The exponential random graph model (ERGM) is a popular model for social networks, which is known to have an intractable likelihood function. Sampling from the posterior for such a model is a long-standing problem in statistical research. We analyze the performance of the stochastic gradient Langevin dynamics (SGLD) algorithm (also known as noisy Longevin Monte Carlo) in tackling this problem, where the stochastic gradient is calculated via running a short Markov chain (the so-called inner Markov chain in this paper) at each iteration. We show that if the model size grows with the network size slowly enough, then SGLD converges to the true posterior in 2-Wasserstein distance as the network size and iteration number become large regardless of the length of the inner Markov chain performed at each iteration. Our study provides a scalable algorithm for analyzing large-scale social networks with possibly high-dimensional ERGMs.

Change point analyses are concerned with identifying positions of an ordered stochastic process that undergo abrupt local changes of some underlying distribution. When multiple processes are observed, it is often the case that information regarding the change point positions is shared across the different processes. This work describes a method that takes advantage of this type of information. Since the number and position of change points can be described through a partition with contiguous clusters, our approach develops a joint model for these types of partitions. We describe computational strategies associated with our approach and illustrate improved performance in detecting change points through a small simulation study. We then apply our method to a financial data set of emerging markets in Latin America and highlight interesting insights discovered due to the correlation between change point locations among these economies.

Three critical issues for causal inference that often occur in modern, complicated experiments are interference, treatment nonadherence, and missing outcomes. A great deal of research efforts has been dedicated to developing causal inferential methodologies that address these issues separately. However, methodologies that can address these issues simultaneously are lacking. We propose a Bayesian causal inference methodology to address this gap. Our methodology extends existing causal frameworks and methods, specifically, two-staged randomized experiments and the principal stratification framework. In contrast to existing methods that invoke strong structural assumptions to identify principal causal effects, our Bayesian approach uses flexible distributional models that can accommodate the complexities of interference and missing outcomes, and that ensure that principal causal effects are weakly identifiable. We illustrate our methodology via simulation studies and a re-analysis of real-life data from an evaluation of India’s National Health Insurance Program. Our methodology enables us to identify new active causal effects that were not identified in past analyses. Ultimately, our simulation studies and case study demonstrate how our methodology can yield more informative analyses in modern experiments with interference, treatment nonadherence, missing outcomes, and complicated outcome generation mechanisms.

Vector autoregressions (VARs) are a widely used tool for modelling multivariate time-series. It is common to assume a VAR is stationary; this can be enforced by imposing the stationarity condition which restricts the parameter space of the autoregressive coefficients to the stationary region. However, implementing this constraint is difficult due to the complex geometry of the stationary region. Fortunately, recent work has provided a solution for autoregressions of fixed order p based on a reparameterization in terms of a set of interpretable and unconstrained transformed partial autocorrelation matrices. In this work, focus is placed on the difficult problem of allowing p to be unknown, developing a prior and computational inference that takes full account of order uncertainty. Specifically, the multiplicative gamma process is used to build a prior which encourages increasing shrinkage of the partial autocorrelations with increasing lag. Identifying the lag beyond which the partial autocorrelations become equal to zero then determines p. Based on classic time-series theory, a principled choice of truncation criterion identifies whether a partial autocorrelation matrix is effectively zero. Posterior inference utilizes Hamiltonian Monte Carlo via Stan. The work is illustrated in a substantive application to neural activity data to investigate ultradian brain rhythms.

We consider the problem of aggregating the judgements of a group of experts to form a single prior distribution representing the judgements of the group. We develop a Bayesian hierarchical model to reconcile the judgements of the group of experts based on elicited quantiles for continuous quantities and probabilities for one-off events. Previous Bayesian reconciliation methods have not been used widely, if at all, in contrast to pooling methods and consensus-based approaches. To address this we embed Bayesian reconciliation within the probabilistic Delphi method. The result is to furnish the outcome of the probabilistic Delphi method with a direct probabilistic interpretation, with the resulting prior representing the judgements of the decision maker. We can use the rationales from the Delphi process to group the experts for the hierarchical modelling. We illustrate the approach with applications to studies evaluating erosion in embankment dams and pump failures in a water pumping station, and assess the properties of the approach using the TU Delft database of expert judgement studies. We see that, even using an off-the-shelf implementation of the approach, it out-performs individual experts, equal weighting of experts and the classical method based on the log score.

We develop a class of nearest-neighbor mixture models that provide direct, computationally efficient, probabilistic modeling for non-Gaussian geospatial data. The class is defined over a directed acyclic graph, which implies conditional independence in representing a multivariate distribution through factorization into a product of univariate conditionals, and is extended to a full spatial process. We model each conditional as a mixture of spatially varying transition kernels, with locally adaptive weights, for each one of a given number of nearest neighbors. The modeling framework emphasizes direct spatial modeling of non-Gaussian data, in contrast with approaches that introduce a spatial process for transformed data, or for functionals of the data probability distribution. We study model construction and properties analytically through specification of bivariate distributions that define the local transition kernels. This provides a general strategy for modeling different types of non-Gaussian data based on the bivariate distribution family, and offers avenues to incorporate spatial association via different dependence measures. Regarding computation, direct spatial modeling facilitates efficient, full simulation-based inference; moreover, the framework leverages its mixture model structure to avoid computational issues that arise from large matrix operations, and thus has the potential to achieve scalability. We illustrate the methodology using synthetic data examples and an analysis of Mediterranean Sea surface temperature observations.

We address the problem of assessing the fit of stochastic epidemic models to data. Two novel model assessment methods are developed, based on disease progression curves, namely the distance method and the position-time method. The methods are illustrated using SIR (susceptible-infective-removed) models. We assume a typical data observation setting in which case-detection times are observed while infection times are not. Both methods involve Bayesian posterior predictive checking, in which the observed data are compared to data generated from the posterior predictive distribution. The distance method does this by calculating distances between disease progression curves, while the position-time method does this pointwise at suitably selected time points. Both methods provide visual and quantitative outputs with meaningful interpretations. The performance of the methods benefits from the development and application of a time-shifting method that accounts for the random time delay until an epidemic takes off. Extensive simulation studies show that both methods can successfully be used to assess the choice of infectious period distribution and the choice of infection rate function.

Functional data are frequently accompanied by a parametric template that describes the typical shapes of the functions. However, these parametric templates can incur significant bias, which undermines both utility and interpretability. To correct for model misspecification, we augment the parametric template with an infinite-dimensional nonparametric functional basis. The nonparametric basis functions are learned from the data and constrained to be orthogonal to the parametric template, which preserves distinctness between the parametric and nonparametric terms. This distinctness is essential to prevent functional confounding, which otherwise induces severe bias for the parametric terms. The nonparametric factors are regularized with an ordered spike-and-slab prior that provides consistent rank selection and satisfies several appealing theoretical properties. The versatility of the proposed approach is illustrated through applications to synthetic data, human motor control data, and dynamic yield curve data. Relative to parametric and semiparametric alternatives, the proposed semiparametric functional factor model eliminates bias, reduces excessive posterior and predictive uncertainty, and provides reliable inference on the effective number of nonparametric terms—all with minimal additional computational costs.

It is common to be interested in rankings or order relationships among entities. In complex settings where one does not directly measure a univariate statistic upon which to base ranks, such inferences typically rely on statistical models having entity-specific parameters. These can be treated as random effects in hierarchical models characterizing variation among the entities. In this paper, we are particularly interested in the problem of ranking basketball players in terms of their contribution to team performance. Using data from the United States National Basketball Association (NBA), we find that many players have similar latent ability levels, making any single estimated ranking highly misleading. The current literature fails to provide summaries of order relationships that adequately account for uncertainty. Motivated by this, we propose a Bayesian strategy for characterizing uncertainty in inferences on order relationships among players and lineups. Our approach adapts to scenarios in which uncertainty in ordering is high by producing more conservative results that improve interpretability. This is achieved through a reward function within a decision theoretic framework. We apply our approach to data from the 2009-10 NBA season.

Many applications in medical statistics and other fields can be described by transitions between multiple states (e.g. from health to disease) experienced by individuals over time. In this context, multi-state models are a popular statistical technique, in particular when the exact transition times are not observed. The key quantities of interest are the transition rates, capturing the instantaneous risk of moving from one state to another. The main contribution of this work is to propose a joint semiparametric model for several possibly related multi-state processes (Seemingly Unrelated Multi-State, SUMS, processes), assuming a Markov structure for the transitions over time. The dependence between different processes is captured by specifying a joint prior distribution on the transition rates of each process. In this case, we assume a flexible distribution, which allows for clustering of the individuals, overdispersion and outliers. Moreover, we employ a graph structure to describe the dependence among processes, exploiting tools from the Gaussian Graphical model literature. It is also possible to include covariate effects. We use our approach to model disease progression in mental health. Posterior inference is performed through a specially devised MCMC algorithm.