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Bộ Mô hình thống kê

Hợp lý cực đại và suy luận Bayes, mô hình tuyến tính, logistic, dữ liệu đếm và hỗn hợp, ARIMA, kiểm tra giả định, biến đổi dữ liệu, lấy mẫu lại và báo cáo mô hình hồi quy.

Bước 1

Học

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

    Đầy đủ

    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)

    Đầy đủ

    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)
Bước 2

Phương pháp và mẫu

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

    Đầy đủ

    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)

    Đầy đủ

    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)

    Đầy đủ

    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)

    Đầy đủ

    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)

    Đầy đủ

    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
Bước 3

Kiểm chứng

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

    Đầy đủ

    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)

    Đầy đủ

    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)

    Đầy đủ

    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
Bước 4

Tài liệu

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

    Đầy đủ

    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)