Related papers: Fast Estimation of Bayesian State Space Models Usi…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
This paper details how to parameterize the posterior distribution of state-space systems to generate improved optimization problems for system identification using variational inference. Three different parameterizations of the assumed…
Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges via a neural network that approximates the…
For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…
In this paper, the problem of state estimation, in the context of both filtering and smoothing, for nonlinear state-space models is considered. Due to the nonlinear nature of the models, the state estimation problem is generally intractable…
Almost all fields of science rely upon statistical inference to estimate unknown parameters in theoretical and computational models. While the performance of modern computer hardware continues to grow, the computational requirements for the…
Due to their uncertainty quantification, Bayesian solutions to inverse problems are the framework of choice in applications that are risk averse. These benefits come at the cost of computations that are in general, intractable. New advances…
Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…
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…
State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…
Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
Complex simulator-based models are now routinely used to perform inference across the sciences and engineering, but existing inference methods are often unable to account for outliers and other extreme values in data which occur due to…
We consider the problem of state estimation in general state-space models using variational inference. For a generic variational family defined using the same backward decomposition as the actual joint smoothing distribution, we establish…
Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…
Sensitivity analyses reveal the influence of various modeling choices on the outcomes of statistical analyses. While theoretically appealing, they are overwhelmingly inefficient for complex Bayesian models. In this work, we propose…
Parametric stochastic simulators are ubiquitous in science, often featuring high-dimensional input parameters and/or an intractable likelihood. Performing Bayesian parameter inference in this context can be challenging. We present a neural…
Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified…
We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit…
It is difficult to use subsampling with variational inference in hierarchical models since the number of local latent variables scales with the dataset. Thus, inference in hierarchical models remains a challenge at large scale. It is…