Measuring the causal impact of an advertising campaign on sales is an essential task for advertising companies. Challenges arise when companies run advertising campaigns in multiple stores which are spatially correlated, and when the sales data have a low signal-to-noise ratio which makes the advertising effects hard to detect. This paper proposes a solution to address both of these challenges. A novel Bayesian method is proposed to detect weaker impacts and a multivariate structural time series model is used to capture the spatial correlation between stores through placing a $\mathcal{G}$-Wishart prior on the precision matrix. The new method is to compare two posterior distributions of a latent variable—one obtained by using the observed data from the test stores and the other one obtained by using the data from their counterfactual potential outcomes. The counterfactual potential outcomes are estimated from the data of synthetic controls, each of which is a linear combination of sales figures at many control stores over the causal period. Control stores are selected using a revised Expectation-Maximization variable selection (EMVS) method. A two-stage algorithm is proposed to estimate the parameters of the model. To prevent the prediction intervals from being explosive, a stationarity constraint is imposed on the local linear trend of the model through a recently proposed prior. The benefit of using this prior is discussed in this paper. A detailed simulation study shows the effectiveness of using our proposed method to detect weaker causal impact. The new method is applied to measure the causal effect of an advertising campaign for a consumer product sold at stores of a large national retail chain.

We introduce a new approach to latent state filtering and parameter estimation for a class of stochastic volatility models (SVMs) for which the likelihood function is unknown. The $\alpha$-stable stochastic volatility model provides a flexible framework for capturing asymmetry and heavy tails, which is useful when modeling financial returns. However, the $\alpha$-stable distribution lacks a closed form for the probability density function, which prevents the direct application of standard Bayesian filtering and estimation techniques such as sequential Monte Carlo and Markov chain Monte Carlo. To obtain filtered volatility estimates, we develop a novel approximate Bayesian computation (ABC) based auxiliary particle filter, which provides improved performance through better proposal distributions. Further, we propose a new particle based MCMC (PMCMC) method for joint estimation of the parameters and latent volatility states. With respect to other extensions of PMCMC, we introduce an efficient single filter particle Metropolis-within-Gibbs algorithm which can be applied for obtaining inference on the parameters of an asymmetric $\alpha$-stable stochastic volatility model. We show the increased efficiency in the estimation process through a simulation study. Finally, we highlight the necessity for modeling asymmetric $\alpha$-stable SVMs through an application to propane weekly spot prices.

Discovering temporal evolution of themes from a time-stamped collection of text poses a challenging statistical learning problem. Dynamic topic models offer a probabilistic modeling framework to decompose a corpus of text documents into “topics”, i.e., probability distributions over vocabulary terms, while simultaneously learning the temporal dynamics of the relative prevalence of these topics. We extend the dynamic topic model of Blei and Lafferty (2006) by fusing its multinomial factor model on topics with dynamic linear models that account for time trends and seasonality in topic prevalence. A Markov chain Monte Carlo (MCMC) algorithm that utilizes Pólya-Gamma data augmentation is developed for posterior sampling. Conditional independencies in the model and sampling are made explicit, and our MCMC algorithm is parallelized where possible to allow for inference in large corpora. Our model and inference algorithm are validated with multiple synthetic examples, and we consider the applied problem of modeling trends in real estate listings from the housing website Zillow. We demonstrate in synthetic examples that sharing information across documents is critical for accurately estimating document-specific topic proportions. Analysis of the Zillow corpus demonstrates that the method is able to learn seasonal patterns and locally linear trends in topic prevalence.

Analysing multiple evidence sources is often feasible only via a modular approach, with separate submodels specified for smaller components of the available evidence. Here we introduce a generic framework that enables fully Bayesian analysis in this setting. We propose a generic method for forming a suitable joint model when joining submodels, and a convenient computational algorithm for fitting this joint model in stages, rather than as a single, monolithic model. The approach also enables splitting of large joint models into smaller submodels, allowing inference for the original joint model to be conducted via our multi-stage algorithm. We motivate and demonstrate our approach through two examples: joining components of an evidence synthesis of A/H1N1 influenza, and splitting a large ecology model.

The functional linear regression model is a common tool to determine the relationship between a scalar outcome and a functional predictor seen as a function of time. This paper focuses on the Bayesian estimation of the support of the coefficient function. To this aim we propose a parsimonious and adaptive decomposition of the coefficient function as a step function, and a model including a prior distribution that we name Bayesian functional Linear regression with Sparse Step functions (Bliss). The aim of the method is to recover periods of time which influence the most the outcome. A Bayes estimator of the support is built with a specific loss function, as well as two Bayes estimators of the coefficient function, a first one which is smooth and a second one which is a step function. The performance of the proposed methodology is analysed on various synthetic datasets and is illustrated on a black Périgord truffle dataset to study the influence of rainfall on the production.

We develop a Bayesian approach to computational solution of multi-step optimization problems, highlighted in the example of financial portfolio decisions. The approach involves mapping the technical structure of a decision analysis problem to that of Bayesian inference in a purely synthetic “emulating” statistical model. This provides access to standard posterior analytic, simulation and optimization methods that yield indirect solutions of the decision problem. We develop this in time series portfolio analysis using classes of economically and psychologically relevant multi-step ahead portfolio utility functions. Studies with multivariate currency time series illustrate the approach and show some of the practical utility and benefits of the Bayesian emulation methodology.

There has been great interest recently in applying nonparametric kernel mixtures in a hierarchical manner to model multiple related data samples jointly. In such settings several data features are commonly present: (i) the related samples often share some, if not all, of the mixture components but with differing weights, (ii) only some, not all, of the mixture components vary across the samples, and (iii) often the shared mixture components across samples are not aligned perfectly in terms of their kernel parameters such as the location and spread in Gaussian kernels, but rather display small misalignments either due to systematic cross-sample difference or more often due to uncontrolled, extraneous causes. Properly incorporating these features in mixture modeling will enhance the efficiency of inference, whereas ignoring them not only reduces efficiency but can jeopardize the validity of the inference due to issues such as confounding. We propose to use two techniques for incorporating these features in modeling related data samples using kernel mixtures. The first technique, called $\psi$-stick breaking, is a joint generative process for the mixing weights through the breaking of both a stick shared by all the samples for the components that do not vary in size across samples and an idiosyncratic stick for each sample for those components that do vary in size. The second technique is to imbue random perturbation into the kernels, thereby accounting for cross-sample misalignment. These techniques can be used either separately or together in both parametric and nonparametric kernel mixtures. We derive efficient Bayesian inference recipes based on Markov Chain Monte Carlo (MCMC) sampling for models featuring these techniques, and illustrate their work through both simulated data and a real flow cytometry data set in prediction/estimation and testing multi-sample differences.

Bayesian hierarchical models are commonly used for modeling spatially correlated areal data. However, choosing appropriate prior distributions for the parameters in these models is necessary and sometimes challenging. In particular, an intrinsic conditional autoregressive (CAR) hierarchical component is often used to account for spatial association. Vague proper prior distributions have frequently been used for this type of model, but this requires the careful selection of suitable hyperparameters. In this paper, we derive several objective priors for the Gaussian hierarchical model with an intrinsic CAR component and discuss their properties. We show that the independence Jeffreys and Jeffreys-rule priors result in improper posterior distributions, while the reference prior results in a proper posterior distribution. We present results from a simulation study that compares frequentist properties of Bayesian procedures that use several competing priors, including the derived reference prior. We demonstrate that using the reference prior results in favorable coverage, interval length, and mean squared error. Finally, we illustrate our methodology with an application to 2012 housing foreclosure rates in the 88 counties of Ohio.

In this paper it is demonstrated how the Bayesian parametric bootstrap can be adapted to models with intractable likelihoods. The approach is most appealing when the computationally efficient semi-automatic approximate Bayesian computation (ABC) summary statistics are selected. The parametric bootstrap approximation is used to form a proposal distribution in ABC algorithms to improve the computational efficiency. The new approach is demonstrated through the sequential Monte Carlo and the ABC importance and rejection sampling algorithms. We found efficiency gains in two simulation studies, the univariate g-and-k quantile distribution, a toggle switch model in dynamic bionetworks, and in a stochastic model describing expanding melanoma cell colonies.

When model uncertainty is handled by Bayesian model averaging (BMA) or Bayesian model selection (BMS), the posterior distribution possesses a desirable “oracle property” for parametric inference, if for large enough data it is nearly as good as the oracle posterior, obtained by assuming unrealistically that the true model is known and only the true model is used. We study the oracle properties in a very general context of quasi-posterior, which can accommodate non-regular models with cubic root asymptotics and partial identification. Our approach for proving the oracle properties is based on a unified treatment that bounds the posterior probability of model mis-selection. This theoretical framework can be of interest to Bayesian statisticians who would like to theoretically justify their new model selection or model averaging methods in addition to empirical results. Furthermore, for non-regular models, we obtain nontrivial conclusions on the choice of prior penalty on model complexity, the temperature parameter of the quasi-posterior, and the advantage of BMA over BMS.

Timely and accurate forecasts of seasonal influenza would assist public health decision-makers in planning intervention strategies, efficiently allocating resources, and possibly saving lives. For these reasons, influenza forecasts are consequential. Producing timely and accurate influenza forecasts, however, have proven challenging due to noisy and limited data, an incomplete understanding of the disease transmission process, and the mismatch between the disease transmission process and the data-generating process. In this paper, we introduce a dynamic Bayesian (DB) flu forecasting model that exploits model discrepancy through a hierarchical model. The DB model allows forecasts of partially observed flu seasons to borrow discrepancy information from previously observed flu seasons. We compare the DB model to all models that competed in the CDC’s 2015–2016 and 2016–2017 flu forecasting challenges. The DB model outperformed all models in both challenges, indicating the DB model is a leading influenza forecasting model.