Nathan Sandholtz

Modeling Human Decision-making in Spatial and Temporal Systems.

In this thesis, we analyze three applications of human decision-making in spatial and temporal environments.   The first two projects are statistical applications to basketball while the third project analyzes an experiment that aims to understand decision-making processes in games.

The first project explores how efficiently players in a basketball lineup collectively allocate shots.  We propose a new metric for allocative efficiency by comparing a player's field goal percentage (FG%) to their field goal attempt (FGA) rate in context of both their four teammates on the court and the spatial distribution of their shots.  Leveraging publicly available data provided by the National Basketball Association (NBA), we estimate player FG% at every location in the offensive half court using a Bayesian hierarchical model.  By ordering a lineup's estimated FG%s and pairing these rankings with the lineup's empirical FGA rate rankings, we detect areas where the lineup exhibits inefficient shot allocation.  Lastly, we analyze the impact that suboptimal shot allocation has on a team's overall offensive potential, finding that inefficient shot allocation correlates with reduced scoring.

In the second basketball application, we model basketball plays as episodes from team-specific nonstationary Markov decision processes (MDPs) with shot clock dependent transition probabilities. Bayesian hierarchical models are employed in the parametrization of the transition probabilities to borrow strength across players and through time. To enable computational feasibility, we combine lineup-specific MDPs into team-average MDPs using a novel transition weighting scheme.  Specifically, we derive the dynamics of the team-average process such that the expected transition count for an arbitrary state-pair is equal to the weighted sum of the expected counts of the separate lineup-specific MDPs.  We then utilize these nonstationary MDPs in the creation of a basketball play simulator with uncertainty propagated via posterior samples of the model components. After calibration, we simulate seasons both on policy and under altered policies and explore the net changes in efficiency and production under the alternate policies.  We also discuss the game-theoretic ramifications of testing alternative decision policies.

For the final project, we take a different perspective on the behavior of the decision-makers.  Broadly speaking, both basketball projects assume the agents (players) act sub-optimally and the goal of the analyses is to evaluate the impact their suboptimal behavior has on point production and scoring efficiency.  By contrast, in the final project we assume that the agents' actions are optimal, but that the criteria over which they optimize are unknown.  The goal of the analysis is to make inference on these latent optimization criteria.  This type of problem can be termed an inverse decision problem.  Our project explores the inverse problem of Bayesian optimization.  Specifically, we seek to estimate an agent's latent acquisition function based on their observed search paths.  After introducing a probabilistic solution framework for the problem, we illustrate our method by analyzing human behavior from an experiment.  The experiment was designed to force subjects to balance exploration and exploitation in search of a global optimum.  We find that subjects exhibit a wide range of acquisition preferences; however, some subject's behavior does not map well to any of the candidate acquisitions functions we consider.  Guided by the model discrepancies, we augment the candidate acquisition functions to yield a superior fit to the human behavior in this task.