Markdown Editor
打开编辑器

统计建模工具包

最大似然与贝叶斯推断、线性、逻辑、计数与混合模型、ARIMA、前提假设检查、数据变换、重抽样和回归模型报告。

第 1 步

学习

  1. Estimation and Maximum Likelihood Concept Card Template (Statistics)

    完整

    Point estimation and maximum likelihood: bias, variance, MSE, method of moments, analytic and numerical MLE (optim, scipy.optimize), SEs from the Hessian, likelihood ratio test, AIC

    Fisher (1922, 1925); Pearson (1894); Wilks (1938); Akaike (1974); NIST/SEMATECH e-Handbook

  2. Bayesian Inference Concept Card Template (Statistics, R and Python)

    完整

    Prior, likelihood and posterior: beta-binomial and normal-normal updates, credible vs confidence intervals, posterior predictive, prior sensitivity, Bayes factor cautions, grid approximation in base R and numpy

    Bayes (1763); Jeffreys (1961); Kass and Raftery (1995); Lindley (1957); Gelman et al. Bayesian Data Analysis (name)
第 2 步

方法与模式

  1. Linear Regression Method Card Template (Statistics, R and Python)

    完整

    Simple and multiple OLS regression: least squares, coefficient tests and CIs, R² and F test, dummies, interactions, diagnostics, HC3 robust SEs, prediction vs confidence intervals, with R and Python

    Least squares (Legendre 1805); Cook (1977); White (1980); MacKinnon and White (1985) HC3; NIST/SEMATECH e-Handbook ch. 4; APA JARS-Quant (name)

  2. Logistic Regression Method Card Template (Statistics, R and Python)

    完整

    Binary logistic regression: logit link, odds ratios, Wald vs likelihood-ratio tests, profile vs Wald CIs, predicted probabilities and marginal effects, classification metrics, calibration, separation and EPV, with R and Python

    Cox (1958); Nelder and Wedderburn (1972); Albert and Anderson (1984); Firth (1993); Hanley and McNeil (1982); Peduzzi et al. (1996); APA JARS-Quant (name)

  3. Count Regression Method Card Template (Statistics, Poisson and NB, R and Python)

    完整

    Poisson and negative binomial regression for counts: rate ratios, offsets for exposure, overdispersion check, quasi-Poisson, theta vs alpha, zero-inflation note, with R and Python

    Nelder and Wedderburn (1972); Lawless (1987); Lambert (1992); Cameron and Trivedi (2013); Venables and Ripley (2002) MASS; NIST/SEMATECH e-Handbook (public domain)

  4. Linear Mixed Models Method Card Template (Statistics, R and Python)

    完整

    Clustered and longitudinal data: random intercepts and slopes, ICC, REML vs ML, lme4 and statsmodels MixedLM side by side, df methods, singular fits, reporting

    Laird and Ware (1982); Patterson and Thompson (1971); Satterthwaite (1946); Kenward and Roger (1997); Bates et al. (2015); NIST/SEMATECH e-Handbook; APA JARS-Quant (name)

  5. Time Series and ARIMA Method Card Template (Statistics, R and Python)

    完整

    Decomposition, ADF and KPSS, ACF and PACF, seasonal ARIMA identification, Ljung-Box checks, forecasts with intervals and hold-out accuracy, in R and Python

    Box and Jenkins (1970); Dickey and Fuller (1979); Kwiatkowski et al. (1992); Ljung and Box (1978); NIST/SEMATECH e-Handbook 6.4; R forecast and statsmodels documentation
第 3 步

验证

  1. Assumption Checklist Template (Statistics, Diagnostics, R and Python)

    完整

    Checking assumptions per method family (t/ANOVA, regression, GLMs, chi-square, correlation, repeated measures and mixed models): diagnostics, R and Python code, judgement rules and remedies

    NIST/SEMATECH e-Handbook of Statistical Methods; Cook (1977); Box and Cox (1964); Levene (1960); Brown and Forsythe (1974); Mauchly (1940); Greenhouse and Geisser (1959); Nelder and Wedderburn (1972); Fox and Weisberg (2019)

  2. Data Transformations Method Card Template (Statistics, R and Python)

    完整

    Data transformations method card – log, sqrt, Box-Cox, Yeo-Johnson, logit, z-scores, centring and ranks, percent-change interpretation and smearing back-transformation, with R and Python

    Box and Cox (1964); Yeo and Johnson (2000); Duan (1983); Warton and Hui (2011); NIST/SEMATECH e-Handbook (Box-Cox)

  3. Bootstrap and Permutation Methods Card Template (Statistics, R and Python)

    完整

    Bootstrap percentile, basic and BCa intervals, exact and Monte Carlo permutation tests, simulation checks and seeds, in R and Python

    Efron (1979); Efron and Tibshirani (1993); Davison and Hinkley (1997); NIST/SEMATECH e-Handbook; R boot and SciPy documentation
第 4 步

编写文档

  1. Regression Model Report Template (Statistics, R and Python)

    完整

    Working report for one regression model: purpose and estimand, data and sample, variables, specification, diagnostics checklist with evidence, results, model comparison, validation, sensitivity, limitations, reproducibility and sign-off

    Shmueli (2010) explain vs predict; Harrell (2015); TRIPOD (Collins et al. 2015) and TRIPOD+AI (Collins et al. 2024), names only; APA JARS-Quant (name); Akaike (1974); Schwarz (1978)