Here’s question 15 of our exam: 15. Consider the following procedure. • Set n = 100 and draw n continuous values x_i uniformly distributed between 0 and 10. Then simulate data from the model y_i = a + bx_i + error_i, for i = 1,…,n, with a = 2, b = 3, and independent errors […]

# Category: Statistics

## space opera by John Scalzi [book review]

John Scalzi, author of the memorable Old Man’s War, has started a trilogy of which I only became aware recently (or more precisely became re-aware!), which has the perk of making two of the three books already published and hence available without a one or two year break. And having the book win the 2018 […]

## smoked tea

The shop of the tea dealer Nathmulls in Darjeeling burned down last week. In possibly suspicious circumstances… While they lost at least 2,000 kg of their tea stock, and most sadly someone died in the fire, Nathmulls can still deliver orders, inc…

## Question 14 of our Applied Regression final exam (and solution to question 13)

Here’s question 14 of our exam: 14. You are predicting whether a student passes a class given pre-test score. The fitted model is, Pr(Pass) = logit^−1(a_j + 0.1x), for a student in classroom j whose pre-test score is x. The pre-test scores range from 0 to 50. The a_j’s are estimated to have a normal […]

## Per stirpes and random walks

If an inheritance is to be divided per stirpes, each descendant gets an equal share. If a descendant has died but has living descendants, his or her share is distributed by applying the rule recursively. Example For example, suppose a man had two children, Alice and Bob, and stipulates in his will that his estate […]

## Naomi Wolf and David Brooks

Palko makes a good point: Parul Sehgal has a devastating review of the latest from Naomi Wolf, but while Sehgal is being justly praised for her sharp and relentless treatment of her subject, she stops short before she gets to the most disturbing and important implication of the story. There’s an excellent case made here […]

## from tramway to Panzer (or back!)…

Although it is usually presented as the tramway problem, namely estimating the number of tram or bus lines in a city given observing one line number, including The Bayesian Choice by yours truly, the original version of the problem is about German tanks, Panzer V tanks to be precise, which total number M was to […]

## Question 13 of our Applied Regression final exam (and solution to question 12)

Here’s question 13 of our exam: 13. You fit a model of the form: y ∼ x + u full + (1 | group). The estimated coefficients are 2.5, 0.7, and 0.5 respectively for the intercept, x, and u full, with group and individual residual standard deviations estimated as 2.0 and 3.0 respectively. Write the […]

## skipping sampler

“The Skipping Sampler is an adaptation of the MH algorithm designed to sample from targets which have areas of zero density. It ‘skips’ across such areas, much as a flat stone can skip or skim repeatedly across the surface of water.” An interesting challenge is simulating from a density restricted to a set C when […]

## SQRL: Secure Quick Reliable Login

Steve Gibson’s Security Now is one of the podcasts I regularly listen to, and so I’ve been hearing him talk about his SQRL for a while. This week he finally released SQRL: Secure Quick Reliable Login. You can read more about SQRL in the white paper posted on the GRC web site. Here’s a tease […]

## Question 12 of our Applied Regression final exam (and solution to question 11)

Here’s question 12 of our exam: 12. In the regression above, suppose you replaced height in inches by height in centimeters. What would then be the intercept and slope of the regression? (One inch is 2.54 centimeters.) And the solution to question 11: 11. We defined a new variable based on weight (in pounds): heavy […]

## another attempt at code golf

I had another lazy weekend go at code golf, trying to code in the most condensed way the following task. Provided with a square matrix A of positive integers, keep iterating the steps take the highest square 𝑥² in A. find the smallest adjacent neighbour 𝑛 replace x² with x and n with nx until […]

## How statistics is used to crush (scientific) dissent.

Lakeland writes: When we interpret powerful as political power, I think it’s clear that Classical Statistics has the most political power, that is, the power to get people to believe things and change policy or alter funding decisions etc… Today Bayes is questioned at every turn, and ridiculed for being “subjective” with a focus on […]

## Question 11 of our Applied Regression final exam (and solution to question 10)

Here’s question 11 of our exam: 11. We defined a new variable based on weight (in pounds): heavy 200 and then ran a logistic regression, predicting “heavy” from height (in inches): glm(formula = heavy ~ height, family = binomial(link = “logit”)) coef.est coef.se (Intercept) -21.51 1.60 height 0.28 0.02 — n = 1984, k = […]

## riddles on Egyptian fractions and Bernoulli factories

Two fairy different riddles on the weekend Riddler. The first one is (in fine) about Egyptian fractions: I understand the first one as Find the Egyptian fraction decomposition of 2 into 11 distinct unit fractions that maximises the smallest fraction. And which I cannot solve despite perusing this amazing webpage on Egyptian fractions and making […]

## Estimating Rates using Probability Theory: Chalk Talk

We are sharing a chalk talk rehearsal on applied probability. We use basic notions of probability theory to work through the estimation of sample size needed to reliably estimate event rates. This expands basic calculations, and then moves to the idea…

## The cost of no costs

The reason businesses have employees rather than contracting out everything is to reduce transaction costs. If a company needs enough graphics work, they hire a graphic artist rather than outsourcing every little project, eliminating the need to evaluate bids, write contracts, etc. Some things are easier when no money has to change hands. But some […]

## Question 10 of our Applied Regression final exam (and solution to question 9)

Here’s question 10 of our exam: 10. For the above example, we then created indicator variables, age18_29, age30_44, age45_64, and age65up, for four age categories. We then fit a new regression: lm(formula = weight ~ age30_44 + age45_64 + age65up) coef.est coef.se (Intercept) 157.2 5.4 age30_44TRUE 19.1 7.0 age45_64TRUE 27.2 7.6 age65upTRUE 8.5 8.7 n […]

## the Kouign-Amann experiment

Having found a recipe for Kouign-Amanns, these excessive cookies from Britanny that are essentially cooked salted butter!, I had a first try that ended up in disaster (including a deep cut on the remaining thumb) and a second try that went better as both food and body parts are concerned. (The name means cake of […]

## Question 9 of our Applied Regression final exam (and solution to question 8)

Here’s question 9 of our exam: 9. We downloaded data with weight (in pounds) and age (in years) from a random sample of American adults. We created a new variables, age10 = age/10. We then fit a regression: lm(formula = weight ~ age10) coef.est coef.se (Intercept) 161.0 7.3 age10 2.6 1.6 n = 2009, k […]