# Messages

We have communicated a bit via "hjelpetråder", mail threads, on both practical matters, material, and exercises.

Exam project: from t_0 = Dec 8 to t_1 = Dec 18; more information later.

Lars Olsen gives his presentation of the Cunen and Hjort (2020) paper, on II-CC-FF (see FocuStat page), on Mon Nov 23. We make it "open".

Exercises, recently: CLP 7.1, 7.2, 7.9, a few others "on the spot".

I'm placing com50b (on optimal CD for a, with competitors, with gamma(a,b) data, low sample size) and com53a (on optimal CD for mu / sigma^2, with competitors, with normal data, low sample size), on the course website.

1. On Mon Oct 12 we went through several exercises, including the Watership Down exercise to estimation the fraction of biological invaders in a population, based on the trinomial counting (X, Y, Z) of aa, aA, AA. We also discussed the main themes of Ch 5. Next week we round off Ch 5, with emphasis on the "supertheorem" about the very best CD, under exponential-type model conditions.

2. There will with high probability *not* be a firetimers skoleeksamen this semester, due to K-19. Nils checks this week whether we're free to go as planned, with a "Nils Project Exam", in that case with time window [t_0, t_1], with t_0 = Mon Dec 7, t_1 = Fri Dec 18.

3, Mon Oct 19 we round off Ch 5. Ch 6 is *not* curriculum material, so after Ch 5 we do half of Ch 7.

4. Exercises for Mon Oct 19:

(1) Four-hour Exam 2016, Exercise 2.

(2) Make an R script for our Watership Down rabbits, where the start population is in HW balance with (p_0, q_0) = (0.25, 0.75) and the...

1. On Mon Oct 5, we discussed Nils Exercises 14, 15, in particular touching on parametric CD inference for Cox type data, (t_i, x_i, \delta_i). We also went through aspects of the somewhat complicated CLP Exercise 4.3, "complicated" in the sense that its interpretation is not quite clear. The Natural Start of modelling the three trinomial probabilities as lambda pr1 + (1-lambda) pr2, where pr1 = (p_1^2, 2 p_1q_1, q_1^2) and pr2 = (p_2^2, 2 p_2q_1, q_2^2), *doesn't work*. Explain why.

2. Note that I've now placed the firetimerseksamen 2016 on the website.

3. Exercises for Mon Oct 12: First, Exercises 1, 3 from this firetimerseksamen set.

Then, consider the following Watership Down scenario. Rabbits have been living for fifty years on an island, and their alleles a, A are in good Hardy-Weinberg balance, with probabilities of the form prob = (p^2, 2pq, q^2) for aa, aA, AA, with known p = 0.25 and q = 0.75. Then there's an invasion of New Rabbits, with t...

1. On Mon Sept 28 we went through several exercises, including Nils Exercises 12, 13, and Lethal Dose 4.12 from the book. We also discussed matters related to Ch 4 in particular, and I started explaining the themes of Ch 5.

2. I've uploaded a new pdf for the Nils Collection, now with 15 exercises.

3. For Mon Oct 5, we do Nils Exercises 14, 15, and CLP 4.3.

1. On Mon Sep 21 we went through CLP Exercises 4.2, 4.6, plus the one on comparing the canonical CD with two Bayesian posteriors, in the prototype situation where y is N(\theta,1) and \theta \ge 0 a priori. We then discussed material from Ch 4, including Markov's 1913 Pushkin work and Markov chain models. I will find something we can delve into later on, with Markov chain models. I was also reminded of wild & farmed salmon, and have written up Exercise 13 on this in the Nils collection.

2. So please note that I've uploaded an updated version of the Nils Collection, now 15 pages.

3. Exercises for Mon Sep 28: Nils Exercises 12, 13, then CLP Exercise 4.12. -- When you've successfully made it, through the partly laborious points of 4.12, you've also learned many things with stor overføringsverdi!

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...

On Mon Sep 7, we went through Exam 2016 Exercise 2, with various related footnotes, about quantile inference, under normality and nonparametrically. I then summarised main themes and results and tools of Chapters 2 and 3.

For Mon Sep 14, we start with these exercises. First, Exercises 7 and 8 from the Nils Collection. Then, do the Exam 2016 Exercise 2 again, for the case where the mothers' weights are assumed to follow a Gamma distribution (a,b), rather than the normal (and yes, the Gamma fits rather better). Here there's no clear pivot, for the 0.10, 0.50, 0.90 quantiles, but do Recipe One and Recipe Two, from large-sample approximations.

I will use *some* more time to round off Chapters 2 and 3, including regression setups, and then we start with Chapter 4.

And yes, PRIO colleague Håvard Nygård and I have won the strenuous privilege of leading a splendid team of researchers at Centre of Advanced Studies, Academy of Sciences, with our Stability and Change p...

1. We're now attempting to move to the previously announced schedule of having *three Blindern hours on Mondays*, 14:15 to 16:45, and no teaching on Thursdays. This takes place from Mon Sept 7 onwards.

2. We've been through Exam 2016 Exercise 1, and I've placed R scripts com34a and com31a on the course website. For Mon Sept 7, attempt to go through all of Exam 2016 Exercise 2.

3. For Mon Sept 7, I'll attempt to sum up the basics of Chapter 3, where we've soon been through the essentials regarding theory and recipes -- but we still need more practice & practice.

4. I've placed an updated pdf of the Nils Collection on the site. For Mon Sept 7, *read through and reflect on* Exercises 7, 8, where we'll be coming back to the details.

** 1. On Mon 31 Aug we discussed the main types of results and uses, of material and methods from Ch 2, for construction of CDs and ccs in Ch 3. These methods involve large-sample approximations of ML and related quantities. Recipe 1 is to use the normal approximation for ML, perhaps after delta method; Recipe 2 is to use the Wilks Theorem, ending with cc = pchisq(deviance,1). We shall se many uses of these in the weeks to come.

I also sketched how a typical R script might look like, starting with data, model, and log-likelihood function. From these ingredients there are a few generic steps, to find the ML, its approximate variance matrix, the delta method, and also the deviance.

** 2. For Thu 3 Sept we use the time 15:15 - 16 to go through Exam 2016, Exercise 1.

** 3. I'll be placing some R scripts on the course website, in a few days. There will also be an updated version of the "Nils Collection".

** 1. I've fallen ill, unfortunately, and need a few days for recovering to normalcy. We're still in theory set up with Mon 14:15 to 16:00 and Thu 15:15 to 16:00, and the plan was and is still to make this into what we called Scenario A: three Blindern hours (a 45 minutes) on Mon, 14:15 to perhaps 16:45, in room 1120 (and nothing on Thu).

Due to my illness at present, however, we do it like this:

Week starting Mon Aug 24: nothing on Mon, but two hours on Thu, 14:15 to 16:00.

Week starting Mon Aug 31: everything on Mon.

** 2. In the course of Mon 24 I'll have put up more exercises in the "Nils Collection" and placed these on the course website. I'll then also tell you which of these we do for Thu 27. There will by all means also be exercises directly from the CLP book.

** 3. After my two-hour introduction on Mon Aug 17, I'll go through a somewhat quick summary of "everything that's important" from Chapter 2. This is about general and often l...

1. We've started! I used the two hours Mon Aug 17 to indicate in suitable broad terms what the CLP course will be about, and we introduced confidence distributions (CD) and confidence curves (cc). Please read Cunen and Hjort's FocuStat Blog Post "Confidence Curves for Dummies"; one of the exercises for Thursday is to go through the details of their first example.

2. I've uploaded "Version A" of the Exercises & Lectures Notes for the course (and this little collection will grow as the course progresses). For Thu Aug 20, 15:15 to 16:00, work through Exercises 1, 2, 3.

3. We'll try to reach an "executive decision" in the course of a week, regarding how to stucture and place our three hours of teaching. Scenario A: we do all three on Mondays, 14:15 to 16:45. Scenario B: two hours Monday 14:15 to 16:00, then one Blindern hour Thursdays 15:15 to 16:00.

A quick discussion on our first day indicates that Scenario A is to be preferred.

1. We've started! I used the two hours Mon Aug 17 to indicate in suitable broad terms what the CLP course will be about, and we introduced confidence distributions (CD) and confidence curves (cc). Please read Cunen and Hjort's FocuStat Blog Post "Confidence Curves for Dummies"; one of the exercises for Thursday is to go through the details of their first example.

2. I've uploaded "Version A" of the Exercises & Lectures Notes for the course (and this little collection will grow as the course progresses). For Thu Aug 20, 15:15 to 16:00, work through Exercises 1, 2, 3.

3. We'll try to reach an "executive decision" in the course of a week, regarding how to stucture and place our three hours of teaching. Scenario A: we do all three on Mondays, 14:15 to 16:45. Scenario B: two hours Monday 14:15 to 16:00, then one Blindern hour Thursdays 15:15 to 16:00.

A quick discussion on our first day indicates that Scenario A is to be preferred.

According to the machinery, so to speak, we're set up for teaching Mondays 14:15 - 16:00 (in room 1120, 11th floor) and Thursdays 14:15 - 16:00 (in room 1020, 10th floor). However, we're *not* going to have four hours per week, so in the course for the first two weeks we determine what's best for us, either 2 + 1 or 1 + 2, and we might also go for "more or less three teaching hours on one of the two days", e.g. 14:15 to 16:45.

Again, you need go get hold of Schweder and Hjort's CLP book (Confidence, Likelihood, Probability, Cambridge University Press, 2016). It will also be a useful start to read through (and think through) Cunen and Hjort's FocuStat Blog Post "Confidence Curves for Dummies":

https://www.mn.uio.no/math/english/research/projects/focustat/the-focustat-blog!/confidence-dummies.html

Welcome to "CLP", Confidence, Likelihood, Probability, autumn semester 2020, starting Mon Aug 17. We'll know in time whether we can have ordinary lectures or if we will need to go partly korona-era-digital.

You need the CLP by Tore Schweder and Nils Lid Hjort, Cambridge Unviversity Press, 2016 -- you can get it from the publisher, via amazon, and I've seen it at eBay. Also, the Akademika bookshop will have a little stack.

Please check out the 2016 version of the website for this course, with exercises, links, stories, and more.

Nils Lid Hjort