The Angry Statistician

Let a die be labeled with increasing positive integers \(a_1,\ldots , a_n\), and let the probability of getting \(a_i\) be \(p_i>0\). We start at 0 and roll the die, adding whatever number we get to the current total. If \({\rm Pr}(N)\) is the probability...

Gambling to optimized your expected bankroll mean is extremely risky, as you wager your entire bankroll for any favorable wager, making ruin almost inevitable. But what if, instead, we wagered not to maximize the expected bankroll mean, but the expected...

In my previous post I looked at how a group of of experts may be combined into a single, more powerful, classifier which I call NaiveBoost after the related AdaBoost. I'll illustrate how it can be used with a few examples.
As before, we're face with making a binary decision, which we can view as an unknown label \( L \in \{ +1, -1 \}\). Furthermore, the prior distribution on \( L \) is assumed to be uniform. Let our experts' independent probabilities be \( p_1 = 0.8, p...

In many situations we're faced with multiple expert opinions. How should we combine them together into one opinion, hopefully better than any single opinion? I'll demonstrate the derivation of a classifier I'll call NaiveBoost.
We'll start with a simple situation, and later gradually introduce more complexity. Let each expert state a yes or no opinion in response to a yes/no question (binary classifiers), each expert be independent of the other experts and assume expert \(i...