exercises for Mon Sep 21

1. On Mon Sep 14 we used time to suitably round off Chs 2-3, with the main large-sample mechanisms that need to work well for Recipes One and Two to work for confidence curves. We also started on Ch 4, with boundary parameters, log-likelihoods for survival analysis models, and more.

2. For Mon Sep 21, we start with the following exercises, before we proceed with more Ch 4 material.

(a) For the very simple model y from N(\theta,1), with \theta \ge 0 a priori, graph the canonical CD C(\theta,y) = \Phi(\theta - y), for the three outcomes y = -0.22, y = 0.66, y = 1.99. For each of these three cases, compare with two Bayesian strategies: the first takes \theta flat on (0,\infty); the second has \theta from a mixture, with 0.50 mass at zero and 0.50 probability flat on (0,\infty).

(b) Exercises 4.2, 4.6 from the CLP book.

(c) In R, the dataset "nhtemp" gives annual average temperatures in New Haven, for n = 60 years, namely 1912 to 1971. Fit the simple linear regression model, y = a + b x + N(0,\sigma^2), with x = year - 1900 (for numerical stability reasons), with y the annual temperature translated to Celsius, please (since Norwegians don't understand Fahrenheit). Find confidence curves for a, for b, for \sigma, and for the time x_0 at which the mean curve a + b x crosses y_0 = 16.00 degrees.