Statistics — Page 9
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Bayesian two-way ANOVA
Bayesian two-way ANOVA extends the classical two-way analysis of variance by replacing p-values with Bayes factors and posterior distributions. It quantifies evidence for or against main effects and their interaction using prior-weighted mo...
Beneish M-Score
The Beneish M-Score is a statistical model developed by Messod Beneish in 1999 to identify whether a company has manipulated its reported earnings. The model combines eight financial-statement ratios into a single composite score using coef...
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...
Besag-York-Mollie Model
The Besag-York-Mollie (BYM) model is the workhorse hierarchical Bayesian model for small-area disease mapping. Proposed by Julian Besag, Jeremy York, and Annie Mollie (1991), it models area-level disease counts with a Poisson likelihood who...
Beta Regression
Beta regression is a generalized linear model introduced by Ferrari and Cribari-Neto (2004) for outcomes that are rates or proportions confined to the open interval (0,1). It models the mean of a beta-distributed response through a link fun...
Between Estimator
The Between Estimator is a panel data regression technique that identifies regression coefficients exclusively from cross-sectional variation across individuals, by collapsing the panel to individual-specific time-averaged observations and...
Bid-Rent Analysis
Bid-rent analysis is the urban-economics theory that explains how land rent and land use are organized by distance to the city centre. Developed by William Alonso in 1964, it represents each land use — commerce, industry, housing — by a bid...
Binomial Option Pricing
The binomial option pricing model, introduced by John Cox, Stephen Ross, and Mark Rubinstein in 1979, prices options by modelling the underlying as a discrete tree in which the price moves up or down by fixed factors at each step. Working b...
Binomial Test
The exact binomial test checks whether the observed number of successes in a fixed number of independent trials is consistent with a pre-specified success probability p₀. Because it computes exact binomial tail probabilities rather than rel...
Bioequivalence Analysis
Bioequivalence Analysis is a regulatory-grade statistical framework used to determine whether a test drug formulation (generic or reformulated) delivers the active ingredient to the systemic circulation at a rate and extent comparable to a...
Biological Age Estimation
Biological age estimation seeks to measure how old a person's body actually is, as distinct from the number of years since their birth. The most influential statistical approach is the Klemera-Doubal method (KDM), introduced in 2006, which...
Biplot
A biplot is a low-dimensional graphical representation of a multivariate data matrix that simultaneously displays both the observations (rows) and the variables (columns) as points or vectors in the same plot. Introduced by Ruben Gabriel in...
Bivariate Probit
The Bivariate Probit Model, introduced by Ashford and Sowden (1970), jointly estimates two binary outcome equations whose error terms are allowed to be correlated. By modeling both outcomes simultaneously under a bivariate normal distributi...
Black-Litterman Model
The Black-Litterman model, introduced by Fischer Black and Robert Litterman in 1992, is a Bayesian portfolio allocation framework that blends market-equilibrium returns with an investor's own views to produce more stable, intuitive portfoli...
Black-Scholes Model
The Black-Scholes-Merton model, published by Fischer Black and Myron Scholes in 1973 with the theoretical framework extended by Robert Merton, gives a closed-form no-arbitrage price for European options. By assuming the underlying asset fol...
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...
Block Bootstrap
Block bootstrap is a resampling method for dependent, autocorrelated time-series data: instead of resampling single observations, it resamples whole blocks of consecutive observations so the serial-correlation structure is preserved. The mo...
Bonferroni Correction
The Bonferroni correction is a conservative, universally applicable method for controlling the family-wise error rate (FWER) when conducting multiple simultaneous hypothesis tests. Grounded in Bonferroni's 1936 probability inequality and fo...
Bonus-Malus System
A Bonus-Malus System (BMS) is an actuarial experience-rating mechanism used primarily in automobile insurance to adjust individual policyholders' premiums based on their personal claim history. Policyholders who remain claim-free receive pr...
Bootstrap Inference
Bootstrap inference, introduced by Bradley Efron in 1979, estimates the sampling distribution of a statistic by repeatedly resampling the observed data with replacement. It requires no distributional assumption and produces reliable confide...
Bootstrap Simulation with Missing Data
Bootstrap simulation with missing data combines resampling-based variance estimation with principled handling of incomplete observations. Rather than deleting cases or assuming complete data, the method integrates imputation or weighting di...
Brand-Switching Markov Model
The brand-switching Markov model treats a consumer's sequence of brand purchases as a Markov chain, in which the probability of buying a given brand next depends only on the brand bought last. Its central object is the brand-to-brand transi...
Brass Relational Logit Model
The Brass relational logit model is a two-parameter system for representing and smoothing a life table by relating it to a chosen standard. Introduced by William Brass in 1971, it transforms the survivorship function with a logit and posits...
Breakdown Point Analysis
Breakdown point analysis quantifies the fraction of outliers an estimator can tolerate before it produces meaningless results. Formalised by Hampel (1971) and Donoho and Huber (1983), it is the standard tool for comparing the robustness of...