliability engineering in engineering, duration analysis or duration modelling in economics, and event history analysis in sociology
Survival_analysis
Statistical hypothesis test
exactly is the test that the variance of a normally distributed population has a given value based on a sample variance. Such tests are uncommon in practice
Chi-squared_test
Probability distribution
arises in the Bayesian analysis of data from a normal family as a compound distribution when marginalizing over the variance parameter. Student's t distribution
Student's_t-distribution
Estimator for quality of a statistical model
(with zero mean), then the model has three parameters: b0, b1, and the variance of the Gaussian distributions. Thus, when calculating the AIC value of
Akaike_information_criterion
Statistical method
estimated from the data. Bootstrapping assigns measures of accuracy (bias, variance, confidence intervals, prediction error, etc.) to sample estimates. This
Bootstrapping_(statistics)
software Analysis of categorical data Analysis of covariance Analysis of molecular variance Analysis of rhythmic variance Analysis of variance Analytic
List_of_statistics_articles
Distribution property in ecology
phenomena where the within-strata variance of its attributes' values is significantly lower than its between-strata variance, such as collections of ecological
Spatial_heterogeneity
Statistical method for resampling
therefore, a form of resampling. It is especially useful for bias and variance estimation. The jackknife pre-dates other common resampling methods such
Jackknife_resampling
Set of statistical processes for estimating the relationships among variables
523–41. Julian C. Stanley, "II. Analysis of Variance," pp. 541–554. Lindley, D.V. (1987). "Regression and correlation analysis," New Palgrave: A Dictionary
Regression_analysis
Month of 1926
Ilya Sobol, Lithuanian-born Russian mathematician known for variance-based sensitivity analysis (the "Sobol indices") and for the Sobol sequence; in Panevėžys
August_1926
Statistical measure of variability
estimator of scale than the sample variance or standard deviation, it works better with distributions without a mean or variance, such as the Cauchy distribution
Median_absolute_deviation
Method of representing a random variable
computation of PCE-based sensitivity indices. Similar results can be obtained for Kriging. Surrogate model Variance-based sensitivity analysis Karhunen–Loève
Polynomial_chaos
Statistical analysis where the sample size is not fixed in advance
In statistics, sequential analysis or sequential hypothesis testing is statistical analysis where the sample size is not fixed in advance. Instead data
Sequential_analysis
Statistical hypothesis test for forecasting
are not able to detect Granger causality in higher moments, e.g., in the variance. Non-parametric tests for Granger causality are designed to address this
Granger_causality
Statistical test
Mauchly's W is a statistical test used to validate a repeated measures analysis of variance (ANOVA). It was developed in 1940 by John Mauchly. Sphericity is
Mauchly's_sphericity_test
Estimate of an interval in which future observations will fall
future observation X in a normal distribution N(μ,σ2) with known mean and variance may be calculated from γ = P ( ℓ < X < u ) = P ( ℓ − μ σ < X − μ σ < u
Prediction_interval
Method used in statistics, pattern recognition, and other fields
later classification. LDA is closely related to analysis of variance (ANOVA) and regression analysis, which also attempt to express one dependent variable
Linear_discriminant_analysis
Decision support tool
Kamiński, B.; Jakubczyk, M.; Szufel, P. (2017). "A framework for sensitivity analysis of decision trees". Central European Journal of Operations Research
Decision_tree
Statistical property
of transformations); for example, the sample variance is a biased estimator for the population variance. These are all illustrated below. An unbiased
Bias_of_an_estimator
Statistical distribution for dependence between random variables
rate prediction using the combination of singular spectrum analysis and copula-based analysis approach". PeerJ. 10 e14601. Bibcode:2022PeerJ..1014601N.
Copula_(statistics)
Statistical interpretation with many tests
focus on correcting for modest numbers of comparisons, often in an analysis of variance. A different set of techniques have been developed for "large-scale
Multiple_comparisons_problem
Statistical measure of the magnitude of a phenomenon
size confidence intervals and tests of close fit in the analysis of variance and contrast analysis" (PDF). Psychological Methods. 9 (2): 164–182. doi:10
Effect_size
Naturally occurring variation in transistor attributes
and predictable variance in the output performance of all circuits but particularly analog circuits due to mismatch. If the variance causes the measured
Process variation (semiconductor)
Process_variation_(semiconductor)
Form of causal modeling that fit networks of constructs to data
of methodologies that seeks to represent hypotheses about the means, variances, and covariances of observed data in terms of a smaller number of 'structural'
Structural_equation_modeling
Open platform for multi-objective optimization
sensitivity analysis has to be used based on a variance-relationship between input and output distribution, such as the Sobol index. With sensitivity
Kimeme
Variable representing a random phenomenon
The purely mathematical analysis of random variables is independent of such interpretational difficulties, and can be based upon a rigorous axiomatic
Random_variable
Statistic measuring inter-rater agreement for categorical items
Gottman, J.M. (1997). Observing interaction: An introduction to sequential analysis (2nd ed.). Cambridge, UK: Cambridge University Press. ISBN 978-0-521-27593-4
Cohen's_kappa
Test used in statistics
statistics, an F-test of equality of variances is a test for the null hypothesis that two normal populations have the same variance. Notionally, any F-test can
F-test of equality of variances
F-test_of_equality_of_variances
Approximation method in statistics
calculation is similar in both cases. Polynomial least squares describes the variance in a prediction of the dependent variable as a function of the independent
Least_squares
Procedure to estimate standard deviation from a sample
result that s2 is an unbiased estimator for the variance σ2 of the underlying population if that variance exists and the sample values are drawn independently
Unbiased estimation of standard deviation
Unbiased_estimation_of_standard_deviation
Periodicity computation method
analysis for unevenly sampled data, one that mitigates these difficulties and has some other very desirable properties, was developed by Lomb, based in
Least-squares spectral analysis
Least-squares_spectral_analysis
Method for uncertainty and sensitivity analysis
input variables for decomposition. One can use sensitivity indices (see variance-based sensitivity analysis) to define the most influential variables for
Simulation_decomposition
Process of understanding a complex topic or substance
method used for data analysis. Among the many such methods, some are: Analysis of variance (ANOVA) – a collection of statistical models and their associated
Analysis
Simultaneous observation and analysis of more than one outcome variable
MVA, each with its own type of analysis: Multivariate analysis of variance (MANOVA) extends the analysis of variance to cover cases where there is more
Multivariate_statistics
Middle quantile of a data set or probability distribution
optimization-based definition of the median is useful in statistical data-analysis, for example, in k-medians clustering. If the distribution has finite variance,
Median
Statistical method for handling multiple comparisons
motivated by, the development in technologies that allowed the collection and analysis of a large number of distinct variables in several individuals (e.g., the
False_discovery_rate
Concept in machine learning
result in a significant overfitting error (an extrapolation of the bias–variance tradeoff), and the empirical observations in the 2010s that some modern
Double_descent
Number of values in the final calculation of a statistic that are free to vary
of linear models, including linear regression and analysis of variance. An explicit example based on comparison of three means is presented here; the
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
Signal processing computational method
Component Analysis by Aapo Hyvärinen, Juha Karhunen, and Erkki Oja This approximation also suffers from the same problem as kurtosis (sensitivity to outliers)
Independent component analysis
Independent_component_analysis
Application of statistical techniques to biological systems
design, data collection methods, data analysis perspectives and costs involved. It is essential to carry the study based on the three basic principles of experimental
Biostatistics
Interpretation of probability
first mathematical treatment of a non-trivial problem of statistical data analysis using what is now known as Bayesian inference. Mathematician Pierre-Simon
Bayesian_probability
Form of cognitive behavioral psychotherapy
psychopathology. A 2005 meta-analysis showed that the six ACT principles, on average, account for 16–29% of the variance in psychopathology (general mental
Acceptance and commitment therapy
Acceptance_and_commitment_therapy
Table that displays the frequency of variables
theory of evolution. Dulau and Co. Ferguson, G. A. (1966). Statistical analysis in psychology and education. New York: McGraw–Hill. Smith, S. C., & Albaum
Contingency_table
Type of Monte Carlo algorithms for signal processing and statistical inference
criterion reflects the variance of the weights. Other criteria can be found in the article, including their rigorous analysis and central limit theorems
Particle_filter
Non-parametric statistical test
repeated measures analysis of variance by ranks. In its use of ranks it is similar to the Kruskal–Wallis one-way analysis of variance by ranks. The Friedman
Friedman_test
Statistical test used to test homoscedasticity
"homogeneity of variance"), that is, if multiple samples are from populations with equal variances. Some statistical tests, such as the analysis of variance, assume
Bartlett's_test
composite analysis#Model identification). In the following, it is assumed that the weights are scaled in such a way that each composite has a variance of one
Confirmatory composite analysis
Confirmatory_composite_analysis
Concept in probability theory and statistics
the variance of Y that is unrelated to Z) is to be explained, so there is less variance of the type that ex cannot explain. In time series analysis, the
Partial_correlation
comparable. Test for common-method variance. The choice of analyses to assess the data quality during the initial data analysis phase depends on the analyses
Data_analysis
Experiment in which information about the test is masked to reduce bias
controlled trials for chronic pain (5.6%). The study concluded, based on an analysis of pooled data, that the overall quality of blinding was poor and
Blinded_experiment
Correlation of a signal with a time-shifted copy of itself, as a function of shift
the variance of a linear combination of the X {\displaystyle X} 's, the variance calculated may turn out to be negative. In time series analysis, the
Autocorrelation
Diagnostic plot of binary classifier ability
Zhang, Jun; Mueller, Shane T. (2005). "A note on ROC analysis and non-parametric estimate of sensitivity". Psychometrika. 70: 203–212. CiteSeerX 10.1.1.162
Receiver operating characteristic
Receiver_operating_characteristic
Class of statistical models
response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized
Generalized_linear_model
Statistical measure of association
using the Pearson's chi-squared test.[citation needed] The formula for the variance of V=φc is known. In R, the function cramerV() from the package rcompanion
Cramér's_V
Portion of the electromagnetic spectrum that is visible to the human eye
superposition of the contributing visual opsins. Variance in the position of the individual opsin spectral sensitivity functions therefore affects the luminous
Visible_spectrum
studentized residuals: Internally studentized residuals: These use a variance estimate based on the entire dataset, including the observation being tested.
Studentization
Fourth standardized moment in statistics
test based on a combination of the sample skewness and sample kurtosis, as is the Jarque–Bera test for normality. For non-normal samples, the variance of
Kurtosis
Metric for fit of statistical models
(see Pearson's chi-square test). In the analysis of variance, one of the components into which the variance is partitioned may be a lack-of-fit sum of
Goodness_of_fit
Statistical measure used in survey research
design on the variance of an estimator for some parameter of a population. It is calculated as the ratio of the variance of an estimator based on a sample
Design_effect
Statistical considerations on how many observations to make
intervals and risk of errors in statistical hypothesis testing. using a target variance for an estimate to be derived from the sample eventually obtained, i.e
Sample_size_determination
Source of statistical bias
literature to reduce aggregation bias during regression analysis. A researcher might correct the variance-covariance matrix using samples from individual-level
Modifiable_areal_unit_problem
Statistical phenomenon
Maher, Mike; Mountain, Linda (2009). "The sensitivity of estimates of regression to the mean". Accident Analysis & Prevention. 41 (4): 861–8. doi:10.1016/j
Regression_toward_the_mean
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