按方法、领域与证据探索科学。

Freeze-Drying (Lyophilization)

Freeze-drying, also called lyophilization, is a low-temperature dehydration process in which water is first frozen solid and then removed by sublimation under reduced pressure, bypassing the liquid phase entirely. Widely used in food science, pharmaceuticals, and biotechnology, it preserves the physical structure, nutr

statistics

Frequency analysis

Frequency analysis is a fundamental descriptive technique that tallies how often each distinct value or category appears in a dataset. It produces absolute counts, relative percentages, and cumulative frequencies, giving an immediate picture of how observations are distributed across categories. It is the natural first

statistics

Friedman test

The Friedman test is a nonparametric hypothesis test that compares three or more related conditions measured on the same blocks or subjects, serving as the rank-based alternative to repeated-measures ANOVA. It was introduced by Milton Friedman in 1937 and works on ordinal or continuous data without assuming normality.

psychometrics

Fuzzy ANOVA

Fuzzy ANOVA extends classical analysis of variance to fuzzy data where observations and group memberships are imprecise or uncertain. Developed by Viertl and others, Fuzzy ANOVA tests whether fuzzy-valued groups differ significantly while accounting for inherent measurement uncertainty.

statistics

Games-Howell Test

The Games-Howell test is a parametric post-hoc multiple comparison procedure that identifies which pairs of group means differ significantly after an omnibus ANOVA reveals a significant overall effect. Proposed by Games and Howell in 1976, it is specifically designed for situations where group variances and/or sample s

statistics

GAMLSS

GAMLSS is a broad class of semi-parametric regression models introduced by Robert Rigby and Mikis Stasinopoulos in 2005. Unlike classical regression, which models only the mean of a response, GAMLSS allows each parameter of a chosen parametric distribution — location (e.g., mean), scale (e.g., variance), and shape (e.g

statistics

Gamma Regression

Gamma regression is a generalized linear model that uses the gamma distribution to model a positive, right-skewed continuous outcome. Developed within the GLM framework of McCullagh and Nelder (1989), it is an alternative to ordinary linear regression for variables such as health-care costs, durations, and income.

econometrics

GARCH

GARCH is an econometric model for the time-varying volatility of financial time series, introduced by Tim Bollerslev in 1986 as a generalisation of Engle's ARCH model. It treats the conditional variance as a function of past squared shocks and past variances, capturing the volatility clustering seen in returns.

econometrics

GARCH Model

The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, introduced by Tim Bollerslev in 1986, models the time-varying conditional variance of a financial time series. It captures volatility clustering and the ARCH effect, and is the standard tool for estimating risk and volatility in return series.

econometrics

GARCH-MIDAS

GARCH-MIDAS decomposes volatility into short-term (GARCH) and long-term (MIDAS) components, allowing low-frequency macroeconomic variables to drive medium-term volatility while high-frequency returns govern daily fluctuations. Introduced by Engle and Ghysels (2012), this framework elegantly separates volatility time sc

machine learning

Gaussian Process

A Gaussian Process (GP) is a non-parametric, fully probabilistic machine learning model that places a prior distribution directly over functions. Rather than predicting a single value, it returns a predictive mean and a calibrated uncertainty estimate at every test point, making it especially valuable for regression on

spatial analysis

Geary's C

Geary's C is a global measure of spatial autocorrelation — whether nearby locations tend to have similar values — introduced by Roy Geary in 1954. Unlike Moran's I, which is built on the covariation of values around the mean, Geary's C is built on the squared differences between neighbouring values, making it more sens

spatial analysis

Geary's C

Geary's C is a global spatial autocorrelation statistic that measures whether nearby areal units share similar attribute values. Unlike Moran's I, it focuses on squared differences between adjacent pairs rather than cross-products of deviations from the mean, making it more sensitive to local dissimilarity and less inf

statistics

Generalized Least Squares

Generalized Least Squares (GLS) is a linear regression estimator that extends ordinary least squares to handle situations where the error terms are correlated or have non-constant variance (heteroscedasticity). Introduced by Alexander Craig Aitken in 1935, GLS achieves the Best Linear Unbiased Estimator (BLUE) under a

statistics

Generalized Linear Model

The Generalized Linear Model is a unified regression framework that extends ordinary linear regression to outcomes from the exponential family — including binary, count, proportion, and continuous positive outcomes. A link function connects the linear predictor to the mean of the response, enabling principled modelling

forensics

Geographic Profiling

Geographic profiling is a spatial analysis method used in forensic investigation to locate offenders based on the locations of their crimes. Developed by David Canter in 1994, it combines geostatistics, probability theory, and crime pattern analysis to identify high-probability crime origin zones. The method has been w

econometrics

Geographic Regression Discontinuity

Geographic Regression Discontinuity (GRD) is a quasi-experimental design that exploits sharp geographic boundaries—borders, policy boundaries, or natural features—to estimate causal effects. Introduced by Dell (2010) and others, it compares outcomes on either side of a boundary where treatment changes abruptly, leverag

spatial analysis

Geographically Weighted PCA

Geographically Weighted Principal Component Analysis (GWPCA) is a local dimensionality-reduction method introduced by Harris, Brunsdon, and Charlton in 2011. It extends classical PCA by fitting a separate weighted PCA at every location in a dataset, allowing eigenstructures — the principal components and their loadings

spatial analysis

Geographically Weighted Random Forest

Geographically Weighted Random Forest (GWRF) is a spatially local ensemble learning method that fits an independent Random Forest model at each observation location, weighting nearby training samples more heavily than distant ones through a spatial kernel function. It was introduced by Stefanos Georganos and colleagues

spatial analysis

Geographically Weighted Regression

Geographically Weighted Regression is a local regression method, introduced by Fotheringham, Brunsdon and Charlton (2002), that allows the regression coefficients to vary across space. Instead of one global equation, it fits a separate set of coefficients at every location, capturing spatial heterogeneity in the relati

spatial analysis

Getis-Ord Gi*

Getis-Ord Gi* is a local spatial statistic, introduced by Getis and Ord in 1992 and refined in 1995, that compares the value at each location and its neighbours against the global mean to identify statistically significant clusters of high values (hot spots) and low values (cold spots).

econometrics

Giacomini-White Test

The Giacomini-White (GW) test, introduced by Raffaella Giacomini and Halbert White in 2006, evaluates whether two competing forecasting methods have equal conditional predictive ability given information available at the time of forecast. Unlike unconditional tests such as the Diebold-Mariano test, it asks whether one

bayesian

Gibbs Sampling

Gibbs sampling is a Markov chain Monte Carlo algorithm that approximates a high-dimensional posterior distribution by repeatedly drawing each parameter from its full conditional distribution given all other parameters and the data. Because each draw is exact from a conditional — not a proposal that may be rejected — th

bayesian

Gibbs Sampling for Model Comparison

Gibbs sampling for model comparison is a Bayesian MCMC approach that simultaneously samples from the space of competing models and their parameters. By augmenting the Gibbs sampler with a discrete model-index variable, posterior model probabilities and Bayes factors are estimated from the resulting Markov chain without

bayesian

Gibbs Sampling with Measurement Error

Gibbs sampling with measurement error is a Bayesian MCMC method that jointly estimates unknown true covariate values and model parameters when the observed data are corrupted by measurement error. By treating the latent true values as additional unknowns, it samples all quantities iteratively from their full conditiona

bayesian

Gibbs Sampling with Missing Data

Gibbs sampling with missing data treats unobserved values as additional unknowns alongside model parameters and samples all of them jointly within a Markov chain Monte Carlo loop. The method alternates between drawing the missing values from their conditional distribution given the parameters and drawing the parameters

spatial analysis

GIS-MCDA

GIS-MCDA combines the map layers of a geographic information system with multi-criteria decision analysis to produce suitability or priority maps — ranking locations by how well they satisfy several weighted criteria at once. It is the standard framework for spatial decisions such as siting hospitals, solar farms, land

econometrics

GJR-GARCH

GJR-GARCH is a variant of the GARCH conditional-volatility model that captures the asymmetric effect of negative shocks on volatility using an indicator variable. It was introduced by Glosten, Jagannathan and Runkle (1993), with a closely related threshold formulation by Zakoian (1994).

spatial analysis

Global Co-Kriging

Global Co-Kriging is a multivariate geostatistical interpolation method that estimates an unsampled primary variable by exploiting its spatial cross-correlation with one or more secondary variables. Unlike local (moving-window) approaches, it fits a single set of variogram and cross-variogram models to the entire study

spatial analysis

Global Getis-Ord Gi*

The Global Getis-Ord Gi* statistic measures the overall degree of spatial clustering of high or low values across an entire study region. It answers whether the study area, taken as a whole, exhibits significant concentration of high values (hot clustering) or low values (cold clustering), returning a single summary Z-

spatial analysis

Global Hot Spot Analysis

Global Hot Spot Analysis uses the Getis-Ord G statistic to determine whether high or low attribute values are spatially concentrated across an entire study area. It answers one question: is there overall clustering of high values (a hot spot tendency) or low values (a cold spot tendency) in the dataset as a whole, prod

spatial analysis

Global Kriging

Global Kriging is the ordinary kriging interpolation procedure applied using all available sample points as the neighborhood — no spatial search window limits which data contribute to each prediction. It produces optimal linear unbiased predictions of an unobserved value at any target location, with associated predicti

spatial analysis

Global Moran's I

Global Moran's I is the most widely used single-number summary of spatial autocorrelation across an entire study area. It compares the attribute value at each location with values at neighbouring locations using a spatial weights matrix, and returns a statistic ranging from −1 (perfect dispersion) through 0 (spatial ra

spatial analysis

Global Ordinary Kriging

Global Ordinary Kriging (GOK) is the canonical geostatistical interpolation method that estimates values at unsampled locations as a weighted linear combination of nearby observations. It fits a single variogram model to the entire dataset, enforcing a global stationarity assumption, and produces optimal unbiased predi

spatial analysis

Global Remote Sensing Classification

Global Remote Sensing Classification assigns every pixel across an entire image or worldwide dataset to a discrete land-cover or thematic class. Treating the scene uniformly — rather than adapting to local subregions — this wall-to-wall approach underpins continental and global land-cover products such as GlobCover, FR

spatial analysis

Global Spatial Autocorrelation

Global Spatial Autocorrelation measures the degree to which similar values cluster together across an entire study area. Rather than identifying where clusters occur, it yields a single summary statistic — most commonly Moran's I — that quantifies whether spatial proximity coincides with value similarity, dissimilarity

spatial analysis

Global Spatial Durbin Model

The Global Spatial Durbin Model extends the spatial lag model by including not only a spatially lagged dependent variable but also spatially lagged independent variables (WX). A single set of global coefficients applies uniformly across all locations, making it suitable for estimating average spillover effects when spa

spatial analysis

Global Spatial Error Model

The Global Spatial Error Model (SEM) is a spatial regression technique that accounts for spatially autocorrelated error terms using a single, globally constant spatial parameter. It separates genuine predictor effects from spatial nuisance dependence in the residuals, yielding unbiased and efficient coefficient estimat

spatial analysis

Global Spatial Panel Model

The Global Spatial Panel Model extends panel data regression by incorporating a global spatial weights matrix that links every location to every other location simultaneously. It jointly accounts for cross-sectional spatial dependence, time-series dynamics, and individual fixed or random effects, making it the standard

spatial analysis

Global Universal Kriging

Global Universal Kriging is a geostatistical interpolation method that models a spatially varying trend (drift) as a deterministic function of coordinates and uses the entire dataset to fit both the trend coefficients and the residual variogram simultaneously. It produces optimal linear unbiased predictions together wi

econometrics

Global VAR

Global VAR (GVAR) is a large-scale macroeconomic modeling framework linking multiple countries (or regions) via trade and financial channels, allowing shocks in one country to propagate through the global system. Introduced by Pesaran et al. (2004), it solves the curse of dimensionality in international VAR models by e

statistics

GMM

The Growth Mixture Model, introduced by Muthén and Shedden in 1999, is a longitudinal latent variable method that identifies distinct subpopulations — latent trajectory classes — each following its own growth curve over time. It extends the standard Latent Growth Curve (LGC) model by allowing the sample to be composed

econometrics

GMM Estimation

The Generalized Method of Moments is a general-purpose econometric estimator that recovers parameters from population moment conditions, introduced by Lars Peter Hansen in 1982. It is widely used for instrumental-variable estimation, dynamic panel-data models (the Arellano-Bond estimator), and time-series applications.

econometrics

Goldfeld-Quandt Test

The Goldfeld-Quandt test, introduced by Stephen Goldfeld and Richard Quandt in 1965, is a classical diagnostic procedure for detecting heteroskedasticity in OLS regression. It operates by sorting observations according to a variable suspected of driving variance, omitting a central block, fitting separate regressions o

model evaluation

Goodness-of-Fit

Goodness-of-fit (GOF) testing is a framework for assessing whether observed data are consistent with a hypothesized probability distribution or model. Originating from Karl Pearson's chi-square test (1900), GOF tests quantify the discrepancy between data and model predictions, yielding p-values to judge whether observe

machine learning

Gradient Boosting

Gradient Boosting is an ensemble learning method, formalised by Jerome H. Friedman in 2001, that combines a sequence of weak learners — typically shallow decision trees — so that each new tree is fitted to minimise the residual errors of the trees before it. It is the core algorithm behind popular implementations such

econometrics

Granger Causality Test

The Granger causality test is a statistical hypothesis test that determines whether past values of one time series help predict future values of another, beyond what that series' own past already explains. Introduced by Clive Granger in 1969, it is the standard approach for assessing predictive causality in VAR-based t

applied physics

Gravitational Wave Matched Filtering

Matched filtering is a signal processing technique used to detect gravitational waves by correlating detector data with theoretical waveform templates. When two massive objects (black holes, neutron stars) merge, they emit gravitational waves that pass through Earth, producing tiny distortions in laser interferometers

quantitative finance

Greeks via Automatic Differentiation

Automatic differentiation (AD) is a computational technique for computing derivatives (Greeks) by differentiating the computer code that computes the option price. AD avoids manual derivation of formulas and finite-difference approximations, yielding exact sensitivities with machine precision. It has become essential f

econometrics

Gregory-Hansen Test

The Gregory-Hansen test, introduced by Allan Gregory and Bruce Hansen in 1996, extends the standard Engle-Granger cointegration framework to allow for a single unknown structural break in the cointegrating relationship. It is designed for researchers who suspect that the long-run equilibrium between integrated variable

bayesian

Hamiltonian Monte Carlo

Hamiltonian Monte Carlo (HMC) is a gradient-based Markov chain Monte Carlo algorithm that uses the geometry of the log-posterior surface to make large, informed jumps through parameter space instead of the small random steps of classical MCMC. Originally introduced for lattice field theory by Duane, Kennedy, Pendleton,

bayesian

Hamiltonian Monte Carlo with Measurement Error

Hamiltonian Monte Carlo (HMC) with measurement error is a Bayesian computational strategy for fitting models where one or more covariates are observed with noise. HMC samples jointly from the posterior over model parameters and the unobserved true covariate values, using gradient-based proposals that explore the high-d

bayesian

Hamiltonian Monte Carlo with Missing Data

Hamiltonian Monte Carlo with missing data extends the gradient-based HMC sampler to handle incomplete observations by treating missing values as additional unknown parameters. The posterior over model parameters and missing values is sampled jointly in one efficient pass, exploiting gradient information to explore the

finance

HAR-RV Model

The HAR-RV model, introduced by Fulvio Corsi in 2009, forecasts realized volatility by decomposing it into daily, weekly, and monthly components. It is a simple linear regression that mirrors how market participants with different investment horizons react to volatility, and it naturally captures the long-memory behavi

econometrics

Hatemi-J Asymmetric Causality

The Hatemi-J asymmetric causality test, introduced by Abdulnasser Hatemi-J in 2012, extends the Granger causality framework to allow causal relationships between the positive and negative components of integrated time series to differ. By decomposing each series into cumulative positive and negative partial sums and em

econometrics

Hatemi-J Cointegration Test

The Hatemi-J cointegration test, introduced by Abdulnasser Hatemi-J in 2008, tests for a long-run equilibrium relationship between integrated time series while allowing for up to two unknown structural breaks in the cointegrating vector. It extends earlier single-break approaches by permitting both the intercept and sl

econometrics

Hausman Test

The Hausman test is a specification test, introduced by Jerry A. Hausman in 1978, that decides between the fixed-effects (FE) and random-effects (RE) estimators in panel data models. The null hypothesis is that the random-effects estimator is consistent and efficient and should be preferred; the alternative is that ran

econometrics

Heckman Selection Model

The Heckman selection model, introduced by James J. Heckman in 1979, is a two-step model that corrects sample selection bias when the outcome is only observed for a non-random subset of cases. A probit selection equation models who is observed, and the outcome equation then corrects for the resulting bias using the inv

economics

Hedonic Pricing

The hedonic pricing model, developed by Sherwin Rosen in 1974 and building on Kevin Lancaster's characteristics theory (1966), is an econometric method for valuing the implicit prices of product attributes by regressing market prices on observed characteristics. It reveals the trade-offs consumers are willing to make a

statistics

Heteroscedasticity-Robust Standard Errors

Heteroscedasticity-robust standard errors are a correction to the covariance matrix of an OLS regression that yields valid inference when the error variance is not constant. Introduced by Halbert White in 1980 and refined into the finite-sample variants HC1-HC4 by MacKinnon and White in 1985, they leave the coefficient