按方法、领域与证据探索科学。

ANCOVA

ANCOVA is a parametric hypothesis test that compares the adjusted means of two or more independent groups while statistically controlling for one or more continuous covariates. By removing the portion of outcome variance explained by the covariate, ANCOVA increases statistical precision and produces fairer group compar

econometrics

ARIMA

ARIMA is a univariate time-series forecasting model that combines autoregressive, integrated (differencing), and moving-average components to predict a single continuous series from its own past. It is the centrepiece of the Box-Jenkins methodology set out in Box, Jenkins, Reinsel & Ljung's Time Series Analysis (5th ed

causal inference

Bayesian Causal Impact Analysis

Bayesian Causal Impact Analysis uses a Bayesian structural time series (BSTS) model to estimate the causal effect of an intervention on a time series outcome. Developed by Brodersen and colleagues at Google in 2015, it builds a probabilistic counterfactual — what the series would have looked like without the interventi

epidemiology

Cox proportional hazards

The Cox proportional hazards model is a semi-parametric regression method that estimates the effect of one or more covariates on the hazard — the instantaneous rate of an event such as death, relapse, or failure — while making no assumption about the shape of the baseline hazard function. Introduced by David Cox in 197

econometrics

Difference-in-Differences

Difference-in-Differences is a causal-inference method that estimates the effect of an intervention by comparing how a treatment group and a control group change over time. Made famous by Card and Krueger's 1994 minimum-wage study and developed in Angrist and Pischke's Mostly Harmless Econometrics, it isolates the trea

experimental design

A/B Test

An A/B test is a randomized controlled experiment that simultaneously exposes two groups of users to a control variant (A) and a treatment variant (B) in order to determine whether a measured outcome differs significantly between them. The modern online controlled experiment framework was systematized by Ron Kohavi and

statistics

Anderson-Darling Test

The Anderson-Darling test is an empirical distribution function (EDF) goodness-of-fit test, introduced by Anderson and Darling in 1952, that checks whether a continuous sample comes from a specified distribution such as the normal, exponential, or Weibull. By weighting deviations more heavily in the tails, it detects d

econometrics

ARCH model

The ARCH model, introduced by Robert Engle in 1982, captures time-varying volatility in financial and macroeconomic time series. It models the conditional variance of today's error as a function of past squared errors, explaining why volatile periods cluster together — a phenomenon known as volatility clustering.

econometrics

ARCH-LM Test

The ARCH-LM test is Robert Engle's (1982) Lagrange multiplier diagnostic for autoregressive conditional heteroscedasticity in the residuals of a fitted time-series model. It checks whether the error variance changes over time and clusters into calm and turbulent periods, and it is the standard pre-test run before fitti

econometrics

ARMA model

The ARMA(p,q) model describes a stationary time series as a combination of two components: an autoregressive part that regresses the current value on its own past p values, and a moving average part that accounts for past q error terms. It is the foundational framework of the Box-Jenkins methodology for univariate time

econometrics

Augmented Dickey-Fuller unit root test

The Augmented Dickey-Fuller test is the standard procedure for determining whether a univariate time series contains a unit root — that is, whether the series is non-stationary. It extends the original Dickey-Fuller test by including lagged difference terms that absorb serial correlation in the residuals, making the te

statistics

Barnard's Exact Test

Barnard's exact test is an unconditional exact hypothesis test for comparing two independent proportions in a 2×2 contingency table, proposed by George A. Barnard in 1945. Unlike Fisher's exact test, it does not condition on both margins being fixed, and is generally more powerful when column totals are not predetermin

psychometrics

Bayesian Confirmatory Factor Analysis

Bayesian confirmatory factor analysis tests a pre-specified factor structure using Bayesian inference. Instead of point estimates with p-values, it produces full posterior distributions for loadings, factor correlations, and residual variances, allowing the researcher to incorporate prior knowledge and propagate parame

causal inference

Bayesian Counterfactual Impact Evaluation

Bayesian Counterfactual Impact Evaluation estimates the causal effect of an intervention by constructing a Bayesian posterior distribution over the counterfactual outcome — what would have happened without treatment. The method, popularized by Brodersen et al. (2015) through the CausalImpact framework, uses Bayesian st

causal inference

Bayesian Difference-in-Differences

Bayesian Difference-in-Differences applies Bayesian statistical inference to the classic DiD design, replacing frequentist point estimates with full posterior distributions over the treatment effect. This yields not only an estimate of the causal effect but also a coherent probability statement about its magnitude and

econometrics

Bayesian Random Effects Model

The Bayesian random effects model combines panel-data random effects with a Bayesian prior framework, allowing unit-specific effects to be treated as draws from a population distribution whose hyperparameters are estimated from the data. This produces regularised, uncertainty-quantified estimates that borrow strength a

econometrics

Bayesian SARIMA Model

The Bayesian SARIMA model combines the classical Box-Jenkins Seasonal ARIMA framework with Bayesian inference to handle seasonal time-series data. Rather than producing a single point estimate, it yields a full posterior distribution over model parameters, propagating parameter uncertainty directly into forecasts and e

econometrics

Bayesian System GMM

Bayesian System GMM combines the Blundell-Bond System Generalized Method of Moments estimator for dynamic panel data with Bayesian prior distributions and posterior inference via MCMC. It handles endogeneity, individual fixed effects, and weak-instrument problems while incorporating prior knowledge and delivering full

statistics

Benjamini-Hochberg Procedure

The Benjamini-Hochberg (BH) procedure, introduced by Yoav Benjamini and Yosef Hochberg in 1995, controls the false discovery rate (FDR) — the expected proportion of false positives among all rejected hypotheses — rather than the probability of any false positive. By tolerating a controlled fraction of false discoveries

statistics

Bland-Altman Analysis

The Bland-Altman analysis is a graphical and statistical technique for assessing agreement between two measurement methods applied to the same subjects. Introduced by J. Martin Bland and Douglas G. Altman in their landmark 1986 Lancet paper, it plots the difference between the two methods against their mean for each su

causal inference

Causal Impact Analysis

Causal Impact Analysis, introduced by Brodersen et al. (2015) at Google, uses Bayesian structural time-series models to estimate what would have happened to an outcome had an intervention never occurred. By constructing a probabilistic counterfactual from pre-treatment data and control covariates, it quantifies point-i

econometrics

Fourier Random Effects Model

The Fourier Random Effects Model extends the standard random effects panel estimator by incorporating trigonometric (Fourier) terms to approximate smooth, gradual structural change in time trends or intercepts. It retains the GLS efficiency advantages of the random effects estimator while allowing parameters to shift c

econometrics

Granger Causality

The Granger causality test, introduced by Clive W. J. Granger in 1969, assesses whether the past values of one time series help predict another beyond what the latter's own past already explains. It defines causality in a strictly predictive sense rather than as a structural or physical cause.

statistics

MANCOVA

MANCOVA (Multivariate Analysis of Covariance) is a parametric hypothesis test that simultaneously compares two or more groups on multiple continuous dependent variables while statistically controlling for one or more covariates. It extends MANOVA by incorporating covariate adjustment, a tradition consolidated in multiv

causal inference

Marginal Structural Model

A marginal structural model is a causal modeling framework designed to estimate the effect of a time-varying treatment in the presence of time-varying confounders that are themselves affected by prior treatment. By reweighting observations with inverse probability of treatment weights, MSMs create a pseudo-population i

statistics

Multivariate Regression

Multivariate regression is a linear regression method that predicts several continuous dependent variables at the same time from a shared set of predictors. As developed in standard treatments such as Johnson and Wichern's Applied Multivariate Statistical Analysis (2007), each response equation can be fitted by ordinar

statistics

One-sample t-test

The one-sample t-test is a parametric hypothesis test that determines whether the mean of a single sample differs significantly from a known or hypothesized population value. Derived from Student's (Gosset's) 1908 t-distribution, it assumes continuous, approximately normally distributed data and is one of the most fund

econometrics

Threshold Regression

Threshold regression is a nonlinear, regime-switching model in which the regression parameters take different values above and below an estimated threshold value of a threshold variable. The sample-splitting and threshold-estimation framework was developed by Bruce E. Hansen (2000) and is widely used for time-series an

econometrics

2SLS Regression

Two-Stage Least Squares is a two-step instrumental-variables estimator that addresses endogeneity, the situation where a regressor is correlated with the error term. In the first stage the endogenous regressor is predicted from instrumental variables, and in the second stage the structural equation is estimated using t

survival

Accelerated Failure Time Model

The Accelerated Failure Time model is a parametric regression approach to survival analysis — formally reviewed and advocated by L. J. Wei in 1992 — in which covariates act as multiplicative factors that directly stretch or compress the time-to-event scale. Unlike the Cox proportional-hazards model, which models how co

machine learning

Active learning Gaussian process

Active Learning Gaussian Process (GP-AL) combines a Gaussian process probabilistic model with an active learning query strategy, using the GP's posterior uncertainty to select the most informative unlabeled examples for labeling. This iterative approach minimizes labeling effort while maximizing predictive accuracy, ma

machine learning

Active Learning Logistic Regression

Active Learning with Logistic Regression is an iterative label-efficient framework in which a logistic regression model selects the unlabeled examples it is most uncertain about, an oracle (human annotator) labels them, and the model is retrained — repeating until a labeling budget or accuracy target is met. It dramati

experimental design

Adaptive A/B test

An Adaptive A/B test is an experimental design that dynamically reallocates traffic or participants toward better-performing variants during the experiment itself, rather than holding allocations fixed until the end. Drawing on multi-armed bandit algorithms such as Thompson Sampling or Upper Confidence Bound (UCB), it

epidemiology

Adaptive Competing Risks Analysis

Adaptive competing risks analysis combines the Fine-Gray subdistribution hazard framework — which models the cumulative incidence of one cause of failure in the presence of other mutually exclusive causes — with adaptive or group-sequential interim monitoring rules. This allows a clinical trial or observational study t

epidemiology

Adaptive Cox Proportional Hazards

The Adaptive Cox Proportional Hazards model extends the classic Cox regression for time-to-event outcomes by adding adaptive LASSO (or related) penalization. It simultaneously estimates hazard ratios and performs variable selection, shrinking irrelevant covariate coefficients exactly to zero. This makes it especially v

statistics

Adjusted Boxplot

The Adjusted Boxplot is a robust descriptive tool introduced by Hubert and Vandervieren (2008) that corrects the classical IQR-based boxplot for skewness using the medcouple statistic, reducing the false labelling of outliers in asymmetric data.

statistics

Aligned Rank Transform ANOVA

The Aligned Rank Transform ANOVA (ART-ANOVA) is a nonparametric factorial hypothesis test that detects main effects and interactions in designs with two or more independent variables, without requiring normality. The procedure was formalized by Wobbrock, Findlater, Gergle, and Higgins in their 2011 CHI paper and operat

finance

Altman Z-Score

The Altman Z-Score is a linear discriminant model developed by Edward I. Altman in 1968 to predict corporate bankruptcy using five accounting-based financial ratios. Derived through multiple discriminant analysis on a matched sample of 66 US manufacturing firms, the model combines liquidity, profitability, leverage, so

research statistics

Analysis of Variance (ANOVA)

ANOVA is a parametric statistical method developed by Ronald A. Fisher in 1925 that tests whether means differ significantly across three or more independent groups. By partitioning total variance into between-group and within-group components, ANOVA determines whether observed differences are likely due to treatment e

accounting

Analytical Procedures in Auditing

Analytical procedures are evaluations of financial information made by studying plausible relationships among both financial and non-financial data. Rather than testing individual transactions, auditors develop expectations about what numbers should be and compare them to actual results, investigating significant diffe

econometrics

Anderson-Hsiao IV

The Anderson-Hsiao IV estimator is a method for consistently estimating dynamic panel data models that include a lagged dependent variable as a regressor. Proposed by Theodore Anderson and Cheng Hsiao in 1981, it resolves the Nickell bias that arises when fixed effects are eliminated by first-differencing, by instrumen

econometrics

APARCH

APARCH, introduced by Ding, Granger, and Engle (1993) while studying long-memory properties of stock market returns, extends the GARCH family by allowing both the power transformation of conditional volatility and an asymmetric response to positive and negative shocks. The model nests at least seven well-known ARCH-typ

simulation

Approximate Bayesian Computation

Approximate Bayesian Computation (ABC) is a family of simulation-based inference methods that estimate posterior distributions without requiring an analytically tractable likelihood function. Introduced by Beaumont, Zhang and Balding (2002) in the context of population genetics, ABC replaced the intractable likelihood

bayesian

Approximate Bayesian Computation with Measurement Error

Approximate Bayesian Computation with measurement error (ABC-ME) extends the standard ABC likelihood-free framework to settings where observed data are themselves noisy or imprecisely recorded. By explicitly incorporating a measurement-error kernel into the acceptance step, ABC-ME targets the correct posterior over mod

bayesian

Approximate Bayesian Computation with Missing Data

Approximate Bayesian Computation with missing data extends the likelihood-free ABC framework to settings where observations are incomplete or partially recorded. By simulating data under a posited model and accepting parameter draws whose simulated summary statistics are close to the observed ones, it bypasses the need

econometrics

ARDL Bounds Test

The ARDL bounds test is an autoregressive distributed lag method that tests for a cointegrating (long-run level) relationship between time series, introduced by Pesaran, Shin and Smith in 2001. Unlike the Johansen procedure, it remains valid whether the variables are I(0), I(1) or a mix of the two, and it is more relia

econometrics

Arellano-Bond GMM estimator

The Arellano-Bond GMM estimator is the standard approach for dynamic panel data models in which the lagged dependent variable appears as a regressor. By first-differencing to remove fixed effects and using deeper lags as instruments, it yields consistent estimates even when the error is serially correlated and regresso

econometrics

ARFIMA Model

ARFIMA is a time series model that captures long-memory behaviour using a fractional differencing parameter d, generalising the integer differencing of ARIMA. It was introduced by Granger and Joyeux (1980) and formalised by Hosking (1981) to describe series whose autocorrelations decay slowly rather than abruptly.

econometrics

ARIMA model

The ARIMA(p,d,q) model is the standard workhorse for univariate time series forecasting. It combines autoregressive terms (past values), differencing to induce stationarity, and moving average terms (past shocks) into a unified linear framework. Developed by Box and Jenkins (1970), it remains one of the most widely app

statistics

Attributes Control Chart

Attributes control charts extend Shewhart's framework to count and proportion data — quality characteristics that are classified rather than measured. The p- and np-charts monitor the proportion or number of defective items using the binomial distribution, while the c- and u-charts monitor the number of defects per uni

econometrics

Augmented Dickey-Fuller Test

The Augmented Dickey-Fuller (ADF) test is the most widely used test for a unit root — that is, for whether a time series is non-stationary and must be differenced before modelling. Introduced by David Dickey and Wayne Fuller in 1979 and extended by Said and Dickey in 1984 to series with higher-order autocorrelation, it

econometrics

Augmented Mean Group Estimator

The Augmented Mean Group estimator, developed by Eberhardt and Teal (2010), is a panel data method for estimating heterogeneous slope coefficients in the presence of cross-sectional dependence. It approximates the unobserved common dynamic process driving all units and folds it into unit-by-unit regressions, then avera

deep learning

Autoformer

Autoformer is a deep learning architecture for long-term time-series forecasting, introduced by Wu et al. from Tsinghua University at NeurIPS 2021. It replaces the standard self-attention mechanism with an Auto-Correlation mechanism that exploits periodic dependencies in the frequency domain, and embeds a progressive s

bayesian

Automatic Differentiation Variational Inference

Automatic Differentiation Variational Inference (ADVI) is a black-box algorithm for approximate Bayesian posterior inference, introduced by Kucukelbir, Tran, Ranganath, Gelman, and Blei (2017, JMLR). Given any probabilistic model whose log-joint density is differentiable, ADVI automatically transforms constrained laten

electrical engineering

Automatic Test Pattern Generation

Automatic Test Pattern Generation (ATPG) is the automated creation of test vectors that detect manufacturing defects in digital circuits. Pioneered by Roth in 1966, ATPG systematically finds inputs that make stuck-at faults observable at outputs, enabling comprehensive fault detection. ATPG is critical for semiconducto

econometrics

Autoregressive model

An autoregressive model of order p — AR(p) — expresses the current value of a time series as a linear function of its own p most recent past values plus a white-noise error. It is the building block of the Box-Jenkins family of time-series models and is widely used for forecasting stationary economic and financial seri

machine learning

Bagging

Bagging, short for Bootstrap Aggregating, is an ensemble meta-algorithm introduced by Leo Breiman in 1996 that trains multiple copies of a base learner on independently drawn bootstrap samples of the training data and combines their predictions — by averaging for regression or majority vote for classification — to prod

ensemble learning

Bagging Ensemble

Bagging, short for bootstrap aggregating, is an ensemble method that reduces variance by training multiple copies of a single learning algorithm on different random subsets of the training data. Each subset is created via bootstrap sampling—randomly drawing samples with replacement. Predictions are combined through maj

econometrics

Bai-Perron Test

The Bai-Perron test, introduced by Jushan Bai and Pierre Perron in their landmark 1998 Econometrica paper, is a least-squares-based procedure for detecting, estimating, and testing the number of structural breaks in a linear regression model estimated on time-series data. Unlike single-break tests, it simultaneously id

statistics

Bartlett's Test

Bartlett's Test is a classical parametric procedure for testing whether two or more independent groups share a common population variance. Introduced by Maurice Stevenson Bartlett in 1937, it formalises the null hypothesis that all group variances are equal by constructing a chi-square statistic from the ratio of poole