按方法、领域与证据探索科学。

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 jump component to returns, making it suitable for pricing options when sudden pric

bayesian

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 more (or less) probable the data are under the alternative hypothesis H₁ than unde

machine learning

Bayesian Active Learning

Bayesian Active Learning (BAL) combines a probabilistic model with an active query strategy to identify the unlabeled examples that, once labeled, would most reduce model uncertainty. Instead of labeling data at random, BAL guides an oracle — typically a human annotator — toward the points where labeling will provide t

econometrics

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 probabilities or Bayes factors under the null (unit root) and alternative (statio

simulation

Bayesian Agent-Based Modeling

Bayesian Agent-Based Modeling integrates Bayesian statistical inference with agent-based simulation to calibrate model parameters and quantify uncertainty. Rather than fixing agent rules and parameters by assumption, this approach treats unknown parameters as probability distributions and updates them systematically ag

statistics

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 quantifies evidence for group differences on a continuous outcome after statistic

bayesian

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 ANOVA, it can also measure evidence in favour of the null hypothesis, making it equa

econometrics

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 estimates, it yields full posterior distributions, enabling principled uncertainty quant

econometrics

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 data likelihood to obtain a full posterior distribution, providing richer uncert

econometrics

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 tabulated critical values, the researcher specifies prior distributions on the model

econometrics

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 uses observed data to update beliefs into a full posterior distribution, enabling

econometrics

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 posterior distributions, naturally incorporating prior knowledge and providing cohe

machine learning

Bayesian Association Rules

Bayesian Association Rules extend classical association rule mining by placing a prior probability distribution over rules and scoring them by their posterior probability given the data. Rather than thresholding on raw support and confidence counts, this Bayesian framework naturally penalises complexity, corrects for m

machine learning

Bayesian Autoencoder Anomaly Detection

Bayesian Autoencoder Anomaly Detection uses a Variational Autoencoder — a probabilistic generative model trained on normal data — to flag anomalies by their high reconstruction error or low likelihood under the learned distribution. By treating the latent space as a probability distribution rather than a fixed point, i

machine learning

Bayesian Bagging

Bayesian Bagging replaces the classical bootstrap with the Bayesian bootstrap — drawing Dirichlet-distributed weights over training observations rather than sampling with replacement — and trains an ensemble of base learners under those weights. The result is a principled ensemble that approximates a Bayesian posterior

network analysis

Bayesian Betweenness Centrality

Bayesian Betweenness Centrality estimates how often a node lies on shortest paths in a network while explicitly quantifying uncertainty arising from incomplete, sampled, or noisy edge observations. Rather than producing a single point estimate, it yields a posterior distribution over betweenness scores, enabling credib

machine learning

Bayesian Boosting

Bayesian boosting integrates probabilistic Bayesian inference with boosting ensemble techniques, combining multiple weak learners while maintaining full uncertainty quantification over predictions. Unlike standard gradient boosting that produces a single point estimate, Bayesian boosting yields a posterior distribution

statistics

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 yields a full posterior distribution for a statistic and allows prior information

experimental design

Bayesian Box-Behnken Design

Bayesian Box-Behnken Design combines the classical Box-Behnken three-level design structure with Bayesian statistical inference to fit and optimize response surface models. It uses mid-edge and center points to efficiently estimate a second-order polynomial response surface while incorporating prior knowledge about mod

statistics

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 principled uncertainty quantification, automatic determination of the number of sha

epidemiology

Bayesian Case Series

Bayesian case series is an observational epidemiological method that applies Bayesian inference to case series data — typically records of patients who experienced both a drug or vaccine exposure and an adverse health event. By incorporating prior evidence and computing posterior estimates of the incidence rate ratio w

epidemiology

Bayesian Case-Control Study

A Bayesian case-control study applies Bayesian statistical inference to the classic case-control epidemiological design, formally combining prior knowledge about exposure-disease associations with observed case and control data to estimate posterior odds ratios and credible intervals. Rather than relying solely on obse

epidemiology

Bayesian Case-Crossover Design

The Bayesian case-crossover design is a self-matched epidemiological method that estimates the transient effect of a time-varying exposure on the risk of an acute event. Each case serves as their own control, eliminating confounding by time-stable individual characteristics. Bayesian inference replaces or supplements t

simulation

Bayesian Cellular Automata

Bayesian Cellular Automata (BCA) couples the local-rule spatial dynamics of classical cellular automata with Bayesian inference to learn or calibrate transition probabilities from observed data. Rather than fixing rules by hand, the analyst encodes prior knowledge about how cells change state and updates those beliefs

statistics

Bayesian chi-square test

The Bayesian chi-square test evaluates independence or goodness-of-fit in frequency tables using Bayes factors rather than classical p-values. It quantifies evidence for or against an association between categorical variables, updating prior beliefs with observed counts and delivering an odds-like ratio that distinguis

bioinformatics

Bayesian ChIP-seq peak calling

Bayesian ChIP-seq peak calling applies probabilistic models — typically Poisson, negative binomial, or hidden Markov models with Bayesian inference — to detect genomic regions enriched for a protein of interest in chromatin immunoprecipitation followed by sequencing experiments. By explicitly modelling read-count noise

statistics

Bayesian Cluster Analysis

Bayesian cluster analysis assigns observations to latent groups by combining a probabilistic model of within-cluster data with prior beliefs about cluster parameters and the number of clusters. It yields posterior probabilities of cluster membership and principled uncertainty estimates, making it more transparent than

spatial analysis

Bayesian Co-Kriging

Bayesian Co-Kriging is a multivariate geostatistical method that uses auxiliary spatially correlated variables to improve predictions of a primary variable of interest. By placing Bayesian priors on cross-covariance parameters, it propagates all uncertainty — including parameter uncertainty — into the prediction interv

causal inference

Bayesian Coarsened Exact Matching

Bayesian Coarsened Exact Matching (Bayesian CEM) combines the coarsening-and-exact-matching framework of Iacus, King, and Porro with Bayesian posterior inference. Covariates are discretised into coarser bins so that treated and control units can be matched exactly within those bins, and Bayesian priors are then placed

research design

Bayesian Cohort Research

Bayesian cohort research follows a defined group of individuals over time to track outcomes, and uses Bayesian statistical inference to update beliefs about risk, incidence, or causal effects as follow-up data accumulate. Prior knowledge — from earlier studies, registries, or expert judgment — is formalised into a prio

epidemiology

Bayesian Cohort Study

A Bayesian cohort study follows a defined group of individuals over time to estimate incidence, risk, or rate of outcomes, while using Bayesian statistical inference to incorporate prior knowledge and quantify uncertainty through posterior probability distributions rather than classical p-values and confidence interval

network analysis

Bayesian Community Detection

Bayesian community detection infers latent group structure in networks by treating community membership as unobserved variables and using Bayesian inference — typically via Markov chain Monte Carlo or variational methods — to compute a posterior distribution over all plausible partitions. Unlike modularity optimisation

epidemiology

Bayesian Competing Risks Analysis

Bayesian competing risks analysis is a time-to-event method for settings where subjects can fail from more than one mutually exclusive cause — such as death from cancer versus death from cardiovascular disease — and prior knowledge or small-sample uncertainty makes a Bayesian framework advantageous. It extends classica

research design

Bayesian Confirmatory Research

Bayesian confirmatory research is a quantitative framework that tests pre-specified hypotheses by computing the Bayes factor — a ratio expressing how much more likely the observed data are under one hypothesis than another. Unlike classical null-hypothesis significance testing (NHST), it provides direct evidence for bo

statistics

Bayesian Conjoint Analysis

Bayesian conjoint analysis estimates individual-level consumer preference weights for product attributes by combining conjoint choice tasks with a hierarchical Bayesian model. It yields part-worth utilities for each respondent rather than only group averages, enabling precise market simulation and segment discovery eve

psychometrics

Bayesian Construct Validity

Bayesian construct validity assessment uses Bayesian confirmatory factor analysis and related Bayesian structural equation models to evaluate whether a scale or test measures the intended latent construct. It yields full posterior distributions for factor loadings, structural coefficients, and model-fit indices rather

experimental design

Bayesian Control Chart

A Bayesian control chart integrates prior knowledge about a process — such as historical mean and variance — with incoming measurement data to produce dynamically updated control limits. Unlike classical Shewhart charts that fix limits from a Phase-I baseline, Bayesian charts update the posterior distribution of proces

psychometrics

Bayesian Convergent Validity

Bayesian convergent validity applies Bayesian statistical inference to assess whether different measures of the same construct converge as theory predicts. Rather than a single-point correlation estimate, it yields a full posterior distribution over the convergent correlation, enabling probability statements about the

bioinformatics

Bayesian Copy Number Variation Analysis

Bayesian copy number variation (CNV) analysis is a probabilistic framework for detecting genomic segments where an individual's DNA copy count deviates from the diploid norm. By placing prior distributions over copy-number states and updating them with array CGH, SNP array, or sequencing read-depth evidence, the approa

epidemiology

Bayesian Cox Proportional Hazards

The Bayesian Cox proportional hazards model combines Cox's classical semiparametric survival regression with Bayesian inference, replacing point estimates and p-values with full posterior distributions over regression coefficients. It handles right-censored time-to-event outcomes, quantifies uncertainty about hazard ra

statistics

Bayesian Cox Regression

Bayesian Cox regression combines the Cox proportional hazards model for time-to-event data with Bayesian inference. Instead of point estimates, it produces full posterior distributions over the hazard ratios, naturally incorporating prior knowledge and providing coherent uncertainty quantification even with small sampl

psychometrics

Bayesian Cronbach's alpha

Bayesian Cronbach's alpha applies Bayesian inference to estimate the classical internal-consistency coefficient, yielding a full posterior distribution over alpha rather than a single point estimate. This allows researchers to quantify uncertainty with credible intervals and incorporate prior knowledge, making reliabil

statistics

Bayesian cross-tabulation analysis

Bayesian cross-tabulation analysis tests whether two categorical variables are associated by computing a Bayes factor that quantifies the evidence for an association model against an independence model. Unlike classical chi-square testing, it provides a continuous measure of evidence, supports the null hypothesis direc

econometrics

Bayesian DCC-GARCH

Bayesian DCC-GARCH estimates time-varying correlations across multiple financial or economic series by combining Engle's DCC-GARCH structure with Bayesian inference. Rather than maximising a likelihood, it places prior distributions over all parameters and uses Markov Chain Monte Carlo (MCMC) sampling to produce full p

machine learning

Bayesian Decision Tree

Bayesian Decision Tree (Bayesian CART) places a prior distribution over tree structures and leaf parameters, then uses Markov chain Monte Carlo to explore the posterior distribution of trees given data. Instead of a single best tree, it produces a distribution of plausible trees whose predictions are averaged, yielding

statistics

Bayesian descriptive statistics

Bayesian descriptive statistics summarizes data by combining observed information with prior knowledge through Bayes' theorem, yielding posterior distributions over parameters such as the mean and variance. Instead of point estimates and p-values, results are expressed as posterior means, medians, and credible interval

experimental design

Bayesian Design of Experiments

Bayesian design of experiments selects experimental runs by maximising a utility function — typically the expected information gain — computed over prior beliefs about model parameters. Unlike classical design, which optimizes algebraic criteria such as D-optimality under fixed assumptions, Bayesian DOE incorporates pr

epidemiology

Bayesian Diagnostic Accuracy Study

A Bayesian diagnostic accuracy study evaluates how well a medical test distinguishes between people who have a condition and those who do not, using Bayesian statistical methods that formally incorporate prior knowledge into the estimation of sensitivity, specificity, and related measures. Unlike classical approaches t

econometrics

Bayesian Difference GMM

Bayesian Difference GMM combines the Arellano-Bond first-differencing strategy for dynamic panel data with a Bayesian inference framework. By treating the GMM moment conditions as a quasi-likelihood and placing priors on parameters, the approach produces a full posterior distribution over coefficients rather than a sin

psychometrics

Bayesian Differential Item Functioning

Bayesian differential item functioning analysis detects whether a test item behaves differently across demographic or cultural groups — such as males vs. females — after accounting for the underlying ability or trait being measured. It applies Bayesian IRT estimation to obtain posterior distributions of item parameters

simulation

Bayesian Discrete-Event Simulation

Bayesian Discrete-Event Simulation (BDES) integrates Bayesian statistical inference with discrete-event simulation. Prior beliefs about system parameters — such as service rates, arrival times, or failure probabilities — are updated with observed data via Bayes' theorem, and the resulting posterior distributions direct

statistics

Bayesian Discriminant Analysis

Bayesian discriminant analysis assigns observations to predefined groups by combining a multivariate Gaussian likelihood for each class with prior distributions over the class means and covariance matrices. Posterior predictive probabilities replace point-estimate decision boundaries, providing principled uncertainty q

psychometrics

Bayesian Discriminant Validity

Bayesian discriminant validity assessment evaluates whether two theoretically distinct latent constructs are empirically separable, using posterior distributions and credible intervals rather than single-point null-hypothesis tests. It is applied within Bayesian confirmatory factor analysis or via the Bayesian heterotr

epidemiology

Bayesian Dose-Response Analysis

Bayesian dose-response analysis models the relationship between the level of exposure (dose) to a substance and the magnitude or probability of a biological response, embedding that model in a Bayesian probabilistic framework. Unlike frequentist approaches that yield a single point estimate with confidence intervals, t

causal inference

Bayesian Doubly Robust Estimation

Bayesian Doubly Robust Estimation combines the classical doubly robust (DR) augmented inverse probability weighting framework with Bayesian inference. It simultaneously models the propensity score and the outcome regression, placing prior distributions over both, and derives a posterior distribution over the average tr

econometrics

Bayesian Dynamic Panel Data Model

The Bayesian dynamic panel data model extends standard dynamic panel models — which include a lagged dependent variable to capture state dependence — by estimating all parameters within a Bayesian framework. Prior distributions are combined with the likelihood to yield a full posterior distribution over model parameter

epidemiology

Bayesian Ecological Study

A Bayesian ecological study combines the group-level observational design of classical ecological epidemiology with Bayesian hierarchical modelling. Rather than treating disease rates as fixed quantities, it places prior distributions over latent spatial or temporal effects — commonly using the Besag-York-Mollié (BYM)

psychometrics

Bayesian EFA

Bayesian exploratory factor analysis applies a full probabilistic framework to the common factor model. By placing prior distributions over factor loadings and unique variances, it yields posterior distributions rather than point estimates, quantifies uncertainty around every loading, and can treat the number of factor

econometrics

Bayesian EGARCH

The Bayesian EGARCH model combines Nelson's (1991) Exponential GARCH specification — which models the log of conditional variance and captures the leverage effect — with Bayesian posterior inference via Markov Chain Monte Carlo (MCMC). This allows full uncertainty quantification of all volatility parameters, including

network analysis

Bayesian Ego Network Analysis

Bayesian ego network analysis applies probabilistic inference to ego-centered (personal) network data, combining a likelihood model for the ego's local network with prior distributions over network parameters. The result is a full posterior distribution that quantifies uncertainty about structural features such as alte