This thesis deals with approximate computational inference, particularly with a relatively recent approach in it known as approximate Bayesian computation (ABC). ABC deals with simulator-based models whose likelihood function is intractable. To overcome the intractability of the likelihood, ABC uses simulations from the model and a principled approximation of the posterior that is traditionally defined via a distance function and a threshold.
I represent the ABC approximation as an approximation of the underlying likelihood function of the simulator-based model. This interpretation provides an intuitive way of understanding the approximation in ABC. I also consider the bias and Monte Carlo error in ABC, and demonstrate that better results can be acquired with a proper approximation than with a corresponding exact method in a given computational time.
I further propose using an approximation of the likelihood function in investigating the reliability of ABC inferences. This approach reveals identifiability issues with a well-known disease transmission model for tuberculosis. A new transmission model is proposed that resolves these issues by more closely modelling the epidemiological process of tuberculosis. Updated estimates of the epidemiological parameters are then provided together with an estimate of the underlying infectious population that is better aligned with the epidemiological knowledge of the disease.
Apart from ABC, I consider modelling computational inference problems with graphs, and how the graph representations can be used in the algorithmic level. The graph representations are used in learning Bayesian networks with more granular dependency structures. Finally, graphs are used for effective modelling of the ABC procedure and streamlining many aspects of the inference in a new open-source software called ELFI. In addition to graph-based modelling, ELFI provides distributed parallelization, data re-use and many other practical features for performing ABC inferences.
- Kaski, Samuel, Supervisor
- Corander, Jukka, Advisor
- Gutmann, Michael U., Advisor
|Publication status||Published - 2019|
|MoE publication type||G5 Doctoral dissertation (article)|
- approximate bayesian computation, simulator-based models