Bayesian Methods

Patrick J. Laub, Young Lee and Thomas Taimre
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Patrick J. Laub: University of Melbourne, Faculty of Business and Economics
Young Lee: Harvard University, Faculty of Arts and Sciences
Thomas Taimre: The University of Queensland, School of Mathematics and Physics

Chapter Chapter 8 in The Elements of Hawkes Processes, 2021, pp 71-77 from Springer

Abstract: Abstract In this chapter, we detail one approach for drawing inferences based on the Bayesian framework for Hawkes processes, in particular using the Markov chain Monte Carlo (MCMC) methodology. MCMC has been developed for the past half a decade or so and has been used widely in physics as well as in statistics and probability. MCMC methods play an important role in Bayesian statistics, especially when parameter estimation cannot be made directly, owing to the complexity of the Bayesian model, for example, when there is no closed-form solution to the posterior distribution of a target parameter which we wish to estimate. MCMC allows one to sample random values from the posterior distribution and these values are subsequently used to estimate quantities of interest, such as the posterior means of model parameters. MCMC methods are typically easy and quick to implement. They also provide an alternative approach to the analysis of Bayesian models even when an analytic solution is possible.

Date: 2021
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DOI: 10.1007/978-3-030-84639-8_8

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