Browsing by Subject "Cox process"

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Bayesian inference for stochastic compartmental models and marginal Cox process
(2024-05) Wang, Shuying, Ph. D.; Walker, Stephen G., 1945-; Gordan Zitkovic; Purnamrita Sarkar; Antonio Linero
This dissertation addresses the computational challenges posed by Bayesian Markov Chain Monte Carlo (MCMC) data augmentation methods in the stochastic compartmental models with partially observed data. We present a novel algorithm for estimating the stochastic SIR/SEIR epidemic model within a Bayesian framework, which can be readily extended to more complex stochastic compartmental models. Specifically, based on the infinitesimal conditional independence properties of the model, we are able to find a proposal distribution for a Metropolis-Hastings algorithm which is very close to the correct posterior distribution. In particular, it acts as a very good proposal for the unknown number of events, such as the number of infected individuals, as well as the times of occurrences. Therefore, rather than perform a Metropolis step updating one missing data point at a time, we are able to have a single proposal for the entire set of missing observations. Moreover, the dissertation explores the theoretical framework of continuous-time count processes, leading to the development of a marginalized Poisson-driven Cox process aimed at addressing over-dispersion in count data. This innovation facilitates a more efficient and precise analysis by enabling the direct calculation of the marginal likelihood function, thus bypassing the complexities of sampling the unobserved stochastic intensity process.