statistical reasoning and data analysis

statistical primitive

slug: topic-map-statistical-primitive-statistical-reasoning-and-data-analysis

Vocabulary:

• Population: Complete set of all items of interest
• Sample: Subset of population selected for analysis
• Parameter: Numerical characteristic of a population
• Statistic: Numerical characteristic of a sample
• Random variable: Variable whose value is subject to randomness
• Probability distribution: Function describing likelihood of outcomes
• Probability density function (PDF): Function for continuous distributions
• Probability mass function (PMF): Function for discrete distributions
• Cumulative distribution function (CDF): Probability X ≤ x
• Expected value: Long-run average of random variable
• Variance: Measure of spread around the mean
• Standard deviation: Square root of variance
• Covariance: Measure of joint variability between two variables
• Correlation: Standardized measure of linear association
• Independence: Events where occurrence of one doesn't affect the other
• Conditional probability: Probability of A given B has occurred
• Bayes' theorem: Method for updating probabilities with new evidence
• Likelihood: Probability of observing data given parameters
• Prior distribution: Initial belief about parameters before seeing data
• Posterior distribution: Updated belief after observing data
• Conjugate prior: Prior that yields posterior in same family
• Central Limit Theorem: Distribution of sample means approaches normal
• Law of Large Numbers: Sample average converges to expected value
• Sampling distribution: Distribution of a statistic across samples
• Standard error: Standard deviation of sampling distribution
• Bias: Systematic deviation from true value
• Unbiased estimator: Estimator whose expected value equals parameter
• Consistency: Estimator converges to true value as n increases
• Efficiency: Estimator with smallest variance among unbiased estimators
• Sufficient statistic: Captures all information about parameter
• Confidence interval: Range likely to contain true parameter
• Confidence level: Probability that interval contains parameter
• Coverage probability: True proportion of intervals containing parameter
• Hypothesis test: Statistical procedure to evaluate claims
• Null hypothesis: Statement of no effect or no difference
• Alternative hypothesis: Statement of effect or difference
• Test statistic: Value computed from sample data for testing
• p-value: Probability of observing data as extreme under null
• Significance level (alpha): Threshold for rejecting null hypothesis
• Type I error: Rejecting true null hypothesis (false positive)
• Type II error: Failing to reject false null hypothesis (false negative)
• Statistical power: Probability of rejecting false null hypothesis
• Effect size: Magnitude of difference or relationship
• Multiple testing correction: Adjustment for testing many hypotheses
• False discovery rate (FDR): Expected proportion of false positives
• Familywise error rate (FWER): Probability of any false positive
• Bonferroni correction: Conservative multiple testing adjustment
• Permutation test: Nonparametric test using resampling
• Bootstrap: Resampling method for estimating distributions
• Jackknife: Resampling by leaving out one observation
• Cross-validation: Method for assessing model performance
• Overfitting: Model captures noise rather than signal
• Underfitting: Model too simple to capture patterns
• Bias-variance tradeoff: Balance between systematic error and variability
• Degrees of freedom: Number of independent pieces of information
• Residual: Difference between observed and predicted values
• Leverage: Influence of observation on fitted values
• Influential point: Observation with large effect on analysis
• Outlier: Observation far from others in dataset
• Robust statistics: Methods resistant to outliers
• Heteroscedasticity: Non-constant variance of errors
• Homoscedasticity: Constant variance of errors
• Autocorrelation: Correlation of variable with itself over time
• Stationarity: Statistical properties don't change over time
• Seasonality: Patterns that repeat at regular intervals
• Trend: Long-term movement in time series
• Confounding variable: Variable that affects both predictor and outcome
• Mediator: Variable through which effect operates
• Moderator: Variable that affects strength of relationship
• Interaction effect: Combined effect differs from sum of main effects
• Simpson's paradox: Trend reverses when data are aggregated
• Ecological fallacy: Inferring individual from aggregate relationships
• Regression to the mean: Extreme values tend toward average on retest
• Selection bias: Non-random sample leads to systematic error
• Survivorship bias: Analyzing only surviving cases
• Measurement error: Difference between measured and true value
• Reliability: Consistency of measurement
• Validity: Whether measurement captures intended construct
• Sensitivity: True positive rate
• Specificity: True negative rate
• Precision (PPV): Proportion of positive predictions that are correct
• Recall: Same as sensitivity
• F1 score: Harmonic mean of precision and recall
• ROC curve: Plot of true vs false positive rates
• AUC: Area under ROC curve
• Likelihood ratio: Ratio of probabilities under two hypotheses
• Information criterion: Measure balancing fit and complexity
• AIC: Akaike Information Criterion
• BIC: Bayesian Information Criterion
• Maximum likelihood estimation (MLE): Finding parameters that maximize likelihood
• Method of moments: Equating sample and population moments
• Least squares: Minimizing sum of squared residuals
• Regularization: Adding penalty to prevent overfitting
• Ridge regression: L2 penalty on coefficients
• Lasso: L1 penalty promoting sparsity
• Elastic net: Combination of L1 and L2 penalties
• Shrinkage: Pulling estimates toward central value
• Empirical Bayes: Using data to estimate prior distribution
• Hierarchical model: Model with multiple levels of variation
• Mixed effects model: Model with fixed and random effects
• Random effects: Effects varying across groups
• Fixed effects: Effects constant across groups
• Marginal effect: Effect of one variable holding others constant
• Counterfactual: What would have happened under different conditions
• Propensity score: Probability of receiving treatment given covariates
• Instrumental variable: Variable affecting outcome only through treatment
• Difference-in-differences: Method comparing changes across groups
• Regression discontinuity: Exploiting threshold in treatment assignment
• Matching: Pairing similar units across treatment groups
• Causal inference: Determining cause-effect relationships
• Directed acyclic graph (DAG): Graph representing causal relationships
• Conditional independence: Independence given another variable
• Collider: Variable caused by two other variables
• Backdoor path: Non-causal path between variables
• Front-door criterion: Identifying causal effects through mediators
• Identifiability: Ability to estimate parameters from data
• Estimand: Quantity we want to estimate
• Estimator: Method or formula for estimation
• Estimate: Numerical result from applying estimator to data
• Score function: Derivative of log-likelihood
• Fisher information: Expected squared score
• Cramér-Rao bound: Lower bound on estimator variance
• Delta method: Approximating distribution of function of estimator
• Wald test: Test based on maximum likelihood estimates
• Likelihood ratio test: Comparing nested models
• Score test: Test based on score function
• Goodness of fit: How well model matches data
• Residual analysis: Examining errors for patterns
• Diagnostic plots: Visual checks of model assumptions
• Q-Q plot: Comparing quantiles to check distributional assumptions
• Leverage plot: Identifying influential observations
• Cook's distance: Measure of observation's influence
• VIF (Variance Inflation Factor): Measure of multicollinearity
• Parsimony: Preference for simpler models
• Occam's razor: Simpler explanations are preferable
• Box-Cox transformation: Family of power transformations
• Logit transformation: Log odds transformation
• Z-score: Standardized value (x - mean) / SD
• Percentile: Value below which percentage of data falls
• Quantile: Generalization of percentile
• Interquartile range (IQR): Difference between 75th and 25th percentiles
• Median absolute deviation (MAD): Robust measure of spread
• Skewness: Measure of asymmetry
• Kurtosis: Measure of tail heaviness
• Moment: Expected value of power of variable
• Moment-generating function: Function encoding all moments
• Characteristic function: Fourier transform of distribution
• Convolution: Distribution of sum of independent variables
• Mixture distribution: Weighted combination of distributions
• Censoring: Observation partially known (e.g., survival past time)
• Truncation: Observations outside range not recorded
• Missing data mechanism: Process generating missingness
• Missing completely at random (MCAR): Missingness unrelated to data
• Missing at random (MAR): Missingness depends on observed data
• Missing not at random (MNAR): Missingness depends on unobserved data
• Imputation: Filling in missing values
• Multiple imputation: Creating multiple completed datasets
• Sensitivity analysis: Examining robustness to assumptions
• Meta-analysis: Statistical synthesis of multiple studies
• Effect heterogeneity: Variation in effects across studies
• Publication bias: Tendency to publish significant results
• Funnel plot: Visual check for publication bias
• Random effects meta-analysis: Modeling between-study variation
• Fixed effects meta-analysis: Assuming common true effect

Concepts:

• Statistical thinking vs deterministic thinking
• Variability as fundamental property of data
• Signal vs noise distinction
• Uncertainty quantification and propagation
• Sampling as basis for inference
• Representative sampling challenges
• Randomization as foundation of inference
• Probability as formalization of uncertainty
• Frequentist interpretation of probability
• Bayesian interpretation of probability
• Subjective vs objective probability
• Aleatory vs epistemic uncertainty
• Law of total probability
• Conditional independence structures
• Exchangeability of observations
• Sufficiency and data reduction
• Ancillary statistics
• Completeness of statistic families
• Information loss in summarization
• Minimal sufficient statistics
• Exponential families of distributions
• Location-scale families
• Transformation of random variables
• Jacobian in transformations
• Order statistics and their distributions
• Asymptotic theory and approximations
• Convergence in probability
• Convergence in distribution
• Almost sure convergence
• Consistency of estimators
• Asymptotic normality
• Delta method for variance approximation
• Slutsky's theorem
• Continuous mapping theorem
• Large sample theory
• Efficiency and relative efficiency
• Cramér-Rao lower bound
• Optimal estimation theory
• Decision theory framework
• Loss functions and risk
• Admissibility of estimators
• Minimax decision rules
• Bayes estimators
• Empirical Bayes methods
• James-Stein estimator and shrinkage
• Stein's paradox
• Hypothesis testing logic
• Neyman-Pearson framework
• Likelihood principle
• Evidential paradigm
• Multiple comparisons problem
• Sequential testing
• Interim analysis considerations
• Stopping rules
• Optional stopping problem
• Pre-registration and registered reports
• Exploratory vs confirmatory analysis
• Data dredging and p-hacking
• HARKing (Hypothesizing After Results Known)
• Researcher degrees of freedom
• Replication crisis and reproducibility
• Statistical vs practical significance
• Clinical vs statistical significance
• Equivalence testing
• Non-inferiority testing
• Bayesian hypothesis testing
• Bayes factors
• Prior elicitation
• Prior sensitivity analysis
• Conjugacy and computational convenience
• Noninformative priors
• Jeffreys prior
• Reference priors
• Maximum entropy priors
• Empirical priors from data
• Hierarchical priors
• Markov Chain Monte Carlo (MCMC)
• Gibbs sampling
• Metropolis-Hastings algorithm
• Hamiltonian Monte Carlo
• Variational inference
• Approximate Bayesian computation
• Posterior predictive checking
• Model comparison via marginal likelihood
• Model averaging
• Model selection vs model averaging
• Information criteria philosophy
• Cross-validation strategies
• Leave-one-out cross-validation
• K-fold cross-validation
• Time series cross-validation
• Nested vs non-nested models
• Parsimony principle
• Model complexity penalties
• Regularization philosophy
• Bias-variance decomposition
• Ensemble methods rationale
• Bootstrap aggregating (bagging)
• Random subspace methods
• Out-of-bag error estimation
• Bootstrap confidence intervals
• Percentile bootstrap
• BCa (bias-corrected and accelerated) bootstrap
• Parametric bootstrap
• Permutation tests logic
• Exact tests vs asymptotic tests
• Monte Carlo hypothesis testing
• Resampling-based inference
• Robust statistics philosophy
• Breakdown point
• Influence functions
• M-estimation
• Rank-based methods
• Nonparametric statistics
• Distribution-free methods
• Kernel density estimation
• Bandwidth selection
• Smoothing parameters
• Local polynomial regression
• Splines and basis functions
• Generalized additive models philosophy
• Semiparametric models
• Functional data analysis concepts
• High-dimensional statistics
• Curse of dimensionality
• Dimension reduction strategies
• Feature selection vs extraction
• Sparse estimation
• Variable screening
• False discovery rate control
• Multiple testing frameworks
• Closed testing procedures
• Holm-Bonferroni method
• Benjamini-Hochberg procedure
• q-values
• Local FDR
• Sequential vs simultaneous inference
• Experimental design principles
• Randomization rationale
• Blocking to reduce variation
• Factorial designs
• Fractional factorial designs
• Confounding in designs
• Aliasing of effects
• Resolution of designs
• Optimal design theory
• D-optimality, A-optimality
• Adaptive designs
• Sequential experimental design
• Response surface methodology
• Latin square designs
• Crossover designs
• Split-plot designs
• Repeated measures designs
• Power analysis and sample size
• Minimal detectable effect
• Precision-based sample size
• Adaptive sample size determination
• Interim analyses and alpha spending
• Group sequential designs
• Futility stopping
• Sample size re-estimation
• Observational study design
• Cohort studies
• Case-control studies
• Cross-sectional studies
• Ecological studies
• Natural experiments
• Quasi-experimental designs
• Instrumental variables intuition
• Regression discontinuity intuition
• Difference-in-differences logic
• Synthetic control methods
• Causal graphs and d-separation
• Identifying assumptions
• Ignorability assumption
• Exchangeability in causal inference
• Positivity assumption
• Consistency assumption (SUTVA)
• Potential outcomes framework
• Counterfactual reasoning
• Average treatment effect (ATE)
• Average treatment on treated (ATT)
• Local average treatment effect (LATE)
• Conditional average treatment effect (CATE)
• Heterogeneous treatment effects
• Subgroup analysis
• Interaction effects interpretation
• Effect modification
• Mediation analysis
• Direct vs indirect effects
• Path analysis
• Structural equation modeling concepts
• Latent variable models
• Factor analysis logic
• Measurement models
• Structural models
• Identification in SEMs
• Model fit indices
• Modification indices
• Time series concepts
• Autocorrelation structure
• Partial autocorrelation
• Stationarity and differencing
• Unit root testing
• Cointegration
• ARIMA models
• Seasonal ARIMA
• State space models
• Kalman filtering
• Exponential smoothing
• Holt-Winters method
• Spectral analysis
• Fourier analysis
• Wavelet analysis
• Change point detection
• Structural breaks
• Intervention analysis
• Transfer function models
• Vector autoregression (VAR)
• Granger causality
• Impulse response functions
• Forecast accuracy measures
• Forecast intervals
• Prediction intervals vs confidence intervals
• Forecast combination
• Longitudinal data structure
• Panel data concepts
• Within vs between variation
• Fixed effects logic
• Random effects logic
• Hausman test intuition
• Clustered standard errors
• Robust variance estimation
• Sandwich estimators
• Generalized estimating equations (GEE)
• Working correlation structures
• Missing data challenges
• Listwise deletion consequences
• Multiple imputation philosophy
• Proper vs improper imputation
• Imputation model specification
• Auxiliary variables in imputation
• Pattern mixture models
• Selection models
• Sensitivity to missingness assumptions
• Measurement error effects
• Attenuation bias
• Classical measurement error
• Berkson measurement error
• Errors-in-variables models
• Instrumental variables for measurement error
• Regression calibration
• SIMEX (simulation-extrapolation)
• Validation study designs
• Reliability vs validity
• Construct validity
• Criterion validity
• Content validity
• Test-retest reliability
• Inter-rater reliability
• Internal consistency
• Cohen's kappa
• Intraclass correlation
• Cronbach's alpha
• Item response theory
• Differential item functioning
• Meta-analysis rationale
• Fixed vs random effects in meta-analysis
• Heterogeneity assessment
• I-squared statistic
• Tau-squared
• Meta-regression
• Publication bias assessment
• Trim and fill method
• Egger's test
• P-curve analysis
• Cumulative meta-analysis
• Prospective meta-analysis
• Individual participant data meta-analysis
• Network meta-analysis
• Indirect comparisons
• Transitivity assumption

Procedures:

• Exploratory Data Analysis (EDA):
  • Examine data structure and types
  • Calculate summary statistics
  • Identify data quality issues
  • Check for outliers and anomalies
  • Visualize distributions
  • Explore relationships between variables
  • Identify patterns and anomalies
  • Document findings and questions
  • Formulate hypotheses for testing
• Data cleaning and preparation:
  • Handle missing values
  • Identify and treat outliers
  • Check for data entry errors
  • Validate data against expectations
  • Transform variables as needed
  • Create derived variables
  • Encode categorical variables
  • Normalize or standardize if needed
  • Split data for validation
• Assessing distributional assumptions:
  • Create histograms and density plots
  • Generate Q-Q plots
  • Perform Shapiro-Wilk test
  • Conduct Kolmogorov-Smirnov test
  • Check Anderson-Darling test
  • Examine skewness and kurtosis
  • Consider transformations if needed
  • Use robust methods if assumptions violated
• Hypothesis test execution:
  • State null and alternative hypotheses
  • Choose appropriate test
  • Check test assumptions
  • Set significance level
  • Calculate test statistic
  • Determine p-value
  • Make decision about null hypothesis
  • Calculate confidence interval
  • Report effect size
  • Interpret results in context
• Sample size calculation:
  • Specify hypotheses or precision goal
  • Determine significance level (alpha)
  • Specify desired power (1-beta)
  • Estimate effect size from literature or pilot
  • Account for expected attrition
  • Consider design complexity (clustering, etc.)
  • Calculate required sample size
  • Assess feasibility
  • Document assumptions
• Power analysis:
  • Specify sample size
  • Define effect size of interest
  • Set significance level
  • Calculate power
  • Create power curves
  • Assess sensitivity to assumptions
  • Consider minimal detectable effect
• Bootstrap confidence intervals:
  • Draw B bootstrap samples with replacement
  • Calculate statistic for each sample
  • Sort bootstrap statistics
  • Extract percentile-based intervals
  • Or calculate BCa intervals with bias correction
  • Assess interval stability
  • Report bootstrap SE and CI
• Permutation test:
  • Calculate observed test statistic
  • Randomly permute group labels (or data)
  • Recalculate test statistic
  • Repeat many times (e.g., 10,000)
  • Compare observed to permutation distribution
  • Calculate p-value as proportion as extreme
  • Assess sensitivity to number of permutations
• Cross-validation procedure:
  • Partition data into K folds
  • For each fold:
    • Train model on K-1 folds
    • Validate on held-out fold
    • Record performance metric
  • Average performance across folds
  • Calculate standard error of performance
  • Select model with best CV performance
  • Refit on full dataset if needed
• Multiple testing correction:
  • Identify family of tests
  • Choose correction method (Bonferroni, FDR, etc.)
  • Calculate adjusted p-values or critical values
  • Apply decision rule
  • Report both raw and adjusted p-values
  • Interpret significant findings
  • Consider power loss from correction
• Model diagnostics for regression:
  • Plot residuals vs fitted values
  • Create Q-Q plot of residuals
  • Check scale-location plot
  • Identify influential points (Cook's D)
  • Calculate VIF for multicollinearity
  • Perform Durbin-Watson test for autocorrelation
  • Test for heteroscedasticity (Breusch-Pagan)
  • Consider remedies if assumptions violated
• Variable selection:
  • Assess univariate associations
  • Check for multicollinearity
  • Use domain knowledge for inclusion
  • Apply stepwise selection (with caution)
  • Use penalized regression (lasso/elastic net)
  • Cross-validate selection process
  • Consider stability of selection
  • Report selection process clearly
• Comparing nested models:
  • Fit reduced (simpler) model
  • Fit full (more complex) model
  • Calculate likelihood ratio statistic
  • Determine degrees of freedom
  • Find p-value from chi-square distribution
  • Or use AIC/BIC for comparison
  • Consider parsimony principle
  • Validate on held-out data
• Time series analysis workflow:
  • Plot time series
  • Check for stationarity (visual and tests)
  • Difference if needed
  • Examine ACF and PACF
  • Identify potential ARIMA orders
  • Fit candidate models
  • Check residual diagnostics
  • Compare models (AIC, BIC)
  • Validate with forecast accuracy
  • Generate forecasts with intervals
• Propensity score analysis:
  • Identify confounders
  • Fit propensity score model
  • Check covariate balance
  • Trim if needed for overlap
  • Apply matching, weighting, or stratification
  • Check balance after adjustment
  • Estimate treatment effect
  • Conduct sensitivity analysis
  • Report assumptions and limitations
• Missing data handling:
  • Assess missingness patterns
  • Determine missingness mechanism (MCAR/MAR/MNAR)
  • Choose handling strategy
  • For multiple imputation:
    • Specify imputation model
    • Include auxiliary variables
    • Generate m imputed datasets
    • Analyze each dataset
    • Pool results using Rubin's rules
  • Conduct sensitivity analysis
  • Report missingness and approach
• Meta-analysis procedure:
  • Define inclusion criteria
  • Search literature systematically
  • Extract effect sizes and SEs
  • Assess study quality/risk of bias
  • Check for heterogeneity
  • Fit fixed or random effects model
  • Create forest plot
  • Assess publication bias (funnel plot, tests)
  • Conduct sensitivity analyses
  • Report with PRISMA guidelines
• Bayesian analysis workflow:
  • Specify likelihood
  • Choose prior distributions
  • Check prior predictive distributions
  • Fit model (MCMC or variational)
  • Check convergence diagnostics (R-hat, ESS)
  • Examine trace plots
  • Check posterior predictive distributions
  • Summarize posterior (mean, median, intervals)
  • Conduct sensitivity to prior
  • Report full posterior, not just point estimates
• Causal inference with DAGs:
  • Draw causal DAG based on domain knowledge
  • Identify confounders, mediators, colliders
  • Determine minimal adjustment set
  • Check if effect is identifiable
  • Assess backdoor criterion
  • Consider front-door criterion if needed
  • Implement adjustment strategy
  • Estimate causal effect
  • Conduct sensitivity analysis
  • Report causal assumptions explicitly
• Designing an experiment:
  • Define research question clearly
  • Identify primary outcome
  • Specify treatment/intervention
  • Determine experimental units
  • Plan randomization scheme
  • Calculate sample size
  • Design data collection protocol
  • Plan statistical analysis in advance
  • Pre-register if appropriate
  • Consider pilot study

Topics:

• Fundamentals of probability theory
• Combinatorics and counting methods
• Random variables and distributions
• Discrete probability distributions
• Continuous probability distributions
• Multivariate distributions
• Joint, marginal, and conditional distributions
• Transformations of random variables
• Moment generating functions
• Characteristic functions
• Order statistics
• Sampling distributions
• Central Limit Theorem and applications
• Law of Large Numbers
• Convergence concepts in probability
• Point estimation theory
• Maximum likelihood estimation
• Method of moments
• Bayesian estimation
• Properties of estimators
• Sufficiency and completeness
• Cramér-Rao lower bound
• Asymptotic theory of estimation
• Robust estimation methods
• M-estimation and robust regression
• Interval estimation
• Confidence intervals construction
• Bayesian credible intervals
• Bootstrap confidence intervals
• Prediction intervals
• Tolerance intervals
• Hypothesis testing foundations
• Neyman-Pearson theory
• Likelihood ratio tests
• Wald tests
• Score tests
• Multiple testing procedures
• False discovery rate control
• Sequential testing methods
• Equivalence and non-inferiority testing
• Bayesian hypothesis testing
• Parametric hypothesis tests
• t-tests and variations
• ANOVA (one-way, two-way, repeated measures)
• ANCOVA
• MANOVA
• Chi-square tests
• Tests for proportions
• Tests for variance
• F-tests
• Nonparametric tests
• Sign test
• Wilcoxon signed-rank test
• Mann-Whitney U test
• Kruskal-Wallis test
• Friedman test
• Rank correlation tests
• Kolmogorov-Smirnov test
• Anderson-Darling test
• Shapiro-Wilk test
• Simple linear regression
• Multiple linear regression
• Polynomial regression
• Regression diagnostics
• Residual analysis
• Influential observations
• Multicollinearity
• Variable selection methods
• Ridge regression
• Lasso regression
• Elastic net
• Principal component regression
• Partial least squares regression
• Generalized linear models
• Logistic regression
• Poisson regression
• Negative binomial regression
• Probit regression
• Ordinal regression
• Multinomial regression
• Zero-inflated models
• Hurdle models
• Survival analysis
• Kaplan-Meier estimation
• Cox proportional hazards
• Parametric survival models
• Competing risks
• Time-varying covariates
• Frailty models
• Longitudinal data analysis
• Mixed effects models
• Random intercept and slope models
• Growth curve modeling
• Generalized estimating equations
• Time series analysis
• ARIMA models
• Seasonal decomposition
• State space models
• GARCH models
• Vector autoregression
• Cointegration analysis
• Forecasting methods
• Exponential smoothing
• Structural time series models
• Multivariate analysis
• Principal component analysis
• Factor analysis
• Discriminant analysis
• Canonical correlation
• Multidimensional scaling
• Correspondence analysis
• Cluster analysis
• Hierarchical clustering
• K-means clustering
• Model-based clustering
• Density-based clustering
• Dimensionality reduction techniques
• Causal inference methods
• Potential outcomes framework
• Propensity score methods
• Instrumental variables
• Regression discontinuity designs
• Difference-in-differences
• Synthetic controls
• Mediation analysis
• Directed acyclic graphs
• Structural equation modeling
• Path analysis
• Measurement models
• Latent variable models
• Experimental design
• Randomized controlled trials
• Factorial designs
• Fractional factorial designs
• Response surface methodology
• Optimal designs
• Sequential designs
• Adaptive designs
• Crossover designs
• Latin squares
• Observational study designs
• Cohort studies
• Case-control studies
• Cross-sectional studies
• Survey sampling methods
• Simple random sampling
• Stratified sampling
• Cluster sampling
• Multistage sampling
• Sampling weights
• Survey variance estimation
• Nonresponse adjustment
• Resampling methods
• Bootstrap methods
• Jackknife methods
• Permutation tests
• Cross-validation techniques
• Monte Carlo methods
• Simulation studies
• Bayesian computational methods
• Markov Chain Monte Carlo
• Gibbs sampling
• Metropolis-Hastings
• Hamiltonian Monte Carlo
• Variational inference
• Approximate Bayesian computation
• Prior elicitation
• Posterior predictive checking
• Model selection and averaging
• Information criteria (AIC, BIC)
• Cross-validation for model selection
• Bayesian model selection
• Model averaging strategies
• Missing data methods
• Multiple imputation
• Maximum likelihood with missing data
• Inverse probability weighting
• Pattern mixture models
• Selection models
• Measurement error models
• Errors-in-variables regression
• Regression calibration
• SIMEX
• Latent class models
• Reliability and validity assessment
• Classical test theory
• Item response theory
• Meta-analysis
• Fixed effects meta-analysis
• Random effects meta-analysis
• Meta-regression
• Publication bias assessment
• Network meta-analysis
• Individual participant data meta-analysis
• Statistical learning theory
• Bias-variance tradeoff
• Regularization methods
• Ensemble methods
• Model interpretation and explanation
• High-dimensional statistics
• Sparse estimation
• Variable screening
• False discovery rate
• Functional data analysis
• Spatial statistics
• Geostatistics
• Kriging
• Spatial point processes
• Spatial regression models
• Nonparametric statistics
• Kernel methods
• Local regression
• Smoothing splines
• Generalized additive models
• Quantile regression
• Robust statistics theory
• Influence functions
• Breakdown points
• Statistical quality control
• Control charts
• Process capability analysis
• Acceptance sampling
• Reliability theory
• Extreme value theory
• Statistical graphics and visualization
• Reproducible research practices
• Statistical computing
• Numerical optimization
• Matrix computations
• Statistical software packages

Categories:

• Probability Theory
• Mathematical Statistics
• Inferential Statistics
• Descriptive Statistics
• Parametric Methods
• Nonparametric Methods
• Regression Analysis
• Time Series Analysis
• Multivariate Statistics
• Bayesian Statistics
• Frequentist Statistics
• Computational Statistics
• Resampling Methods
• Experimental Design
• Survey Methodology
• Causal Inference
• Survival Analysis
• Longitudinal Data Analysis
• Spatial Statistics
• High-Dimensional Statistics
• Robust Statistics
• Missing Data Analysis
• Measurement Theory
• Meta-Analysis
• Statistical Learning
• Stochastic Processes
• Extreme Value Statistics
• Quality Control Statistics
• Biostatistics
• Econometrics
• Psychometrics
• Statistical Computing

Themes:

• Uncertainty quantification and management
• Inference from samples to populations
• Balancing model complexity and interpretability
• Assumptions and their verification
• Robustness to departures from assumptions
• Signal detection in noisy data
• Multiple perspectives on probability and inference
• Trade-offs between different statistical properties
• Importance of study design for valid inference
• Causation vs correlation distinction
• Replication and reproducibility
• Transparency in statistical practice
• Context-dependent choice of methods
• Integration of domain knowledge and data
• Ethics in data analysis and reporting
• Communication of uncertainty
• Computational advances enabling new methods
• Bridging classical and modern approaches
• Handling real-world data complexities
• Adaptation to non-standard data structures
• Unification of statistical frameworks
• Model criticism and validation
• Sensitivity to modeling choices
• Multiplicity and its consequences
• Pre-specification vs exploratory analysis
• Theory-driven vs data-driven approaches

Trends:

• Increased focus on causal inference methods
• Bayesian methods becoming more accessible
• Machine learning integration with statistics
• Emphasis on prediction vs explanation
• High-dimensional and sparse methods
• Advances in computational Bayesian methods
• Reproducibility and replication emphasis
• Pre-registration of analyses
• Open data and open science movement
• Registered reports in journals
• Transparency and robustness checks
• Sensitivity analysis as standard practice
• Multiverse analysis
• Specification curve analysis
• Quantifying researcher degrees of freedom
• Model-agnostic interpretation methods
• Conformal prediction
• Distribution-free inference
• Robust inference without strong assumptions
• Adaptive and sequential designs
• Platform trials
• Master protocols
• Real-world evidence methods
• Integration of multiple data sources
• Privacy-preserving statistical methods
• Differential privacy
• Federated learning
• Statistical methods for algorithmic fairness
• Causal ML and double machine learning
• Targeted learning
• Reinforcement learning for treatment optimization
• Network and graphical models expansion
• Topological data analysis
• Functional data analysis growth
• Distributional regression
• Expectile regression beyond quantiles
• AI-assisted statistical analysis
• Automated model selection and tuning
• Interpretable ML vs black-box trade-offs
• Uncertainty quantification in ML
• Probabilistic programming languages
• Stan, PyMC, TensorFlow Probability
• Cloud-based statistical computing
• Big data statistical methods
• Streaming data analysis
• Online learning and updating
• Spatial and temporal big data
• Integration of structured and unstructured data
• Text as data methods
• Image and video data statistical analysis
• Wearable device data analysis
• Electronic health records analysis
• Environmental and climate statistics
• Statistical methods for complex surveys at scale
• Small area estimation advances
• Synthetic data generation
• Data fusion techniques

Use_cases:

• Clinical trial design and analysis
• Drug efficacy and safety evaluation
• Biomarker discovery and validation
• Genome-wide association studies
• Differential gene expression analysis
• Proteomics and metabolomics data analysis
• Epidemiological outbreak investigation
• Disease surveillance systems
• Risk factor identification
• Diagnostic test evaluation
• Survival and time-to-event analysis
• Meta-analysis of medical literature
• Health policy evaluation
• Quality of care assessment
• A/B testing and experimentation
• Customer segmentation and profiling
• Churn prediction and prevention
• Market mix modeling
• Pricing optimization
• Demand forecasting
• Inventory optimization
• Supply chain analytics
• Credit risk modeling
• Fraud detection
• Algorithmic trading strategies
• Portfolio optimization
• Risk management and VaR estimation
• Econometric modeling
• Policy impact evaluation
• Labor market analysis
• Housing market analysis
• Inflation and growth forecasting
• Survey data analysis
• Election forecasting
• Public opinion polling
• Census data analysis
• Social program evaluation
• Education intervention effectiveness
• Test score analysis and equating
• Learning analytics
• Environmental impact assessment
• Climate change modeling
• Species distribution modeling
• Pollution monitoring and prediction
• Water quality analysis
• Agricultural field trials
• Crop yield prediction
• Weather forecasting
• Reliability analysis for engineering systems
• Quality control in manufacturing
• Process optimization
• Accelerated life testing
• Fatigue analysis
• Six Sigma projects
• Psychometric test development
• Personality assessment validation
• Neuroimaging data analysis
• Behavioral experiment analysis
• Sports analytics and performance evaluation
• Player evaluation and scouting
• Game strategy optimization
• Sensor data analysis for IoT
• Predictive maintenance
• Network traffic analysis
• Cybersecurity threat detection
• Natural language processing applications
• Search engine ranking
• Recommendation systems
• User behavior modeling
• Content optimization
• Social network analysis
• Information diffusion studies
• Archaeological dating and analysis
• Historical data reconstruction
• Legal evidence evaluation
• Forensic statistics
• Insurance pricing and reserves
• Actuarial modeling
• Astronomy and cosmology data analysis
• Particle physics experiments
• Geospatial analysis
• Transportation planning
• Real estate valuation
• Energy consumption modeling