UM Data Science Research Seminar with SBE

Schedule

LECTURE 1: 12:00 - 12:30

Speaker: Paulo Rodrigues (FIN)

Subject: "Solving Dynamic Portfolio and Consumption Problems by Going Forward in Time" 

Abstract: The standard approach to solving dynamic portfolio and consumption problems numerically uses backward induction, which complicates the solution if decisions at time t depend on past decisions. In contrast, our solution algorithm goes forward in time. We use the insight that the main task in solving dynamic optimization problems consists of finding policy functions that use the current value of state variables as inputs and give the optimal decisions as outputs. Instead of assuming a functional form for these policy functions, we use a neural network for the estimation of the functions.
 

LECTURE 2: 12:30 - 13:00

Speaker: Tim Lindner (KE)

Subject: "Drivers of Success: A Bayesian State Space Approach to disentangling latent Driver and Constructor Effects in Formula One"

Abstract: The outcomes of a Formula One qualifying and race depend on directly observed factors, such as weather conditions and track characteristics, but also unobserved ones, such as driver ability and car (equivalently team) quality. The latter, unobserved factors, are particularly interesting, as they jointly affect qualifying and race results and there is an interaction between them. 

We propose a novel dynamic latent variable model for Formula One results using a Bayesian state space approach. Here, qualifying outcomes are defined as normalized qualifying times and race outcomes as race rankings. The qualifying times and race rankings jointly depend on observed factors and unobserved states that evolve dynamically on the Grand Prix level, emphasizing the importance of momentum. Identification of unobserved time-varying driver abilities and car qualities is achieved by modeling qualifying and race results jointly over multiple Formula One seasons. The proposed model is capable of disentangling latent driver and car effects since (1) each team competes with two cars (i.e., two drivers) at a Grand Prix and (2) drivers are contracted to different teams over the course of their careers. 

Our model also accounts for ”did not finish” (DNF) race results, which occur, for example, due to crashes and car reliability issues. DNFs are modeled by integrating the race finishing probabilities as unobserved states on the driver as well as car level. To obtain the posterior results for both simulated data and data from the Formula One hybrid era (2014-2021), we apply Stan’s Markov chain Monte Carlo algorithm, specifying weakly informative priors. 

We show that the proposed model can separate the two unobserved states and provide distributions of qualifying times and race rankings in Formula One. We identify time-varying driver abilities and car qualities within and across several seasons. The overall qualifying and race outcomes are affected to different extents by heterogeneous driver abilities, car qualities, as well as external factors. The proposed methodology has widespread applications outside of sports statistics when multiple unobserved factors affect multiple time series through individual and group structures.