Statistics — Page 3
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
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...
BCa Bootstrap
The BCa bootstrap is a resampling method, introduced by Bradley Efron in 1987, that produces more accurate confidence intervals than the plain percentile bootstrap by applying a bias correction and an acceleration adjustment. It is recommen...
BEKK-GARCH
BEKK-GARCH, proposed by Engle and Kroner (1995), is a multivariate GARCH specification that models the time-varying conditional covariance matrix of a system of financial return series. Named after Baba, Engle, Kraft, and Kroner, it is the...
BG/NBD Model
The BG/NBD (Beta-Geometric/Negative Binomial Distribution) model is a probabilistic buy-till-you-die model that predicts how many times a customer will transact in the future and whether that customer is still active, using only their past...
BIS/BAS Scales
The BIS/BAS Scales, developed by Carver and White in 1994, are self-report measures of two fundamental motivational systems proposed by Gray's reinforcement sensitivity theory. The Behavioral Inhibition System (BIS) governs sensitivity to p...
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 mode...
Banister TRIMP
The Training Impulse (TRIMP) model, developed by Eric Banister and colleagues (1975), quantifies the physiological stimulus of a training session by combining duration and intensity. The Banister fitness-fatigue model proposes that training...
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 be...
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 va...
Bass Diffusion Model
The Bass diffusion model is a parsimonious mathematical model of how a new product or technology spreads through a market over time, introduced by Frank Bass in 1969. It represents adoption as the combined effect of two forces—external infl...
Bates Model
The Bates model (1996) combines stochastic volatility and jump diffusion to capture both the volatility smile and the implied volatility skew observed in equity and currency option markets. It extends the Heston model by adding a Poisson ju...
Bayes Factor Test
The Bayes factor test, formalised by Harold Jeffreys in 1961, is a Bayesian method for comparing two competing hypotheses. Rather than returning a binary reject/retain verdict, it produces a continuous ratio BF₁₀ that quantifies how much mo...
Bayesian ADF unit root test
The Bayesian Augmented Dickey-Fuller (BADF) unit root test re-frames the classical ADF test within a Bayesian framework. Rather than computing a frequentist p-value, it quantifies evidence for or against a unit root by comparing posterior p...
Bayesian ANCOVA
Bayesian Analysis of Covariance (Bayesian ANCOVA) extends classical ANCOVA by placing prior distributions on group effects and covariate slopes, then updating them with observed data to obtain posterior distributions and Bayes factors. It q...
Bayesian ANOVA
Bayesian ANOVA, formalised by Rouder, Morey, Speckman and Province (2012), tests whether group means differ by quantifying the evidence for the alternative hypothesis relative to the null using the Bayes Factor (BF₁₀). Unlike classical ANOV...
Bayesian AR model
The Bayesian AR model estimates an autoregressive time-series process by combining a likelihood derived from the AR structure with prior distributions over the lag coefficients and error variance. Rather than producing single point estimate...
Bayesian ARCH model
The Bayesian ARCH model estimates Engle's Autoregressive Conditional Heteroskedasticity specification within a Bayesian framework. Instead of maximising a likelihood, it combines a prior distribution over the volatility parameters with the...
Bayesian ARDL Bounds Test
The Bayesian ARDL Bounds Test extends the classical Pesaran-Shin-Smith (2001) bounds testing approach to cointegration by embedding it within a Bayesian inferential framework. Instead of relying on frequentist F- and t-statistics with tabul...
Bayesian ARIMA model
The Bayesian ARIMA model combines the classical Box-Jenkins ARIMA framework with Bayesian inference. Instead of obtaining single point estimates for autoregressive and moving average parameters, it places prior distributions over them and u...
Bayesian ARMA model
The Bayesian ARMA model applies Bayesian inference to the classical autoregressive moving average framework for stationary univariate time series. Rather than producing single point estimates for the AR and MA parameters, it yields full pos...
Bayesian Bootstrap
The Bayesian Bootstrap, introduced by Donald B. Rubin in 1981, is a resampling method that produces a Bayesian counterpart to the frequentist bootstrap by assigning each observation a random weight drawn from a Dirichlet distribution. It yi...
Bayesian Canonical Correlation Analysis
Bayesian canonical correlation analysis is a probabilistic generative model that identifies shared latent structure between two or more sets of observed variables. It extends classical CCA by placing priors on model parameters, enabling pri...
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 probabilisti...
Bayesian Chronological Modeling
Bayesian chronological modeling refines archaeological chronologies by combining the calibrated probability distributions of individual radiocarbon dates with prior archaeological knowledge — most importantly the stratigraphic order of samp...