Jonathan Landy

Queries ping a certain computer server at random times, on average \(\lambda\) arriving per second.

A common task in applied statistics is the pairwise comparison of the responses of \(N\) treatment groups in some statistical test -- the goal being to decide which pairs exhibit differences that are statistically significant.

Two microphones are placed in a room where two conversations are taking place simultaneously.

In this post, we review two facts about maximum-likelihood estimators: 1) They are consistent, meaning that they converge to the correct values given a large number of samples, \(N\), and 2) They satisfy the Cramer-Rao lower bound for unbiased parameter e…

We review the two essentials of principal component analysis ("PCA"): 1) The principal components of a set of data points are the eigenvectors of the correlation matrix of these points in feature space. 2) Projecting the data onto the subspace spanned by…

Here, we review parameter regularization, which is a method for improving regression models through the penalization of non-zero parameter estimates.

Let \(a_1, a_2, \ldots\) be an infinite set of non-negative samples taken from a distribution \(P_0(a)\), and write $$\tag{1} \label{problem} S = 1 + a_1 + a_1 a_2 + a_1 a_2 a_3 + \ldots. $$ Notice that if the \(a_i\) were all the same, \(S\) would be a r…

This will be the first of a series of short posts relating to subject matter discussed in the text, "An Introduction to Statistical Learning".

What is the best method for ranking items that have positive and negative reviews?

The Cramer-Rao inequality addresses the question of how accurately one can estimate a set of parameters \(\vec{\theta} = \{\theta_1, \theta_2, \ldots, \theta_m \}\) characterizing a probability distribution \(P(x) \equiv P(x; \vec{\theta})\), given only s…

This post contains our crib notes on the basics of decision trees and forests.

Here, we introduce -- and outline a solution to -- a generalized SIR model for infectious disease.

Here, we give a quick (< 30 mins) introduction to the open source database software package MySQL.

There were a number of upsets in the NBA this past Christmas week.

Here, we discuss some methods for carrying out classification when only positive examples are available.