Publications by ALT
Kernel Density Estimates & Truncated Normals
Earlier today I read a post about truncated normals, and one plot in particular jumped out at me:By definition, the truncated normal should have zero density everywhere to the left of the truncation point, but that’s not what we see in the plot. What’s going on? The catch is that this isn’t a plot of the true density, but rath...
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Men with Hats
Suppose N people (and their hats) attend a party (in the 1950s). For fun, the guests mix their hats in a pile at the center of the room, and each person picks a hat uniformly at random. What is the probability that nobody ends up with their own hat?EstimateProbability <- function(n.people, n.simulations=10000) { NobodyGotTheirHat ...
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A Plot of 250 Random Walks
For some reason I feel like plotting some random walks. Nothing groundbreaking, but hopefully this post will be useful to someone. Here’s my R code:# Generate k random walks across time {0, 1, ... , T} T <- 100 k <- 250 initial.value <- 10 GetRandomWalk <- function() { # Add a standard normal at each step initial.value + c(0, ...
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A Currency Graph
Here’s a graph in which nodes (and edges) represent currencies (and exchange rates):library(igraph) currencies <- factor(c("EUR", "USD", "JPY", "GBP")) df <- subset(expand.grid(from=currencies, to=currencies), from != to) GetExchangeRates <- function(from, to) { urls <- sprintf("%s/d/quotes.csv?s=%s%s=X&f=b", ...
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A Bayesian Guessing Game
You, the player, must think of some set, eg “odd numbers” or “perfect squares,” and that’ll be your little secret. Now think of some numbers that live in the intersection of your set and the integers {1, 2, … , 100} — for example, if you’ve chosen odd numbers, you might draw 3, 5 and 91 (but not 103). Below is some R...
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S&P 500 Returns
I’ll begin with a familiar image:That plot shows the closing values of the S&P 500 index from 1990 until today. It’s a useful representation — at a glance, you can tell when the market rose and fell. That said, it does have some problems: we’re looking at absolute movements in the index, when we really care about relative c...
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