Approximate Bayesian computation with applications to time series data and spread of covid-19
Typ
Examensarbete för kandidatexamen
Program
Publicerad
2021
Författare
Häggström, Henrik
Wagner, Samuel
Jäghagen, Jesper
Ndaw Berbres, Jibbril
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
Bayesian statistical methods are one of the most popular tools for parameter inference. However,
due to their dependence on a well defined and analytically tractable likelihood function,
they are not always applicable to models of arbitrary complexity. Approximate Bayesian computation
(ABC) methods counteract this by introducing a Bayesian framework utilising model
simulations to bypass the need for a closed-form likelihood function. In this thesis we explore
two ABC methods, the ABC rejection algorithm and the sequential Monte Carlo ABC (SMCABC)
algorithm. We use them to infer parameters for the autoregressive AR(2) model, the
Lotka-Volterra model for predators and prey, and the SIR-model for modeling the spread of
Covid19 in Sweden. Subsequently, we compare the generated parameter distributions to the
exact posteriors produced by the more well-known Metropolis-Hastings algorithm. The results
indicate that the ABC methods produce posterior distributions comparable to those generated
by the Metropolis-Hastings algorithm, that the SMC-ABC algorithm is more computationally
efficient than the ABC rejection algorithm, and that the resulting posterior distributions are
quite independent of the choice of prior.