Motivated by an increasing demand for models that can effectively describe features of complex multivariate time series, e.g. from sensor data in biomechanics, motion analysis, and sports science, we introduce a novel state-space modeling framework where the state equation encodes the evolution of latent partitions of the data over time. Building on the principles of dynamic linear models, our approach develops a random partition model capable of linking data partitions to previous ones over time, using a straightforward Markov structure that accounts for temporal persistence and facilitates changepoint detection. The selection of changepoints involves multiple dependent decisions, and we address this time-dependence by adopting a non-marginal false discovery rate control. This leads to a simple decision rule that ensures more stringent control of the false discovery rate compared to approaches that do not consider dependence. The method is efficiently implemented using a Gibbs sampling algorithm, leading to a straightforward approach compared to existing methods for dependent random partition models. Additionally, we show that the proposed method can be adapted to handle multiview clustering scenarios. Simulation studies and the analysis of a human gesture phase dataset collected through specific sensing technologies show the effectiveness of the method in dynamically clustering multivariate time series and detecting changepoints.

In recent years, new cancer treatments have improved survival in multiple histologies. Some of these therapeutics, and in particular treatment combinations, are often associated with severe treatment-related adverse events (AEs). Therefore, It is important to identify alternative de-intensified therapies, such as dose-reduced therapies with reduced AEs and similar efficacy. We introduce a sequential design for multi-arm de-intensification studies. Based on joint modeling of toxicity and efficacy endpoints, the design evaluates multiple de-intensified therapies at different dose levels, one at a time. We study the utility of the design in oropharynx cancer de-intensification studies. We use a joint Bayesian model for efficacy and toxicity outcomes to define decision rules at interim and final analyses. Interim decisions include early termination of the study due to inferior survival of experimental arms compared to a standard of care (SOC), and the transitions from one de-intensified treatment arm to another with a further reduced dose when there is sufficient evidence of non-inferior survival. We evaluate the operating characteristics of the design using data from recent de-intensification studies in oropharynx cancer.

As a regression technique in spatial statistics, the spatiotemporally varying coefficient model (STVC) is an important tool for discovering nonstationary and interpretable response-covariate associations over both space and time. However, it is difficult to apply STVC for large-scale spatiotemporal analyses due to its high computational cost. To address this challenge, we summarize the spatiotemporally varying coefficients using a third-order tensor structure and propose to reformulate the spatiotemporally varying coefficient model as a special low-rank tensor regression problem. The low-rank decomposition can effectively model the global patterns of large data sets with a substantially reduced number of parameters. To further incorporate the local spatiotemporal dependencies, we use Gaussian process (GP) priors on the spatial and temporal factor matrices. We refer to the overall framework as Bayesian Kernelized Tensor Regression (BKTR), and kernelized tensor factorization can be considered a new and scalable approach to modeling multivariate spatiotemporal processes with a low-rank covariance structure. For model inference, we develop an efficient Markov chain Monte Carlo (MCMC) algorithm, which uses Gibbs sampling to update factor matrices and slice sampling to update kernel hyperparameters. We conduct extensive experiments on both synthetic and real-world data sets, and our results confirm the superior performance and efficiency of BKTR for model estimation and parameter inference.

Robust Bayesian analysis has been mainly devoted to detecting and measuring robustness w.r.t. the prior distribution. Many contributions in the literature aim to define suitable classes of priors which allow the computation of variations of quantities of interest while the prior changes within those classes. The literature has devoted much less attention to the robustness of Bayesian methods w.r.t. the likelihood function due to mathematical and computational complexity, and because it is often arguably considered a more objective choice compared to the prior. In this contribution, we propose a new approach to Bayesian local robustness, mainly focusing on robustness w.r.t. the likelihood function. Successively, we extend it to account for robustness w.r.t. the prior, as well as the prior and the likelihood jointly. This approach is based on the notion of distortion function introduced in the literature on risk theory. The novel robustness measure is a local sensitivity measure that turns out to be very tractable and easy to compute for several classes of distortion functions. Asymptotic properties are derived, and numerical experiments illustrate the theory and its applicability for modelling purposes.

We introduce Group Spike-and-Slab Variational Bayes (GSVB), a scalable method for group sparse regression. A fast co-ordinate ascent variational inference (CAVI) algorithm is developed for several common model families including Gaussian, Binomial and Poisson. Theoretical guarantees for our proposed approach are provided by deriving contraction rates for the variational posterior in grouped linear regression. Through extensive numerical studies, we demonstrate that GSVB provides state-of-the-art performance, offering a computationally inexpensive substitute to Markov Chain Monte Carlo (MCMC), whilst performing comparably or better than existing maximum a posteriori (MAP) methods. Additionally, we analyze three real world datasets wherein we highlight the practical utility of our method, demonstrating that GSVB provides parsimonious models with excellent predictive performance, variable selection and uncertainty quantification.

In this article, we introduce mixture representations for likelihood ratio ordered distributions. Essentially, the ratio of two probability densities, or mass functions, is monotone if and only if one can be expressed as a mixture of one-sided truncations of the other. To illustrate the practical value of the mixture representations, we address the problem of density estimation for likelihood ratio ordered distributions. In particular, we propose a nonparametric Bayesian solution which takes advantage of the mixture representations. The prior distribution is constructed from Dirichlet process mixtures and has large support on the space of pairs of densities satisfying the monotone ratio constraint. Posterior consistency holds under reasonable conditions on the prior specification and the true unknown densities. To our knowledge, this is the first posterior consistency result in the literature on order constrained inference. With a simple modification to the prior distribution, we can test the equality of two distributions against the alternative of likelihood ratio ordering. We develop a Markov chain Monte Carlo algorithm for posterior inference and demonstrate the method in a biomedical application.

The Hawkes process, a self-exciting point process, has a wide range of applications in modeling earthquakes, social networks and stock markets. The established estimation process requires that researchers have access to the exact time stamps and spatial information. However, available data are often rounded or aggregated. We develop a Bayesian estimation procedure for the parameters of a Hawkes process based on aggregated data. Our approach is developed for temporal, spatio-temporal, and mutually exciting Hawkes processes where data are available over discrete time periods and regions. We show theoretically that the parameters of the Hawkes process are identifiable from aggregated data under general specifications. We demonstrate the method on simulated data under various model specifications in the presence of one or more interacting processes, and under varying coarseness of data aggregation. Finally, we examine the internal and cross-excitation effects of airstrikes and insurgent violence events from February 2007 to June 2008, with some data aggregated by day.

Monitoring the spread of infectious diseases during an epidemic or pandemic presents a great challenge to public health systems worldwide. To facilitate informed decision-making, concerned parties usually rely on short-term daily or weekly projections generated via predictive modeling. Traditional epidemiological models, particularly growth models, are frequently employed with the assumption that epidemics or pandemics exhibit a single-peaked pattern in case numbers or mortality rates. However, this may not hold true for all diseases, as evidenced by the prolonged and multi-peaked nature of infectious diseases like COVID-19. Additionally, government interventions have led to time-varying disease transmission rates, making the observed data multi-modal. In response to these complexities, this paper presents BAGELS, a generalized Bayesian stochastic growth model augmented by a change-point detection mechanism to account for multiple peaks. A trans-dimensional reversible jump Markov chain Monte Carlo algorithm is used to sample the posterior distributions of interpretable epidemiological parameters while estimating the number and locations of change-points. We demonstrate the effectiveness of BAGELS through extensive evaluations using both simulated data and COVID-19 data from major U.S. states. Not only does this work offer a robust tool for longitudinal epidemiological studies, but it also advances the Bayesian change-point detection methodology for growth curves.

Probabilistic Graphical Bayesian models of causation have continued to impact on strategic analyses designed to help evaluate the efficacy of different interventions on systems. The standard causal algebras upon which these inferences are based typically assume that the intervened population does not react intelligently to frustrate an intervention. In an adversarial setting this is rarely an appropriate assumption. In this paper, we extend an established Bayesian methodology called Adversarial Risk Analysis to apply it to settings that can legitimately be designated as causal in this graphical sense. To embed this technology we first need to generalise the concept of a causal graph. We then import recent developments in ARA into the generalised causal graph. These are used to demonstrate how the intelligent reactions of an adversary to defensive interventions can be modelled and thus predicted by the defender. The new methodologies and supporting protocols are illustrated through applications associated with an adversary attempting to infiltrate a friendly state. Disclaimer The views and opinions expressed are those of the authors and not those of any entities they are attached to.