Bayesian Inference for Stochastic Cusp Catastrophe Model with Partially Observed Data

The purpose of this paper is to develop a data augmentation technique for statistical inference concerning stochastic cusp catastrophe model subject to missing data and partially observed observations. We propose a Bayesian inference solution that naturally treats missing observations as parameters and we validate this novel approach by conducting a series of Monte Carlo simulation studies assuming the cusp catastrophe model as the underlying model. We demonstrate that this Bayesian data augmentation technique can recover and estimate the underlying parameters from the stochastic cusp catastrophe model.

BSImp: imputing partially observed methylation patterns for evaluating methylation heterogeneity

DNA methylation is one of the most studied epigenetic modifications that has applications ranging from transcriptional regulation to aging, and can be assessed by bisulfite sequencing (BS-seq) at single base-pair resolution. The permutations of methylation statuses at bisulfite converted reads reflect the methylation patterns of individual cells. These patterns at specific genomic locations are sought to be indicative of cellular heterogeneity within a cellular population, which are predictive of developments and diseases; therefore, methylation heterogeneity has potentials in early detection of these changes. Computational methods have been developed to assess methylation heterogeneity using methylation patterns formed by four CpGs, but the nature of shotgun sequencing often give partially observed patterns, which makes very limited data available for downstream analysis. While many programs are developed to impute methylation levels genomewide, currently there is only one method developed for recovering partially observed methylation patterns; however, the program needs lots of data to train and cannot be used directly; therefore, we developed a probabilistic-based imputation method that uses information from neighbouring sites to recover partially observed methylation patterns speedily. It is demonstrated to allow for the evaluation of methylation heterogeneity at three times more regions genome-wide with high accuracy for data with moderate depth. To make it more user-friendly we also provide a computational pipeline for genome-screening, which can be used in both evaluating methylation levels and profiling methylation patterns genomewide for all cytosine contexts, which is the first of its kind. Our method allows for accurate estimation of methylation levels and makes evaluating methylation heterogeneity available for much more data with reasonable coverage, which has important implications in using methylation heterogeneity for monitoring changes within the cellular populations that were impossible to detect for the assessment of development and diseases.

Inference for epidemic models with time varying infection rates: tracking the dynamics of oak processionary moth in the UK

Invasive pests pose a great threat to forest, woodland and urban tree ecosystems. The oak processionary moth (OPM) is a destructive pest of oak trees, first reported in the UK in 2006. Despite great efforts to contain the outbreak within the original infested area of South-East England, OPM continues to spread. Here we analyse data of the numbers of OPM nests removed each year from two parks in London between 2013 and 2020. Using a state-of-the-art Bayesian inference scheme we estimate the parameters for a stochastic compartmental SIR (susceptible, infested, removed) model with a time varying infestation rate to describe the spread of OPM. We find that the infestation rate and subsequent basic reproduction number have remained constant since 2013 (with R_0 between one and two). This shows further controls must be taken to reduce R_0 below one and stop the advance of OPM into other areas of England. Our findings demonstrate the applicability of the SIR model to describing OPM spread and show that further controls are needed to reduce the infestation rate. The proposed statistical methodology is a powerful tool to explore the nature of a time varying infestation rate, applicable to other partially observed time series epidemic data.spread and show that further controls are needed to reduce the infestation rate. The proposed statistical methodology is a powerful tool to explore the nature of a time varying infestation rate, applicable to other partially observed time series epidemic data.

Approximate confidence intervals for the difference in proportions for partially observed binary data

We consider partially observed binary matched-pair data. We assume that the incomplete subjects are missing at random. Within this missing framework, we propose an EM-algorithm based approach to construct an interval estimator of the proportion difference incorporating all the subjects. In conjunction with our proposed method, we also present two improvements to the interval estimator through some correction factors. The performances of the three competing methods are then evaluated through extensive simulation. Recommendation for the method is given based on the ability to preserve type-I error for various sample sizes. Finally, the methods are illustrated in two real-world data sets. An R-function is developed to implement the three proposed methods.