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Approximate Bayesian Computation (ABC) can be viewed as an analytic approximation of an intractable likelihood coupled with an elementary simulation step. Such a view, combined with a suitable instrumental prior distribution permits…

With continued advances in Geographic Information Systems and related computational technologies, statisticians are often required to analyze very large spatial datasets. This has generated substantial interest over the last decade, already…

We put forward a new Bayesian modeling strategy for spatiotemporal count data that enables efficient posterior sampling. Most previous models for such data decompose logarithms of the response Poisson rates into fixed effects and spatial…

As the amount of economic and other data generated worldwide increases vastly, a challenge for future generations of econometricians will be to master efficient algorithms for inference in empirical models with large information sets. This…

Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take…

We propose an efficient way to sample from a class of structured multivariate Gaussian distributions which routinely arise as conditional posteriors of model parameters that are assigned a conditionally Gaussian prior. The proposed…

Bayesian predictive probabilities are commonly used for interim monitoring of clinical trials through efficacy and futility stopping rules. Despite their usefulness, calculation of predictive probabilities, particularly in pre-experiment…

When dealing with datasets containing a billion instances or with simulations that require a supercomputer to execute, computational resources become part of the equation. We can improve the efficiency of learning and inference by…

Performing exact posterior inference in complex generative models is often difficult or impossible due to an expensive to evaluate or intractable likelihood function. Approximate Bayesian computation (ABC) is an inference framework that…

Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…

The topic of deep learning has seen a surge of interest in recent years both within and outside of the field of Statistics. Deep models leverage both nonlinearity and interaction effects to provide superior predictions in many cases when…

Bayesian inverse problems use data to update a prior probability distribution on uncertain parameter values to a posterior distribution. Such problems arise in many structural engineering applications, but computational solution of Bayesian…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

Some machine learning applications require continual learning - where data comes in a sequence of datasets, each is used for training and then permanently discarded. From a Bayesian perspective, continual learning seems straightforward:…

This paper is concerned with the numerical solution of model-based, Bayesian inverse problems. We are particularly interested in cases where the cost of each likelihood evaluation (forward-model call) is expensive and the number of un-…

Information theoretic active learning has been widely studied for probabilistic models. For simple regression an optimal myopic policy is easily tractable. However, for other tasks and with more complex models, such as classification with…

In this paper we extend existing Bayesian methods for variable selection in Gaussian process regression, to select both the regression terms and the active covariates in the spatial correlation structure. We then use the estimated posterior…

Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high…

We discuss an approach for deriving robust posterior distributions from $M$-estimating functions using Approximate Bayesian Computation (ABC) methods. In particular, we use $M$-estimating functions to construct suitable summary statistics…

The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…