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Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…
The vast majority of the literature on learning dynamical systems or stochastic processes from time series has focused on stable or ergodic systems, for both Bayesian and frequentist inference procedures. However, most real-world systems…
Bayesian regression determines model parameters by minimizing the expected loss, an upper bound to the true generalization error. However, the loss ignores misspecification, where models are imperfect. Parameter uncertainties from Bayesian…
The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…
An informative sampling design leads to unit inclusion probabilities that are correlated with the response variable of interest. However, multistage sampling designs may also induce higher order dependencies, which are typically ignored in…
Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…
We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…
Model Predictive Control (MPC) is a powerful framework for constrained control, but its performance and safety can be severely degraded when the prediction model is learned online and thus remains uncertain. In this work, we develop a…
We derive conditions for posterior consistency when the responses are independent but not identically distributed ($i.n.i.d$) and the model is "misspecified" to be a family of densities parametrized by a possibly infinite dimensional…
Mathematical models of real life phenomena are highly nonlinear involving multiple parameters and often exhibiting complex dynamics. Experimental data sets are typically small and noisy, rendering estimation of parameters from such data…
A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude…
We address the problem of providing inference from a Bayesian perspective for parameters selected after viewing the data. We present a Bayesian framework for providing inference for selected parameters, based on the observation that…
We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…
In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…
In this work the issue of Bayesian inference for stationary data is addressed. Therefor a parametrization of a statistically suitable subspace of the the shift-ergodic probability measures on a Cartesian product of some finite state space…
Bayesian networks are a versatile and powerful tool to model complex phenomena and the interplay of their components in a probabilistically principled way. Moving beyond the comparatively simple case of completely observed, static data,…
Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…
Bayesian methods are a popular choice for statistical inference in small-data regimes due to the regularization effect induced by the prior. In the context of density estimation, the standard nonparametric Bayesian approach is to target the…
This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…
Models of updating a set of priors either do not allow a decision maker to make inference about her priors (full bayesian updating or FB) or require an extreme degree of selection (maximum likelihood updating or ML). I characterize a…