Statistics Probability skills for AI agents

Triggers when users need help with Bayesian inference, prior selection, posterior computation, or probabilistic modeling. Activate for questions about prior distributions, conjugate priors, Bayesian vs frequentist approaches, MCMC methods, Metropolis-Hastings, Gibbs sampling, Hamiltonian Monte Carlo, Bayesian model comparison, hierarchical models, Stan, PyMC, and probabilistic programming.

Triggers when users need help establishing causal relationships from data, whether experimental or observational. Activate for questions about potential outcomes, Rubin causal model, DAGs, Pearl's framework, propensity scores, instrumental variables, difference-in-differences, regression discontinuity, synthetic control, mediation analysis, and sensitivity analysis for unmeasured confounding.

Triggers when users need help summarizing, describing, or exploring data distributions. Activate for questions about mean, median, mode, variance, standard deviation, IQR, skewness, kurtosis, five-number summary, box plots, histograms, outlier detection, data summarization, and exploratory data analysis techniques.

Triggers when users need help designing experiments, clinical trials, or A/B tests. Activate for questions about randomized controlled trials, factorial designs, block designs, Latin square, split-plot designs, A/B testing methodology, power analysis, randomization, blinding, confounding, observational study design, and quasi-experimental methods.

Triggers when users need help with hypothesis testing, confidence intervals, or drawing conclusions from sample data. Activate for questions about null and alternative hypotheses, p-values, Type I and II errors, statistical power, t-tests, ANOVA, chi-square tests, effect sizes, multiple comparisons, Bonferroni correction, FDR, and sample size determination.

Triggers when users need help analyzing datasets with multiple variables simultaneously. Activate for questions about PCA, principal component analysis, factor analysis, canonical correlation, MANOVA, discriminant analysis, cluster analysis, k-means, hierarchical clustering, DBSCAN, multidimensional scaling, correspondence analysis, and structural equation modeling.

Triggers when users need help with distribution-free statistical methods or robust alternatives to parametric tests. Activate for questions about Mann-Whitney U, Wilcoxon signed-rank, Kruskal-Wallis, Spearman correlation, kernel density estimation, bootstrapping, permutation tests, rank-based methods, when to use nonparametric vs parametric tests, and robust statistics.

Triggers when users need help with regression modeling, prediction, or understanding relationships between variables. Activate for questions about linear regression, multiple regression, polynomial regression, logistic regression, generalized linear models, Ridge, Lasso, Elastic Net regularization, residual analysis, multicollinearity, heteroscedasticity, variable selection, and interaction effects.

Triggers when users need help analyzing geographically referenced data or spatial patterns. Activate for questions about spatial autocorrelation, Moran's I, geostatistics, kriging, variograms, point process models, spatial regression, areal data analysis, GIS integration, spatial clustering, hot spot analysis, and applications in epidemiology, ecology, and urban planning.

Triggers when users need help designing surveys, selecting samples, or analyzing complex survey data. Activate for questions about simple random sampling, stratified sampling, cluster sampling, multistage sampling, systematic sampling, survey design, weighting, calibration, non-response adjustment, variance estimation for complex surveys, and questionnaire design principles.

Triggers when users need help analyzing time-to-event data, censored observations, or hazard modeling. Activate for questions about censoring, Kaplan-Meier estimator, log-rank test, Cox proportional hazards model, accelerated failure time models, competing risks, time-varying covariates, survival curves, reliability analysis, and customer churn modeling.

Triggers when users need help with temporal data, forecasting, or time-dependent modeling. Activate for questions about stationarity, autocorrelation, ARIMA models, seasonal decomposition, exponential smoothing, GARCH, state space models, spectral analysis, change point detection, forecasting accuracy metrics, Prophet, and modern time series approaches.