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The generalized linear mixed model (GLMM) is widely used for analyzing correlated data, particularly in large-scale biomedical and social science applications. Scalable Bayesian inference for GLMMs is challenging because the marginal…
In this paper we first introduce the general stochastic epidemic model for the spread of infectious diseases. Then we give methods for inferring model parameters such as the basic reproduction number $R_0$ and vaccination coverage $v_c$…
Performing model selection for coupled hidden Markov models (CHMMs) is highly challenging, owing to the large dimension of the hidden state process. Whilst in principle the hidden state process can be marginalized out via forward filtering,…
Agent-based models of disease transmission involve stochastic rules that specify how a number of individuals would infect one another, recover or be removed from the population. Common yet stringent assumptions stipulate interchangeability…
Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Existing work on Bayesian decision trees uses MCMC.…
Markov chain Monte Carlo (MCMC) has transformed Bayesian model inference over the past three decades: mainly because of this, Bayesian inference is now a workhorse of applied scientists. Under general conditions, MCMC sampling converges…
We consider the problem of model choice for stochastic epidemic models given partial observation of a disease outbreak through time. Our main focus is on the use of Bayes factors. Although Bayes factors have appeared in the epidemic…
Sequential Monte Carlo methods are a powerful framework for approximating the posterior distribution of a state variable in a sequential manner. They provide an attractive way of analyzing dynamic systems in real-time, taking into account…
We propose a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step. Because of a highly discrete character of the process, the analysis cannot use the continous approximation,…
With the unfolding of the COVID-19 pandemic, mathematical modeling of epidemics has been perceived and used as a central element in understanding, predicting, and governing the pandemic event. However, soon it became clear that long term…
In this paper, we address a social planner's optimal control problem for a partially observable stochastic epidemic model. The control measures include social distancing, testing, and vaccination. Using a diffusion approximation for the…
Statistical inference in evolutionary models with site-dependence is a long-standing challenge in phylogenetics and computational biology. We consider the problem of approximating marginal sequence likelihoods under dependent-site models of…
Decision trees are flexible models that are well suited for many statistical regression problems. In a Bayesian framework for regression trees, Markov Chain Monte Carlo (MCMC) search algorithms are required to generate samples of tree…
Combined inference for heterogeneous high-dimensional data is critical in modern biology, where clinical and various kinds of molecular data may be available from a single study. Classical genetic association studies regress a single…
The effects of demographic stochasticity in the long term behaviour of endemic infectious diseases have been considered for long as a necessary addition to an underlying deterministic theory. The latter would explain the regular behaviour…
We discuss various models for epidemics on networks that rely on Markov chains. Random walks on graphs are often used to predict epidemic spread and to investigate possible control actions to mitigate them. In this study, we demonstrate…
We consider the problem of Bayesian inference for bi-variate data observed in time but with observation times which occur non-synchronously. In particular, this occurs in a wide variety of applications in finance, such as high-frequency…
One of the popular dynamics on complex networks is the epidemic spreading. An epidemic model describes how infections spread throughout a network. Among the compartmental models used to describe epidemics, the…
The increasing size of data sets has lead to variable selection in regression becoming increasingly important. Bayesian approaches are attractive since they allow uncertainty about the choice of variables to be formally included in the…
Markov chain Monte Carlo (MCMC) methods are simulated by local exploration of complex statistical distributions, and while bypassing the cumbersome requirement of a specific analytical expression for the target, this stochastic exploration…