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Posterior Distribution
In Bayesian data analysis, a posterior distribution is a probability distribution over hypotheses, possible parameter values, or statistical models, conditional on the observed data. It differs from a prior distribution in that the prior distribution is not conditional on the observed data. The posterior distribution can be a discrete probability distribution or a continuous probability distribution and reflects the credence a rational agent should give to hypotheses, possible parameter values, or statistical models, after observing a set of data. It is one of the applications of the Bayes theorem.
Posterior Distribution Over Hypotheses
A posterior distribution may be used for hypothesis testing when a discrete probability distribution is assigned to two possible outcomes: the hypothesis is true and the hypothesis is false. For example, if the posterior ...
- Bayesian Statistics
- Descriptive Statistics
- Central Tendency, Measures of
- Cohen’s d Statistic
- Cohen’s f Statistic
- Correspondence Analysis
- Descriptive Statistics
- Effect Size, Measures of
- Eta-Squared
- Factor Loadings
- Mean
- Median
- Mode
- Partial Eta-Squared
- Range
- Relative Measures of Dispersion
- Standard Deviation
- Statistic
- Trimmed Mean
- Variability, Measure of
- Variance
- Distributions
- z Distribution
- Bernoulli Distribution
- Beta Distribution
- Binomial Distribution
- Copula Functions
- Cumulative Frequency Distribution
- Distribution
- Frequency Distribution
- Kurtosis
- Law of Large Numbers
- Negative Hypergeometric Distribution
- Normal Distribution
- Normalizing Data
- Poisson Distribution
- Quetelet’s Index
- Sampling Distributions
- Weibull Distribution
- Winsorize
- Graphical Displays of Data
- Bar Chart
- Box-and-Whisker Plot
- Column Graph
- Data Visualization
- Exponential Random Graph Models
- Forest Plot
- Frequency Table
- Funnel Plot
- Graph Theory
- Graphical Display of Data
- Growth Curve
- Histogram
- L’Abbé Plot
- Line Graph
- Nomograms
- Ogive
- Pie Chart
- Radial Plot
- Residual Plot
- Scatterplot
- Spaghetti Plot
- U-Shaped Curve
- Visual Analysis
- Visual Display of Quantitative Information
- Hypothesis Testing
- p Value
- Alternative Hypotheses
- Beta
- Critical Value
- Decision Rule
- Equivalence Hypothesis Testing
- Hypothesis
- Nondirectional Hypotheses
- Nonsignificance
- Null Hypothesis
- One-Tailed Test
- Power
- Power Analysis
- Significance Level, Concept of
- Significance Level, Interpretation and Construction
- Significance, Statistical
- Two-Tailed Test
- Type I Error
- Type II Error
- Type III Error
- Important Publications
- “Coefficient Alpha and the Internal Structure of Tests”
- “Convergent and Discriminant Validation by the Multitrait–Multimethod Matrix”
- “Meta-Analysis of Psychotherapy Outcome Studies”
- “On the Theory of Scales of Measurement”
- “Probable Error of a Mean, The”
- “Psychometric Experiments”
- “Sequential Tests of Statistical Hypotheses”
- “Structural Holes: The Social Structure of Competition”
- “Technique for the Measurement of Attitudes, A”
- “Validity”
- Aptitudes and Instructional Methods
- Doctrine of Chances, The
- Logic of Scientific Discovery, The
- Nonparametric Statistics for the Behavioral Sciences
- Probabilistic Models for Some Intelligence and Attainment Tests
- Social Network Analysis Methodsand Applications
- Statistical Power Analysis for the Behavioral Sciences
- Strength of Weak Ties
- Structural Equivalence of Individuals in Social Networks
- Teoria Statistica Delle Classi e Calcolo Delle Probabilità
- Inferential Statistics
- Association, Measures of
- Coefficient of Concordance
- Coefficient of Variation
- Coefficients of Alienation and Determination
- Confidence Intervals
- Correlation Coefficient
- Margin of Error
- Nonparametric Statistics
- Odds Ratio
- Parameters
- Parametric Statistics
- Partial Correlation
- Pearson Product-Moment Correlation Coefficient
- Polychoric Correlation Coefficient
- Q-Statistic
- R2
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- Regression Coefficient
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- Spearman Rank Order Correlation
- Standard Error of Estimate
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- Student’s t Test
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- Weights
- Item Response Theory
- Mathematical Concepts
- Measurement Concepts
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- Ceiling Effect
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- False Positive
- Gain Scores, Analysis of
- Instrumentation
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- Then-Test
- True Positive
- Organizations
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- Reliability
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- Standard Error of Measurement
- Test–Retest Reliability
- True Score
- Research Design Concepts
- Aptitude–Treatment Interaction
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- Confounding
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- Good Clinical Research Practice
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- Mortality
- Multiple Case Study
- Natural Experiments
- Network Analysis
- Peer Effects
- Placebo
- Reciprocity
- Replication
- Research
- Research Design Principles
- Treatment(s)
- Triangulation
- Unit of Analysis
- Yoked Control Procedure
- Research Designs
- A Priori Monte Carlo Simulation
- Action Research
- Adaptive Designs in Clinical Trials
- Alternating Treatments Design
- Applied Research
- Balanced Incomplete Block Design
- Basket Trials Design
- Behavior Analysis Design
- Block Design
- Blockmodeling
- Case-Only Design
- Causal-Comparative Design
- Changing Criterion Design
- Cohort Design
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- Confirmatory Research
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- Cross-Sectional Design
- Double-Blind Procedure
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- Experimental Design
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- Factorial Design
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- Meta-Analysis
- Mixed Methods Design
- Mixed Model Design
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- Nested Factor Design
- Nonexperimental Designs
- Observational Research
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- Pilot Study
- Pragmatic Study
- Pre-Experimental Designs
- Pretest–Posttest Design
- Propensity Score Matching
- Prospective Study
- Quadratic Assignment Procedure
- Quantitative Research
- Quasi-Experimental Design
- Randomized Block Design
- Repeated Measures Design
- Response Surface Design
- Retrospective Study
- Sequential Design
- Single-Blind Study
- Single-Case Research Design
- Split-Plot Factorial Design
- Stepped-Wedge Design
- Stepwise Model Selection
- Thought Experiments
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- Umbrella Trials Design
- Wennberg Design
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- Follow-Up
- Inference: Deductive and Inductive
- Last Observation Carried Forward
- Masking
- Multisite Research Studies
- Operationalizing
- Primary Data Source
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- Type III Error
- Wave
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- Bias
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- John Henry Effect
- Multiple Treatment Interference
- Multivalued Treatment Effects
- Nonclassical Experimenter Effects
- Order Effects
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- Pretest Sensitization
- Random Assignment
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- Regression to the Mean
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- Validity of Research Conclusions
- Volunteer Bias
- White Noise
- Sampling
- Cluster Sampling
- Comparison-Focused Sampling
- Convenience Sampling
- Demographics
- Error
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- Experience Sampling Method
- Gibbs Sampler
- Nested Sampling
- Network Sampling
- Nonprobability Sampling
- Population
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- Proportional Sampling
- Quota Sampling
- Random Sampling
- Random Selection
- Sample
- Sample Size
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- Sampling
- Sampling Error
- Sequential Sampling
- Stratified Sampling
- Survey Sampling
- Systematic Sampling
- Theoretical Sampling
- Underrepresented Groups
- Scaling
- Social Network Analysis
- Alters
- Connectivity
- Core-Periphery Structure
- Ego-Centric Networks
- International Network for Social Network Analysis
- Name Generator
- Network Boundaries
- Network Composition
- Network Density
- Network Distance
- Network Matrices
- Network Meta-Analysis
- Network Sampling
- Network Size
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- Node, Relationship, and Network Attributes
- Nodes and Relationships
- One-Mode Data
- Social Network Analysis
- Sociograms
- Structural Holes
- Two-Mode Data
- Whole Networks
- Software Applications
- Statistical Assumptions
- Statistical Concepts
- Akaike Information Criterion
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- Biased Estimator
- Centrality
- Cohen’s Kappa
- Collinearity
- Correlation
- Criterion Problem
- Critical Difference
- Data Mining
- Data Snooping
- Degrees of Freedom
- Directional Hypothesis
- Disturbance Terms
- Error Rates
- Expected Value
- Factorial Invariance
- Fixed-Effects Model
- Hedges’ g
- Heterogeneity
- Inclusion Criteria
- Influence Statistics
- Influential Data Points
- Intraclass Correlation
- Latent Change Score
- Latent Variable
- Likelihood Principle
- Likelihood Ratio Statistic
- Loglinear Models
- Machine Learning
- Main Effects
- Markov Chains
- McDonald’s Omega Hierarchical
- Method Variance
- Mixed- and Random-Effects Models
- Multilevel Modeling
- Multiplicity Problem
- Neural Networks
- Nuisance Parameters
- Odds
- Omega Squared
- Orthogonal Comparisons
- Outlier
- Overfitting
- Partial Factorial Invariance
- Pooled Variance
- Precision
- Quality Effects Model
- Random-Effects Models
- Regression Artifacts
- Regression Discontinuity
- Residuals
- Restriction of Range
- Robust
- Robust Maximum Likelihood
- Root Mean Square Error
- Rosenthal Effect
- Semi-Interquartile Range
- Serial Correlation
- Shrinkage
- Simple Main Effects
- Simpson’s Paradox
- Stochastic Processes
- Sums of Squares
- Statistical Procedures
- F Test
- t Test, Independent Samples
- t Test, One Sample
- t Test, Paired Samples
- Accuracy in Parameter Estimation
- Analysis of Covariance
- Analysis of Variance
- Bartlett’s Test
- Barycentric Discriminant Analysis
- Behrens–Fisher t’ Statistic
- Bivariate Regression
- Bonferroni Procedure
- Bootstrapping
- Canonical Correlation Analysis
- Categorical Data Analysis
- Chi-Square Test
- Cluster Analysis
- Confirmatory Factor Analysis
- Contingency Table Analysis
- Contrast Analysis
- Descriptive Discriminant Analysis
- Diagnostic Classification Modeling
- Dummy Coding
- Duncan’s Multiple Range Test
- Dunnett’s Test
- Effect Coding
- Estimation
- Exploratory Factor Analysis
- Fisher’s Least Significant Difference Test
- Friedman Test
- Greenhouse–Geisser Correction
- Hidden Markov Model
- Hierarchical Linear Modeling
- Holm’s Sequential Bonferroni Procedure
- Jackknife
- Kolmogorov–Smirnov Test
- Kruskal–Wallis Test
- Latent Class Analysis
- Latent Growth Modeling
- Latent Profile Analysis
- Least Squares, Methods of
- Logistic Regression
- Mann–Whitney U Test
- Mauchly Test
- Maximum Likelihood Estimation
- McNemar’s Test
- Mean Comparisons
- Missing Data, Imputation of
- Multidimensional Scaling
- Multiple Comparison Tests
- Multiple Comparisons With Modeling Techniques
- Multiple Regression
- Multivariate Analysis of Variance
- Newman–Keuls Test
- Omnibus Tests
- Pairwise Comparisons
- Path Analysis
- Post Hoc Analysis
- Post Hoc Comparisons
- Predictive Discriminant Analysis
- Principal Components Analysis
- Propensity Score Analysis
- Scheffé Test
- Sequential Analysis
- Sign Test
- Stepwise Model Selection
- Stepwise Regression
- Structural Equation Modeling
- Survival Analysis
- Trend Analysis
- Tukey’s Honestly Significant Difference
- Welch’s t Test
- Wilcoxon Rank Sum Test
- Yates’s Correction
- Statistical Tests
- F Test
- t Test, Independent Samples
- t Test, One Sample
- t Test, Paired Samples
- z Test
- Bartlett’s Test
- Behrens–Fisher t’ Statistic
- Chi-Square Test
- Cochran–Armitage Test for Trend
- Duncan’s Multiple Range Test
- Dunnett’s Test
- Fisher’s Least Significant Difference Test
- Friedman Test
- Hosmer-Lemeshow Test
- Kolmogorov–Smirnov Test
- Kruskal–Wallis Test
- Mann–Whitney U Test
- Mauchly Test
- McNemar’s Test
- Multiple Comparison Tests
- Newman–Keuls Test
- Omnibus Tests
- Scheffé Test
- Sign Test
- Tukey’s Honestly Significant Difference
- Welch’s t Test
- Wilcoxon Rank Sum Test
- Structural Equation Modeling
- Theories, Laws, and Principles
- Central Limit Theorem
- Classical Test Theory
- Correspondence Principle
- Critical Theory
- Diffusion of Innovation Theory
- Falsifiability
- Game Theory
- Gauss–Markov Theorem
- Generalizability Theory
- Graph Theory
- Grounded Theory
- Item Response Theory
- Likelihood Principle
- Machine Learning
- Models
- Neural Networks
- Occam’s Razor
- Paradigm
- Positivism
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- Probability, Laws of
- Social Capital Theory
- Social Support Theory
- Structural Paradigm
- Theory
- Theory of Attitude Measurement
- Toulmin Method
- Weber–Fechner Law
- Types of Variables
- Validity of Scores
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