Jonathan Landy

We present a minimal model for elections in two-party systems [1].

This is a companion article to our post PCA response to scaling.

The PCA algorithm is sensitive to changes in measurement scale.

Here, we review the time value of money concept and its application to optimizing marketing (or other asset investment) spend.

A regression fit can sometimes look surprisingly poor when plotted on top of data, with the two having visually different slopes.

Here, we consider the problem of allocating limited inventory across demand sites, given the availability of a lower-quality substitute that can be used when inventory runs out.

We ask at which floors we should place a set of idle elevators in a building so as to minimize the expected wait time of the next caller.

When steady traffic limits the speed on a road, we argue that its throughput becomes independent of traffic density.

We review the classical framework for profit-maximizing pricing under steady demand.

Forecast error leads to misallocation of inventory across demand channels, driving lost sales.

Brands often sell through both the direct-to-consumer (DTC) and wholesale channels, with demand in each uncertain before the season starts.

Retailers prefer to carry products that have both high expected demand and low demand uncertainty.

We consider the problem of allocating a fixed inventory across multiple locations.

E-commerce apparel return rates today average around 20% — but this average is rising, and rates on individual products vary widely.

Why do grocery stores often carry over 100 options for both cheese and wine — but just a handful for pasta?

I'm obsessed with optimizing complex assortments – catalogs in categories like apparel, wine, and beauty, where many products compete for the same customer attention.

The newsvendor model provides inventory planners with a framework for setting optimal order quantities when demand is uncertain and there is a limited selling window – as in seasonal apparel.

In our last note, we discussed safety stock analysis — how to decide when to reorder.

In this back-to-basics post, we review three results from safety stock theory that can help retailers to maintain a lean inventory without compromising service levels.

Merchandisers often carry a single garment in multiple prints or colorways.

Accurately identifying a garment's color is essential for many modeling applications.

It's risky for a business to invest in new, unproven products.

I confess I sometimes don't pay the parking meter when I just need to pop into a store to quickly grab an item.

My friend Andrew is an advocate of the "spaced repetition" technique for memorization of a great many facts [1].

There are four ways to make change for \(N=10\) cents: \(\{\)10 pennies; 1 nickel and 5 pennies; 2 nickels; 1 dime\(\}\).

In this note, I consider a generalization of Dollar Cost Averaging -- a popular investing strategy that involves gradually building up one's holding in a stock over a pre-specified period of time.

Textbook proofs of the duality theorem often apply abstract arguments that offer little tangible insight into the relationship between a linear program and its dual.

We review how one can price a dividend-bearing stock by simply discounting its dividend stream using the value suggested by the Capital Asset Pricing Model (CAPM).

A person's happiness does not depend only on their current lot in life, but also on the rate of change of their lot.

I was struck the other day by the following: The cooking instructions on my Bob's tri-colored quinoa package said to combine 2 cups of water with 1 cup of dried quinoa, which would ultimately create 4 cups of cooked quinoa.

Pooling of test samples can be used to reduce the mean number of test counts required to determine who in a set of subjects carries a disease.

CPPI* is a risk management tactic that can be applied to any investment portfolio.

We consider the equilibrium drawdown distribution for a biased random walk -- in the context of a repeated investment game, the drawdown at a given time is how much has been lost relative to the maximum capital held up to that time.

We give a simple class for marking the time at different points in a code block and then printing out the time gaps between adjacent marked points.

Here, we highlight one of the most important benefits of tax protected accounts (eg Traditional and Roth IRAs and 401ks).

We consider how the GDP or utility output of a city depends on the number of people living within it.

We use a simple argument to estimate the speed of traffic on a highway as a function of the density of cars.

We illustrate the application of two linear compression algorithms in python: Principal component analysis (PCA) and least-squares feature selection.

This is a tutorial post relating to our python feature selection package, linselect.

This note addresses the typical applied problem of estimating from data how a target "conversion rate" function varies with some available scalar score function -- e.g., estimating conversion rates from some marketing campaign as a function of a targeting…

We review the math and code needed to fit a Gaussian Process (GP) regressor to data.

Here, I give a quick review of the concept of a Martingale.

We review binary logistic regression.

I review -- and provide derivations for -- some basic properties of Normal distributions.

The AUC score is a popular summary statistic that is often used to communicate the performance of a classifier.

We demo a script that converts python numerical commands to LaTeX format.

Here, we provide a brief introduction to reinforcement learning (RL) -- a general technique for training programs to play games efficiently.

Here, we briefly review a subtlety associated with machine-learning model selection: the fact that the optimal hyperparameters for a model can vary with training set size, \(N.\) To illustrate this point, we derive expressions for the optimal strength for…

We review the Metropolis algorithm -- a simple Markov Chain Monte Carlo (MCMC) sampling method -- and its application to estimating posteriors in Bayesian statistics.

We review classical linear regression using vector-matrix notation.