footBayes - Fitting Bayesian and MLE Football Models
This is the first package allowing for the estimation,
visualization and prediction of the most well-known football
models: double Poisson, bivariate Poisson, Dixon-Coles,
negative binomial, Skellam, student_t, diagonal-inflated
bivariate Poisson, and zero-inflated Skellam. It supports both
maximum likelihood estimation (MLE, for 'static' models only)
and Bayesian inference. Team abilities can be static or dynamic
over weeks or seasons, with alternative specifications of the
evolution variance: a common variance (Owen, 2011), variance
inflation after the summer break (Koopman and Lit, 2015)
<doi:10.1111/rssa.12042>, and weighted dynamic models with
commensurate priors (Macrì-Demartino, Egidi and Torelli, 2026)
<doi:10.1093/jrsssc/qlag032>. Historical team strengths can be
estimated through a Bayesian Bradley-Terry-Davidson model and
used as a covariate. For Bayesian methods, it incorporates
several techniques: MCMC sampling with Hamiltonian Monte Carlo,
variational inference using either the Pathfinder algorithm or
Automatic Differentiation Variational Inference (ADVI), and the
Laplace approximation. The package compiles all the 'CmdStan'
models once during installation using the 'instantiate'
package. The model construction relies on the most well-known
football references, such as Dixon and Coles (1997)
<doi:10.1111/1467-9876.00065>, Karlis and Ntzoufras (2003)
<doi:10.1111/1467-9884.00366> and Egidi, Pauli and Torelli
(2018) <doi:10.1177/1471082X18798414>.
