按方法、领域与证据探索科学。

Hiemstra-Jones Causality

The Hiemstra-Jones test, introduced in 1994, is a nonparametric procedure for detecting nonlinear causal relationships between two time series after removing their linear interdependencies. Developed in the context of stock price and trading volume dynamics, it extends the standard linear Granger causality framework by

bayesian

Hierarchical Approximate Bayesian Computation

Hierarchical ABC is a likelihood-free Bayesian inference method designed for multilevel data structures in which individual-level parameters are themselves drawn from a population-level distribution. By combining simulation-based rejection sampling with hierarchical pooling, it recovers both within-group and between-gr

bayesian

Hierarchical Bayesian Inference

Hierarchical Bayesian inference is a probabilistic modeling framework that organises parameters into levels, placing priors on the group-level parameters and hyperpriors on the parameters governing those priors. It enables partial pooling of information across groups, balancing the extremes of treating each group as in

bayesian

Hierarchical Bayesian Model Averaging

Hierarchical Bayesian model averaging (HBMA) combines Bayesian model averaging with hierarchical model structure, averaging posterior quantities over a set of candidate models weighted by each model's posterior probability. Rather than selecting a single best model, HBMA propagates model uncertainty through a hierarchi

bayesian

Hierarchical Bayesian Network

A hierarchical Bayesian network is a probabilistic graphical model that organizes variables across multiple levels of abstraction. Higher-level nodes govern the prior distributions of lower-level nodes through hyperparameters, enabling structured sharing of information across groups, contexts, or data subsets while pre

bayesian

Hierarchical Bootstrap Simulation

Hierarchical bootstrap simulation is a resampling technique designed for data with nested or clustered structure — students within schools, patients within hospitals, repeated measures within subjects. It preserves the natural grouping of the data by resampling at each level of the hierarchy in sequence, producing a sa

research design

Hierarchical Causal-Comparative Research

Hierarchical causal-comparative research is a non-experimental quantitative design that compares pre-existing groups on an outcome variable while explicitly modeling the nested structure of the data. Participants are clustered within higher-level units — students within classrooms, employees within organizations — and

research design

Hierarchical Confirmatory Research

Hierarchical confirmatory research is a quantitative design that tests pre-specified hypotheses about relationships or group differences in data that have a natural nested (hierarchical) structure — such as students clustered within classrooms, patients within hospitals, or employees within organizations. By explicitly

research design

Hierarchical Cross-Sectional Research

Hierarchical cross-sectional research is a quantitative observational design that collects data from individuals nested within higher-level units — such as students within schools, patients within hospitals, or employees within organizations — at a single point in time. By accounting for the non-independence of cluster

research design

Hierarchical Descriptive Research

Hierarchical descriptive research is an observational design that documents the current state of a phenomenon across two or more nested levels — for example, students within classrooms within schools, or employees within teams within organizations. Rather than testing hypotheses or explaining causation, it describes di

research design

Hierarchical Exploratory Quantitative Research

Hierarchical exploratory quantitative research is a survey and observational design that structures both sampling and analysis across nested population levels — such as students within classrooms within schools — to explore patterns, distributions, and relationships in numerical data without a pre-specified directional

bayesian

Hierarchical Hamiltonian Monte Carlo

Hierarchical Hamiltonian Monte Carlo (Hierarchical HMC) applies Hamiltonian Monte Carlo sampling to Bayesian hierarchical models, addressing the severe geometric challenges those models pose. By combining non-centered parameterizations with HMC's gradient-driven proposals, it achieves efficient posterior exploration of

bayesian

Hierarchical Kalman Filter

The Hierarchical Kalman Filter (HKF) extends the classic Kalman filter to systems with multiple levels or scales of state representation. It applies Kalman recursions at each level of a hierarchy — from coarse to fine resolution or from global to local subsystems — and passes information across levels via upward and do

statistics

Hierarchical Linear Model

The Hierarchical Linear Model (HLM) is a multilevel regression method designed for data in which lower-level units (e.g., students, patients) are nested within higher-level groups (e.g., schools, hospitals). It simultaneously models within-group relationships and between-group variation, producing unbiased estimates an

statistics

Hierarchical Linear Modeling

Hierarchical Linear Modeling (HLM), also known as Multilevel Modeling (MLM), is a parametric statistical method for analyzing nested or clustered data — for example students within classrooms, patients within hospitals, or employees within organizations. Formalized by Raudenbush and Bryk in their 2002 seminal text (bui

bayesian

Hierarchical Markov Chain Monte Carlo

Hierarchical Markov chain Monte Carlo applies MCMC sampling to hierarchical Bayesian models, jointly drawing from the posterior over both observation-level parameters and the hyperparameters that govern them. This allows principled uncertainty propagation across all levels of a multilevel structure, from individuals to

research design

Hierarchical Model Testing Research

Hierarchical model testing research is a quantitative design that evaluates theoretically derived models using data with a nested or clustered structure — for example, students within classrooms, employees within organisations, or patients within hospitals. It applies hierarchical linear models (HLM) or multilevel stru

bayesian

Hierarchical Particle Filter

A hierarchical particle filter extends Sequential Monte Carlo to state-space models with multiple levels of latent variables. Particles are propagated at each level of the hierarchy, allowing the method to track both fine-grained state dynamics and slower-varying hyperparameters simultaneously, yielding calibrated post

research design

Hierarchical Relational Survey

A hierarchical relational survey combines the correlational goals of relational survey research with a multilevel data structure in which respondents are nested within higher-level units such as classrooms, schools, hospitals, or organizations. The design acknowledges that observations within the same group are not ind

research design

Hierarchical Survey Research

Hierarchical survey research is a quantitative design that collects survey data from respondents who are naturally nested within higher-level units — such as students within classrooms, employees within organizations, or patients within hospitals — and uses multilevel (hierarchical linear) modeling to analyze variation

bayesian

Hierarchical Variational Inference

Hierarchical variational inference (HVI) extends standard variational inference by placing a richer, hierarchical structure on the variational family itself. Instead of using a simple mean-field approximation, HVI introduces auxiliary latent variables that capture dependencies among the main latent variables, yielding

health outcomes

HIT-6

The HIT-6 is a brief, validated measure of headache impact on daily functioning and quality of life. Developed by Mark Kosinski and colleagues in 2003, this 6-item questionnaire quantifies how headache (migraine or other types) affects work, social activities, sleep, and emotional well-being. It is widely used in heada

quantitative finance

HJM Framework

The Heath-Jarrow-Morton (HJM) framework (1992) is a general no-arbitrage approach to modeling the entire term structure of forward rates. Unlike short-rate models, HJM works directly with forward rates f(t,T) and specifies their volatility; the drift is then determined by arbitrage constraints. This flexibility enables

statistics

Holm Correction

The Holm correction, introduced by Sture Holm in 1979, is a step-down multiple-comparison procedure that controls the family-wise error rate (FWER) at level α while rejecting at least as many hypotheses as the classical Bonferroni correction. It orders the observed p-values from smallest to largest and compares each ag

econometrics

Holt-Winters

Holt-Winters triple exponential smoothing is a forecasting model that extends Holt's double smoothing by adding a seasonal component, introduced by Peter Winters in 1960 building on Charles Holt's work. It tracks three evolving quantities — level, trend, and season — and combines them to forecast a continuous time seri

spatial analysis

Hot Spot Analysis

Hot Spot Analysis uses the Getis-Ord Gi* local spatial statistic to identify geographic locations where high or low attribute values cluster together to a degree that is statistically significant. Each feature is evaluated in relation to its neighbours, producing a z-score that flags genuine spatial hot spots and cold

statistics

Hotelling's T² Test

Hotelling's T² test is a multivariate parametric hypothesis test that simultaneously compares the mean vectors of two independent groups across multiple continuous outcome variables. It was introduced by Harold Hotelling in 1931 as the direct multivariate generalization of Student's t-test, replacing the scalar mean di

econometrics

HP Filter

The Hodrick-Prescott (HP) filter is a penalized least-squares technique used in macroeconomics and empirical finance to decompose a time series into a smooth long-run trend component and a short-run cyclical component. Introduced by Hodrick and Prescott (1997) using postwar U.S. business cycle data, it has become one o

spectroscopy

HSQC

Heteronuclear Single-Quantum Coherence (HSQC) is a 2D NMR technique that correlates proton and carbon-13 (or other heteronuclei) chemical shifts through one-bond coupling constants (1JHX). Developed in the early 1980s, HSQC rapidly became the workhorse of structural chemistry because it directly maps which carbons bear

statistics

Huber Regression

Huber regression is a robust linear regression method, introduced by Peter J. Huber in 1964, that resists the influence of outliers by treating small and large residuals differently. It applies a squared (OLS-like) loss to small residuals and a milder absolute-value loss to large ones, so extreme observations cannot do

spatial analysis

Huff Model

Proposed by David Huff in 1964, the Huff Model is a probabilistic spatial interaction model that estimates the likelihood that consumers located in a given geographic zone will choose to shop at a particular retail outlet. It extends deterministic gravity models by assigning each consumer zone a probability of patronag

quantitative finance

Hull-White Model

The Hull-White model (1990) is a one-factor short-rate model with time-dependent mean reversion and volatility, designed to fit the initial yield curve exactly. It generalizes the Vasicek model to allow better calibration to observed bond and derivative prices, and is widely used for pricing interest rate exotics and m

statistics

Hurdle Model

The hurdle model is a two-part count-data model introduced by Mullahy (1986). A first stage models the binary choice of crossing a hurdle (a zero versus a non-zero count), and a second stage models the strictly positive counts with a zero-truncated distribution such as a zero-truncated Poisson or negative binomial.

experimental design

Hybrid Event Tree Analysis

Hybrid Event Tree Analysis (Hybrid ETA) extends classical Event Tree Analysis by integrating complementary methods — such as Bayesian networks, fuzzy set theory, or Monte Carlo simulation — to overcome ETA's limitations in handling uncertainty, dependency between events, and sparse data. It is applied in safety-critica

experimental design

Hybrid Fault Tree Analysis

Hybrid Fault Tree Analysis (Hybrid FTA) extends classical Fault Tree Analysis by integrating complementary modelling paradigms — most commonly fuzzy set theory, Bayesian networks, or event-tree logic — to overcome the strict data requirements and static assumptions of traditional FTA. The hybrid approach allows analyst

signal processing

IIR Filter Design

Infinite Impulse Response (IIR) filters are recursive digital filters that use feedback to achieve sharp frequency response characteristics with minimal filter order. Unlike FIR filters which depend only on past inputs, IIR filters also use past output values, allowing them to achieve steep rolloff with fewer coefficie

econometrics

Im-Pesaran-Shin Test

The Im-Pesaran-Shin (IPS) test, introduced by Im, Pesaran, and Shin in 2003, is a panel unit-root test designed for heterogeneous panels where the autoregressive coefficient is allowed to differ across cross-sectional units. It averages individual Augmented Dickey-Fuller (ADF) t-statistics and constructs a standardized

econometrics

Impulse Response Function

The Impulse Response Function (IRF) traces the dynamic response of each variable in a Vector Autoregression (VAR) system to a one-unit shock in one of its error terms over a user-specified forecast horizon. It is the primary tool for structural analysis following VAR estimation and is widely used in macroeconomics, mon

pharmacology

In Vitro-In Vivo Correlation

IVIVC is a mathematical relationship between in vitro and in vivo properties of a drug, developed to predict oral bioavailability from dissolution data. Introduced by Amidon and colleagues in the 1995 Biopharmaceutics Classification System, it bridges laboratory measurements and clinical outcomes to streamline drug dev

statistics

Independent samples t-test

The independent samples t-test is a parametric hypothesis test that determines whether the means of two independent, unrelated groups differ significantly on a continuous outcome variable. Derived from Gosset's 1908 t-distribution, it is one of the most widely used inferential tests in social, behavioral, biomedical, a

statistics

Independent t-test

The independent samples t-test is a parametric hypothesis test that compares the means of two independent groups to decide whether they differ significantly. It builds on the t-distribution introduced by Student (W. S. Gosset) in 1908 and assumes the measured values are continuous, approximately normally distributed, a

statistics

Influence Diagnostics

Influence diagnostics are a family of post-fit measures that quantify how much each single observation affects a fitted regression. Cook's distance was introduced by R. Dennis Cook in 1977, with leverage and DFFITS formalised by Belsley, Kuh and Welsch in 1980, to flag the observations that most strongly pull the estim

econometrics

Interactive Fixed Effects

Interactive Fixed Effects (IFE) extends standard fixed-effects panel models by allowing unit-specific intercepts to vary not just at the individual level but also with unobserved common time-varying factors. Introduced by Bai (2009), it models heterogeneity as the interaction of individual characteristics and common sh

finance

Interest Rate Models

Interest rate models are structural models that describe how interest rates evolve over time within a stochastic differential equation framework. The family covers Vasicek's normal short-rate process (1977), the CIR square-root process, the adjustable Hull-White extension, and the Nelson-Siegel approach to fitting the

psychometrics

Interrater Reliability

Interrater reliability quantifies the degree to which two or more independent raters produce consistent scores when evaluating the same individuals or products. The family encompasses Cohen's kappa, introduced in 1960 for categorical judgments, and the Intraclass Correlation Coefficient (ICC) for continuous ratings, to

statistics

Intraclass Correlation Coefficient

The Intraclass Correlation Coefficient (ICC) is a parametric reliability statistic that quantifies the degree of agreement or consistency among repeated measurements or multiple raters on a continuous outcome. The modern six-form taxonomy was established by Shrout and Fleiss in 1979 and remains the standard framework f

spatial analysis

Inverse Distance Weighting

Inverse distance weighting is a simple, deterministic method for estimating values at unsampled locations by taking a weighted average of nearby measured points, where closer points carry more weight. Introduced by Donald Shepard in 1968, it embodies the first law of geography — near things are more related than distan

statistics

Jackknife

The jackknife is a classical resampling method that estimates the bias and variance of a statistic by systematically recomputing it with one observation left out at a time. Introduced by Quenouille in 1956 and later reviewed by Miller in 1974, it predates the bootstrap and remains a simple, deterministic tool for asses

statistics

Jackknife Estimation

Jackknife estimation is a classical resampling technique that computes the bias and variance of a statistical estimator by systematically leaving out one observation at a time and re-computing the statistic on each reduced sample. Introduced by Maurice Quenouille in 1956 for bias correction and extended by John Tukey i

finance

Johansen Cointegration Test

The Johansen procedure is a multivariate cointegration framework, introduced by Søren Johansen in 1991, that tests for long-run equilibrium relationships among several I(1) time series. It determines how many cointegrating vectors link the series and then builds a Vector Error Correction Model (VECM) to describe the sh

survival

Joint Model for Longitudinal and Survival Data

The joint model for longitudinal and time-to-event data, formalised by Tsiatis and Davidian in 2004 and extended comprehensively by Rizopoulos in 2012, simultaneously estimates a mixed-effects model for repeatedly measured biomarkers and a survival model for the time to an event, linking the two processes through share

statistics

Jonckheere-Terpstra Test

The Jonckheere-Terpstra test is a nonparametric hypothesis test that detects a monotone trend across k ordered groups — testing whether the outcome rises (or falls) systematically as the group order increases. Developed independently by T. J. Terpstra (1952) and A. R. Jonckheere (1954), it is the directional, ordered-a

finance

Jump-Diffusion Model

The Merton Jump-Diffusion model, introduced by Robert C. Merton in 1976, extends Geometric Brownian Motion by adding sudden price jumps generated by a Poisson process. It captures the volatility smile and the fat-tailed return behaviour that standard Black-Scholes cannot explain, and is widely used in option pricing an

bayesian

Kalman Filter

The Kalman filter is an optimal recursive algorithm for estimating the hidden state of a linear dynamical system from noisy measurements. At each time step it alternates between a prediction step — projecting the state forward using the system model — and an update step that corrects the prediction with the new observa

finance

Kalman Filter (Finance)

The Kalman filter is a recursive algorithm that estimates financial models with time-varying parameters, hidden factors, and noisy observations inside a dynamic state-space framework. The structural time series treatment was set out by Harvey (1989), with state-space and regime-switching extensions developed by Kim and

bayesian

Kalman Filter with Measurement Error

The Kalman filter with measurement error is a recursive Bayesian state-space algorithm that estimates the true hidden state of a dynamic system from noisy observations. It explicitly separates process noise (system dynamics uncertainty) from measurement noise (observation uncertainty), propagating both sources of error

bayesian

Kalman Filter with Missing Data

The Kalman filter with missing data extends the classical Kalman filter to handle time series in which some observations are absent. When an observation is missing at time t the update step is skipped and the state estimate is carried forward from the prediction step alone. Combined with the Expectation-Maximisation (E

survival

Kaplan-Meier

The Kaplan-Meier estimator, introduced by Kaplan and Meier in 1958, is a non-parametric method that estimates the survival curve — the probability of remaining event-free over time — from right-censored time-to-event data. The log-rank test is the companion procedure used to compare survival curves between groups.

epidemiology

Kaplan-Meier Analysis

Kaplan-Meier (KM) analysis is a nonparametric method for estimating the survival function from time-to-event data. Introduced by Kaplan and Meier in 1958, it produces the classic step-function survival curve that shows the probability of surviving beyond each observed event time, correctly accounting for censored obser

statistics

Kaplan-Meier Estimator

The Kaplan-Meier estimator is a nonparametric method for estimating the survival function S(t) — the probability that an individual survives beyond time t — from data that include censored observations. Introduced by Edward L. Kaplan and Paul Meier in their landmark 1958 JASA paper, it is the standard first step in any