you need to nerd out

you need to nerd out Done when: you derive the MLE and Fisher information for Bernoulli and Normal unaided. Week 2—Linear algebra = the regression machine (~16 h) Intuition: 3Blue1Brown - Essence of Linear Algebra (full series) (3h) Mechanics: Khan - Linear Algebra - matrix mult, transpose, inverse (A1), rank, identity (4 h) Quadratic forms, symmetric matrices, positive-definiteness (covariance matrices), eigenvalues (A2) (3h) Regression in matrix form: y = Xβ + ε = β = (X'X)⁻¹X'y -> hat matrix H = X(X'X)⁻¹X' -> fitted values as a projection. ISLR Ch 3 + Fahrmeir et al., Regression (the shared regression reference) (4 h) R: vectors, data frames, first 1m() (2h) Done when: you can write the least-squares solution in matrix form and explain what the hat matrix does. Week 3—Distributions bridge + likelihood concepts + R (~16 h) Distributions toolkit (pmf/pdf, mean, variance): Normal, Bernoulli/Binomial, Poisson, Exponential, Gamma, Beta. Note the conjugate pairs (Beta-Binomial, Gamma-Poisson, Normal- Normal) for Bayesian. Blitzstein - targeted (4 h) Exponential family form (Likelihood part 2 + GLMs) (2 h) Likelihood machine, run 2: Poisson + Binomial. Then the concepts: standard error, Wald / score / likelihood-ratio tests, profile likelihood. Primary text below (5 h) R: 1m() summaries, residual plots, swirl package (3 h) Review loose ends (2 h) Done when: you can state pmf/pdf + mean + variance of the main distributions and recognise a conjugate pair. Week 4—R fluency + Bayes + consolidate + retest (~16 h) R for your courses: 1m(), glm(), aov(), reviewing summaries, diagnostics. Meler - ANOVA and Mixed Models (free, R-based) + R4DS (5 h) Bayesian by hand: posterior ∝ prior × likelihood, normalizing constant as an integral, a full Beta-Binomial conjugate update, and the Laplace approximation idea (Taylor around the mode -> ties back to Week 1) (4 h) Arduino Tutorial 12: Understanding Potentiometers Sketch uses 3122 bytes (9%) Global variables use 200 bytes (9%) of dynar Tutorial 10 Reading voltage from our setup: PinMode(readpin, INPUT); Serial.begin(9600); loop: V2= analogRead(readpin) Serial.println(V2) Readvalue between 0 0V 1023 Real voltage = 5/1023 * ReadV L'U R U' L' U R' R U R' U R U2 R' U: UPWARD FACE, 90° CW 1 make the daisy 2 white cross 3 solve bottom layer 4 Second layer solved 5 yellow edge piece FUR U'R'F' -2 yellow edge piece (line, orient towards you: FUR U'R'F' -2 yellow pieces on line and then FUR U'R'F 5. yellow 6. yellow -es (rotate until yellow left R' F -> R U R' U R U2 R' L' U R U' L' U R' R U R' U R U2 R' # Search best set of hyperparameters alpha and p (ONLY RUN THIS ONCE AND THEN SAVE PARAMETERS) -> import numpy as np # errors in LEVEL space: y_(t+h) - y_hat_(t+h) errors = actual_s - pred_s rmse = np.sqrt(np.mean(errors**2)) cv_rmse.append( "Maturity": target_col, "Horizon": h, "alpha": alpha, "p": p, "CV_RMSE": rmse, "H_Forecasts": len(errors) )) ridge_cv_results = pd.DataFrame(cv_rmse) ridge_cv_results = ridge_cv_results.set_index(["Maturity", "Horizon"]).sort_index() print("ridge CV results (by target, evaluated on levels; first rows):") display(ridge_cv_results.head()) # Choose best (alpha, p) per (Maturity, Horizon) ridge_best_params = {} for (mat, h), group in ridge_cv_results.groupby(level=[0, 1]): best_row = group.sort_values("CV_RMSE").iloc[0] ridge_best_params[(mat, h)] = { "p": int(best_row["p"]), "CV_RMSE": best_row["CV_RMSE"], "H_Forecasts": int(best_row["H_Forecasts"]) } print("\nBest Ridge hyperparameters per (Maturity, Horizon) (by target):") for key, val in ridge_best_params.items(): mat, h = key print(f"Maturity: {mat}, Horizon: {h} -> alpha={val['alpha']}, p={val['p']},") print(f" "CV_RMSE={val['CV_RMSE']}, H={val['H_Forecasts']}") Alpha grid: [0.0, 0.1, 0.15, 0.2, 0.3, 0.4] Lag grid: [0, 1, 5, 10] CV for Ridge (by target): target=0052, h=1 (DEBUG RIDGE CV) origin=2014-01-02, train_end_date(h=0)=2013-12-31, max_train_t=2013-12-31, forecast_date(t+h)=2014-01-03 (DEBUG RIDGE CV) origin=2014-01-09, train_end_date(h=0)=2014-01-07, max_train_t=2014-01-07, forecast_date(t+h)=2014-01-10 (DEBUG RIDGE CV) origin=2014-01-16, train_end_date(h=0)=2014-01-14, max_train_t=2014-01-14, forecast_date(t+h)=2014-01-17 4.4.2 Diebold-Mariano Test ADD HAC ESTIMATOR VARIANCE array; Leybourne, and Newbold (1997). Testing the equality of prediction mean squared errors, International Journal of Forecasting, 13(2), 281-289. RMSE alone does not indicate whether differences in forecast performance are statistically meaningful. To test whether two models achieve the same predictive accuracy, we apply the Diebold-Mariano test as introduced by Diebold and Mariano (1995). The test compares the squared forecast errors of two competing models. Let L(e_t+h) = (e_t+h)² denote the loss, and define the loss differential as d_t+h = L(e_t+h) - L(e_t+h) The DM statistic is computed as DM = d_bar / sqrt(V_hat(d_bar) / T) where d_bar accounts for serial correlation in forecast errors. A significant value indicates that there is a significant difference in predictive accuracy between the two models (Diebold and Mariano 1995, p. 254).