Tag Archives: Statistics & Econometrics

An easy one this week: Yours truly wants to distribute 30 one-dollar coins among his kids Linnea, David, and Tora. In how many ways can this be done if he wants all of them to get at least one coin? 

Monte Carlo simulations — no substitute for thinking In some fields—physics, geophysics, climate science, sensitivity analysis, and uncertainty quantification in particular—there is a popular impression that probabilities can be estimated in a ‘neutral’ or ‘automatic’ way by doing Monte Carlo simulations: just let the computer reveal the distribution … Setting aside other issues in numerical modeling, Monte Carlo simulation is a way to substitute...

In econometrics one often gets the feeling that many of its practitioners think of it as a kind of automatic inferential machine: input data and out comes causal knowledge. This is like pulling a rabbit from a hat. Great, but as renowned statistician David Freedman had it, first you must put the rabbit in the hat. And this is where assumptions come into the picture. The assumption of imaginary ‘superpopulations’ is one of the many dubious assumptions used in modern...

Weekend combinatorics work problem (IV) When my daughter (who studies mathematics) and yours truly solve a combinatorics problem together it takes 12 minutes. If my daughter tries to solve the problem herself it takes her 10 minutes more than it takes when I solve it alone. How long does it take me to solve the problem?

An easy one this week: At a small economics conference, a photographer wants to line up nine participants for a photo. Two of them — Robert and Milton — insist on standing next to each other. How many different arrangements (lineups) are possible?

Chebyshev’s and Markov’s Inequality Theorems Chebyshev’s Inequality Theorem — named after Russian mathematician Pafnuty Chebyshev (1821-1894) — states that for a population (or sample) at most 1/k2 of the distribution’s values can be more than k standard deviations away from the mean. The beauty of the theorem is that although we may not know the exact distribution of the data — e.g. if it’s normally distributed  — we may still say with certitude (since the...

How to prove things .[embedded content] Great lecture series. Yours truly got Solow’s book when he was studying mathematics back in the 80s. Now in its 6th edition, it’s better than ever.

The dangers of using unproved assumptions The unpopularity of the principle of organic unities shows very clearly how great is the danger of the assumption of unproved additive formulas. The fallacy, of which ignorance of organic unity is a particular instance, may perhaps be mathematically represented thus: suppose f(x) is the goodness of x and f(y) is the goodness of y. It is then assumed that the goodness of x and y together is f(x) + f(y) when it is...

.[embedded content] Bra föreläsningsserie från Chalmers! När jag själv läste matematik i Lund på 80-talet tyckte jag bäst om kurserna i diskret matematik. Mycket logik och problem av ‘tankenötskaraktär’. Och kul hjärngympa att lägga några timmar på när man vill pausa lite från schackspel och korsord …

The Binomial and Poisson distributions (student stuff) .[embedded content]