按方法、领域与证据探索科学。

Bayesian Entropy Balancing

Bayesian Entropy Balancing extends the classical entropy balancing approach — which reweights control units so that their covariate moments match the treated group exactly — by embedding this reweighting within a Bayesian framework. This allows researchers to incorporate prior beliefs about treatment propensities, prop

bioinformatics

Bayesian epigenome-wide association study

A Bayesian EWAS is a genome-scale association analysis that links epigenetic marks — most commonly CpG-site DNA methylation — to a phenotype or trait of interest, replacing or supplementing the classical frequentist p-value framework with a Bayesian probabilistic model. It yields posterior probabilities of association

bioinformatics

Bayesian epigenome-wide association study in educational research

A Bayesian epigenome-wide association study (Bayesian EWAS) scans hundreds of thousands of DNA methylation sites across the genome to identify those statistically associated with an educational outcome — such as cognitive ability, attainment, or socioeconomic exposure during schooling. Unlike classical frequentist EWAS

bioinformatics

Bayesian eQTL analysis

Bayesian eQTL analysis identifies genetic variants (eQTLs) that regulate gene expression by combining genotype and RNA-seq data within a probabilistic framework. Unlike frequentist approaches that rely on p-value thresholds, the Bayesian formulation produces posterior probabilities of association, enabling principled f

causal inference

Bayesian Event Study Design

Bayesian Event Study Design extends the classical event study framework by replacing frequentist significance testing with a full Bayesian inferential framework. It estimates how an event (policy change, announcement, shock) alters an outcome trajectory by learning a prior model from the estimation window and updating

experimental design

Bayesian Event Tree Analysis

Bayesian Event Tree Analysis (B-ETA) is a quantitative risk assessment method that extends classical event tree analysis by incorporating Bayesian inference to assign and update branch probabilities. Starting from an initiating event, it maps sequences of successes and failures through safety barriers, using prior dist

research design

Bayesian Ex Post Facto Design

Bayesian ex post facto design investigates possible causal relationships among variables that have already occurred, without researcher manipulation of those variables, and quantifies uncertainty about those relationships using Bayesian statistical inference. The researcher selects groups that differ on an outcome or a

network analysis

Bayesian Exponential Random Graph Model

The Bayesian Exponential Random Graph Model (Bayesian ERGM or BERGM) extends the classical ERGM framework by placing prior distributions over the model parameters and using Markov chain Monte Carlo methods to obtain full posterior distributions. Introduced by Caimo and Friel (2011), it allows researchers to quantify pa

bayesian

Bayesian Factor Analysis

Bayesian Factor Analysis is a probabilistic latent-variable method that places prior distributions on the factor loading matrix and the residual variances, then infers a full posterior over these parameters from the observed data. Developed prominently in the Bayesian framework by Lopes and West (2004), it extends clas

experimental design

Bayesian failure mode and effects analysis

Bayesian FMEA extends the classical Failure Mode and Effects Analysis framework by replacing fixed point-estimate risk scores with probability distributions, allowing prior engineering knowledge and observed failure data to be formally combined through Bayes' theorem. The result is a probabilistic Risk Priority Number

experimental design

Bayesian Fault Tree Analysis

Bayesian Fault Tree Analysis (BFTA) extends classical fault tree analysis by converting the fault tree structure into an equivalent Bayesian network, enabling probabilistic inference in both forward (prediction) and backward (diagnosis) directions. This integration allows analysts to update failure probability estimate

machine learning

Bayesian Federated Learning

Bayesian Federated Learning combines federated learning — where model training is distributed across multiple clients without sharing raw data — with Bayesian inference, so that each client maintains a posterior distribution over model parameters rather than a single point estimate. This yields principled uncertainty q

machine learning

Bayesian Few-Shot Learning

Bayesian few-shot learning combines Bayesian inference with meta-learning to enable a model to generalize from as few as one to five labeled examples per class. By treating task-specific parameters as random variables and learning an informative prior across many training tasks, the method produces calibrated uncertain

statistics

Bayesian Fisher's exact test

The Bayesian Fisher's exact test evaluates independence between two categorical variables in a 2x2 table by computing a Bayes factor rather than a p-value. Using conjugate priors on cell probabilities — most commonly the Gunel-Dickey framework — it quantifies how much the observed data favor an association model over a

econometrics

Bayesian Fixed Effects Model

The Bayesian fixed effects model applies Bayesian inference to the classical within-group panel estimator. Unit-specific intercepts capture time-invariant unobserved heterogeneity, while prior distributions on all parameters allow probability statements about coefficients and full uncertainty quantification via the pos

experimental design

Bayesian Fractional Factorial Design

Bayesian fractional factorial design integrates Bayesian prior information into the selection and analysis of fractional factorial experiments. Rather than running every combination of factor levels, only a carefully chosen subset of runs is executed, with Bayesian inference used to estimate effects and quantify uncert

experimental design

Bayesian Full Factorial Design

Bayesian full factorial design combines the complete combinatorial structure of classical full factorial experiments — running every combination of factor levels — with a Bayesian inferential framework that incorporates prior knowledge about factor effects and yields full posterior distributions over main effects, inte

causal inference

Bayesian Fuzzy Regression Discontinuity

Bayesian Fuzzy Regression Discontinuity (Bayesian Fuzzy RD) combines the quasi-experimental logic of fuzzy regression discontinuity design with full Bayesian inference. It estimates a local average treatment effect at a policy threshold where treatment assignment is probabilistic rather than deterministic, placing prio

econometrics

Bayesian GARCH model

The Bayesian GARCH model combines the GARCH framework for time-varying volatility with Bayesian posterior inference. Instead of maximising a likelihood, it specifies prior distributions for the GARCH parameters and draws from the resulting posterior — typically via Markov chain Monte Carlo (MCMC) — to quantify both poi

machine learning

Bayesian Gaussian Mixture Model

The Bayesian Gaussian Mixture Model places prior distributions over all mixture parameters and infers their posteriors — typically via Variational Bayes or MCMC — rather than fitting fixed point estimates. This yields principled uncertainty quantification, automatic selection of the effective number of components, and

machine learning

Bayesian Gaussian Process

A Bayesian Gaussian Process (GP) places a probability distribution directly over functions, using a kernel to encode similarity between inputs. After observing data, Bayes' rule converts this prior into a posterior that yields not just point predictions but calibrated uncertainty estimates at every new input — making i

spatial analysis

Bayesian Geary's C

Bayesian Geary's C embeds the classical Geary contiguity ratio within a Bayesian hierarchical framework. Instead of a single point estimate and asymptotic p-value, it produces a posterior distribution over the statistic (or over spatially structured random effects), quantifying uncertainty about spatial autocorrelation

bioinformatics

Bayesian Gene Set Enrichment Analysis

Bayesian gene set enrichment analysis (Bayesian GSEA) applies a probabilistic framework to determine whether predefined sets of genes — representing biological pathways, cellular processes, or functional categories — are collectively more differentially expressed than expected by chance. Unlike classical frequentist GS

statistics

Bayesian Generalized additive model

Bayesian Generalized Additive Models extend the frequentist GAM framework by placing prior distributions over the smooth functions and any additional model parameters. This yields full posterior distributions over each smooth effect, enabling principled uncertainty quantification, automatic smoothness selection via hyp

statistics

Bayesian Generalized Linear Model

A Bayesian Generalized Linear Model (Bayesian GLM) extends the classical GLM framework by placing prior distributions on the regression coefficients and updating them with data via Bayes' theorem. This yields a full posterior distribution over parameters rather than single point estimates, enabling richer uncertainty q

bioinformatics

Bayesian genome-wide association study in educational research

Bayesian genome-wide association study (Bayesian GWAS) applies Bayesian statistical models to millions of single-nucleotide polymorphisms (SNPs) to identify genetic variants associated with educational outcomes such as years of schooling or cognitive test scores. Unlike classical frequentist GWAS, Bayesian approaches a

spatial analysis

Bayesian Geographically Weighted Regression

Bayesian Geographically Weighted Regression combines the spatially varying coefficient framework of GWR with Bayesian inference, placing Gaussian process priors on the locally varying regression coefficients. This yields full posterior distributions over each coefficient at every location, providing principled uncertai

econometrics

Bayesian Granger Causality

Bayesian Granger causality tests whether past values of one time series carry predictive information about another, framing the hypothesis through Bayesian inference rather than frequentist p-values. It combines a vector autoregressive (VAR) structure with prior distributions over coefficients and evaluates causal clai

bioinformatics

Bayesian GWAS

Bayesian GWAS applies Bayesian statistical inference to genome-wide association studies, replacing classical p-value thresholds with Bayes factors and posterior probabilities. This framework naturally incorporates prior knowledge about effect sizes and variant frequencies, quantifies evidence for association on a conti

econometrics

Bayesian Hausman Test

The Bayesian Hausman test is a Bayesian reformulation of Hausman's (1978) classical specification test, used to assess endogeneity or to choose between fixed effects and random effects panel models. Instead of a chi-squared test statistic, it uses posterior model probabilities or Bayes factors to compare competing spec

statistics

Bayesian Hierarchical Clustering

Bayesian hierarchical clustering is a probabilistic agglomerative algorithm that builds a tree of nested cluster merges using Bayesian model comparison at each step. Rather than minimising a geometric linkage criterion, it evaluates at every candidate merge whether the data from two clusters are better explained by a s

statistics

Bayesian Hierarchical Linear Model

The Bayesian Hierarchical Linear Model (Bayesian HLM) estimates linear relationships in nested or clustered data by placing prior distributions on all model parameters and updating them with observed data. It simultaneously models variation within groups and between groups, propagating uncertainty fully through posteri

bayesian

Bayesian Hierarchical Model

Bayesian hierarchical modelling, popularised by Gelman and Hill (2006), is a Bayesian approach to nested data structures — such as students within schools within districts — that estimates separate parameters at each level while allowing those levels to share statistical strength through a mechanism called partial pool

bayesian

Bayesian Hierarchical Model with Missing Data

A Bayesian hierarchical model with missing data treats unobserved values as additional unknowns and samples them jointly with all model parameters from the posterior. The nested structure of the hierarchy borrows strength across groups, while the Bayesian framework naturally propagates uncertainty from missingness thro

spatial analysis

Bayesian Hot Spot Analysis

Bayesian Hot Spot Analysis identifies spatial clusters of elevated risk or intensity by combining observed data with prior beliefs about spatial structure. It uses Bayesian smoothing — pooling information across neighboring areas — to stabilize estimates in small areas and then flags locations where the posterior proba

research design

Bayesian Hypothesis Testing Research

Bayesian hypothesis testing research is a quantitative design in which competing hypotheses are evaluated by updating prior beliefs with observed data to produce posterior probabilities and Bayes factors. Unlike frequentist null-hypothesis significance testing, it quantifies the relative evidence for each hypothesis, s

statistics

Bayesian Independent Samples t-test

The Bayesian independent samples t-test quantifies evidence for or against a mean difference between two independent groups using a Bayes factor rather than a p-value. Rooted in Jeffreys's probability framework and popularized by Rouder et al. (2009), it places a Cauchy prior on the standardized effect size and returns

statistics

Bayesian Inference

Bayesian inference is a statistical paradigm in which probability represents degrees of belief rather than long-run frequencies. It encodes prior knowledge about parameters in a prior distribution, combines that prior with the likelihood of observed data via Bayes' theorem, and produces a posterior distribution that qu

bayesian

Bayesian Inference with Measurement Error

Bayesian inference with measurement error extends the standard Bayesian framework to situations where one or more covariates or outcomes are observed with noise or misclassification. By treating the true unobserved values as latent variables and assigning them priors, the model jointly estimates the true exposure distr

bayesian

Bayesian Inference with Missing Data

Bayesian inference with missing data treats unobserved values as unknown parameters and integrates them out of the posterior distribution. Rather than deleting or ad hoc imputing incomplete records, the method jointly models observed and missing data under an explicit missing-data mechanism, producing fully calibrated

model evaluation

Bayesian Information Criterion

The Bayesian Information Criterion is an information-theoretic model selection criterion that approximates Bayesian model comparison. Introduced by Gideon Schwarz in 1978, BIC penalizes model complexity more heavily than AIC by using a sample-size-dependent penalty, making it particularly suitable for identifying the t

causal inference

Bayesian Instrumental Variables

Bayesian Instrumental Variables combines the instrumental variable strategy for addressing endogeneity with Bayesian posterior inference. Instead of relying on asymptotic sampling distributions, it places prior distributions over all structural parameters and recovers a full posterior distribution for the causal effect

causal inference

Bayesian Inverse Probability Weighting

Bayesian Inverse Probability Weighting (Bayesian IPW) extends the classical IPW estimator by placing prior distributions over the propensity-score model parameters and propagating that uncertainty into the causal-effect estimate. The result is a posterior distribution for the average treatment effect that fully account

psychometrics

Bayesian Item Analysis

Bayesian item analysis applies Bayesian inference to estimate item-level statistics — difficulty, discrimination, and distractor effectiveness — by combining observed response data with prior knowledge. It produces full posterior distributions over item parameters rather than single point estimates, providing richer un

statistics

Bayesian K-means clustering

Bayesian K-means clustering extends the classical K-means algorithm by placing prior distributions over cluster centroids and mixing proportions. This probabilistic framework provides uncertainty estimates for cluster assignments, allows principled model selection for the number of clusters, and regularises centroid es

machine learning

Bayesian k-nearest neighbors

Bayesian k-Nearest Neighbors (Bayesian KNN) extends the classical KNN algorithm by placing a prior distribution over the neighborhood size k and combining likelihood evidence from neighbors with that prior to produce calibrated posterior class probabilities. It retains KNN's intuitive instance-based logic while adding

epidemiology

Bayesian Kaplan-Meier analysis

Bayesian Kaplan-Meier analysis extends the classical Kaplan-Meier estimator by placing a prior distribution over the survival function and updating it with observed time-to-event data to obtain a full posterior distribution for the survival curve. This approach, rooted in Susarla and Van Ryzin's 1976 Dirichlet-process

spatial analysis

Bayesian Kernel Density Estimation

Bayesian Kernel Density Estimation (BKDE) is a nonparametric method for estimating the probability density function of a spatial or attribute variable by combining a kernel smoother with a Bayesian prior over the bandwidth parameter. The posterior distribution of the bandwidth propagates uncertainty into the final dens

network analysis

Bayesian Knowledge Graph Analysis

Bayesian knowledge graph analysis applies probabilistic Bayesian inference to knowledge graphs — structured representations of entities and their relations — to reason under uncertainty, complete missing links, and quantify confidence in inferred facts. It treats unknown graph edges as random variables and updates beli

spatial analysis

Bayesian Kriging

Bayesian Kriging embeds classical geostatistical interpolation inside a full probabilistic framework. Instead of treating variogram parameters as fixed point estimates, it places prior distributions on them and updates these priors with observed spatial data to obtain a posterior distribution. Predictions at unsampled

statistics

Bayesian LASSO Regression

Bayesian LASSO regression places double-exponential (Laplace) priors on regression coefficients, which is the Bayesian analogue of the classical LASSO penalty. It simultaneously shrinks small coefficients toward zero and performs soft variable selection, all within a coherent posterior inference framework that naturall

statistics

Bayesian Latent Class Analysis

Bayesian latent class analysis extends classical LCA by placing prior distributions on all model parameters and using posterior inference — typically via MCMC — to classify individuals into unobserved categorical groups, quantify uncertainty around class membership, and select the number of classes in a principled, pro

machine learning

Bayesian LightGBM

Bayesian LightGBM combines LightGBM — a highly efficient histogram-based gradient boosting framework — with Bayesian hyperparameter optimization. Instead of exhaustive grid search or random search, a probabilistic surrogate model guides the search for optimal hyperparameters, dramatically reducing the number of costly

bayesian

Bayesian Linear Regression

Bayesian linear regression is a probabilistic extension of the ordinary linear model, introduced through Bayes' rule and formalised in its modern computational workflow by Gelman et al. (2013). Rather than returning a single point estimate for each coefficient, it combines a user-specified prior distribution with the l

spatial analysis

Bayesian Local Indicators of Spatial Association

Bayesian Local Indicators of Spatial Association extend the classical LISA framework by embedding local spatial association statistics within a Bayesian hierarchical model. Rather than relying on asymptotic permutation-based significance tests, this approach places prior distributions on spatial parameters and derives

bayesian

Bayesian Logistic Regression

Bayesian logistic regression is a classification model that applies Bayesian inference to a logistic (sigmoid) likelihood for binary or multinomial outcomes. Developed within the weakly-informative prior framework formalised by Gelman, Jakulin, Pittau and Su (2008), it places a prior distribution over the coefficients

econometrics

Bayesian MA model

The Bayesian MA model estimates a moving average time series model within a fully Bayesian framework, placing prior distributions on the MA parameters and error variance and updating them via Bayes' theorem. This approach yields full posterior distributions over model parameters and produces probabilistic forecasts wit

statistics

Bayesian Mann-Whitney U test

The Bayesian Mann-Whitney U test is a nonparametric Bayesian procedure for comparing two independent groups when data are ordinal or non-normal continuous. Instead of a binary reject/fail-to-reject decision, it quantifies the relative evidence for the null and alternative hypotheses through a Bayes factor, allowing res

statistics

Bayesian MANOVA

Bayesian Multivariate Analysis of Variance (Bayesian MANOVA) extends the classical MANOVA framework by replacing null-hypothesis significance testing with Bayesian inference. It uses prior distributions on multivariate group means and covariance structures, updates them with data to yield posterior distributions, and q

causal inference

Bayesian Marginal Structural Model

Bayesian Marginal Structural Model (Bayesian MSM) combines the causal identification power of inverse-probability-weighted marginal structural models with Bayesian posterior inference. Rather than relying on point estimates and asymptotic standard errors, it propagates uncertainty through a full posterior distribution