Bayesian inference on the number of recurrent events: A joint model of recurrence and survival

The number of recurrent events before a terminating event is often of interest. For instance, death terminates an individual’s process of rehospitalizations and the number of rehospitalizations is an important indicator of economic cost. We propose a model in which the number of recurrences before termination is a random variable of interest, enabling inference and prediction on it. Then, conditionally on this number, we specify a joint distribution for recurrence and survival. This novel conditional approach induces dependence between recurrence and survival, which is often present, for instance, due to frailty that affects both. Additional dependence between recurrence and survival is introduced by the specification of a joint distribution on their respective frailty terms. Moreover, through the introduction of an autoregressive model, our approach is able to capture the temporal dependence in the recurrent events trajectory. A non-parametric random effects distribution for the frailty terms accommodates population heterogeneity and allows for data-driven clustering of the subjects. A tailored Gibbs sampler involving reversible jump and slice sampling steps implements posterior inference. We illustrate our model on colorectal cancer data, compare its performance with existing approaches and provide appropriate inference on the number of recurrent events.

A Bayesian semiparametric accelerate failure time mixture cure model

The accelerated failure time mixture cure (AFTMC) model is widely used for survival data when a portion of patients can be cured. In this paper, a Bayesian semiparametric method is proposed to obtain the estimation of parameters and density distribution for both the cure probability and the survival distribution of the uncured patients in the AFTMC model. Specifically, the baseline error distribution of the uncured patients is nonparametrically modeled by a mixture of Dirichlet process. Based on the stick-breaking formulation of the Dirichlet process, the techniques of retrospective and slice sampling, an efficient and easy-to-implement Gibbs sampler is developed for the posterior calculation. The proposed approach can be easily implemented in commonly used statistical softwares, and its performance is comparable to fully parametric method via comprehensive simulation studies. Besides, the proposed approach is adopted to the analysis of a colorectal cancer clinical trial data.

Ensemble slice sampling

Slice sampling has emerged as a powerful Markov Chain Monte Carlo algorithm that adapts to the characteristics of the target distribution with minimal hand-tuning. However, Slice Sampling’s performance is highly sensitive to the user-specified initial length scale hyperparameter and the method generally struggles with poorly scaled or strongly correlated distributions. This paper introduces Ensemble Slice Sampling (ESS), a new class of algorithms that bypasses such difficulties by adaptively tuning the initial length scale and utilising an ensemble of parallel walkers in order to efficiently handle strong correlations between parameters. These affine-invariant algorithms are trivial to construct, require no hand-tuning, and can easily be implemented in parallel computing environments. Empirical tests show that Ensemble Slice Sampling can improve efficiency by more than an order of magnitude compared to conventional MCMC methods on a broad range of highly correlated target distributions. In cases of strongly multimodal target distributions, Ensemble Slice Sampling can sample efficiently even in high dimensions. We argue that the parallel, black-box and gradient-free nature of the method renders it ideal for use in scientific fields such as physics, astrophysics and cosmology which are dominated by a wide variety of computationally expensive and non-differentiable models.

Assessment for Voltage Violations considering Reactive Power Compensation Provided by Smart Inverters in Distribution Network

Due to the high proportion of renewable energies, traditional voltage regulation methods such as on-load tap changers (OLTCs) and switching capacitors (SCs) are currently facing the challenge of providing fast, step-less, and low-cost reactive power to reduce the increasing risks of voltage violations in distribution networks (DNs). To meet such increasing demand for voltage regulation, smart inverters, including photovoltaics (PVs) and electric vehicle (EV) chargers, stand out as a feasible approach for reactive power compensation. This paper aims to assess the voltage violation risks in DNs considering the reactive power response of smart inverters. Firstly, reactive power compensation models of PVs and EV chargers are investigated and voltage deviation indexes of the regulation results are proposed. Moreover, kernel density estimation (KDE) and slice sampling are adopted to provide the PV output and EV charging demand samples. Then, the risk assessment is carried out with a voltage regulation model utilizing OLTCs, SCs, and available smart inverters. Numerical studies demonstrate that the reactive power support from smart inverters can significantly mitigate the voltage violation risks and reduce the switching and cost of OLTCs and capacitors in DNs.