Sequential Bayesian inference with intractable likelihoods: A sequential mixture model method for posterior and likelihood estimation
Typ
Examensarbete för masterexamen
Master's Thesis
Master's Thesis
Program
Engineering mathematics and computational science (MPENM), MSc
Publicerad
2023
Författare
Häggström, Henrik
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
In a Bayesian setting with realistic models it is not unusual that it is not possible to perform exact parameter inference. This is typically due to the fact that
the likelihood function is not available in closed form or is intractable. Likelihood-free methods perform parameter inference in models where evaluating the likelihood
is an intractable problem, but sampling data from a generative model is possible.
With the expansion of machine learning, recent approaches learn the posterior distribution of the parameters by sequential updates of neural-network based density
estimators. While these methods perform well, they require a network architecture
to be specified and training the neural-network can be computationally demanding
and time consuming. In this work we present a Bayesian inference method which,
in place of neural networks, uses Gaussian mixtures sequentially learned through
an expectation-maximization procedure. Posterior samples are then obtained via
MCMC through an informative and self-tuned proposal sampler. Only the number
of components in the Gaussian mixture needs to be specified to run the algorithm.
We show the feasibility of this method and benchmark it against two neural-network
based state-of-the-art Bayesian methods in 4 simulation studies. The results show
that the proposed method is competitive and in some cases even outperforms the
other methods in terms of simulation efficiency. Additionally, it is in most cases
significantly faster to run.
Beskrivning
Ämne/nyckelord
Bayesian inference, simulation-based inference, likelihood-free methods, multimodal posteriors, posterior estimation, likelihood estimation, R, Python.