Related papers: A Geometric View of Posterior Approximation
Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are…
The Rician distribution, a well-known statistical distribution frequently encountered in fields like magnetic resonance imaging and wireless communications, is particularly useful for describing many real phenomena such as signal process…
Approximate Bayesian computation (ABC) refers to a family of inference methods used in the Bayesian analysis of complex models where evaluation of the likelihood is difficult. Conventional ABC methods often suffer from the curse of…
Approximate Bayesian Computation (ABC) is a popular inference method when likelihoods are hard to come by. Practical bottlenecks of ABC applications include selecting statistics that summarize the data without losing too much information or…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation (ABC) has become a popular approach to overcome this issue, in which one simulates…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…
Bayesian methods estimate a measure of uncertainty by using the posterior distribution. One source of difficulty in these methods is the computation of the normalizing constant. Calculating exact posterior is generally intractable and we…
The Laplace approximation is a popular method for constructing a Gaussian approximation to the Bayesian posterior and thereby approximating the posterior mean and variance. But approximation quality is a concern. One might consider using…
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…
Most computational approaches to Bayesian experimental design require making posterior calculations repeatedly for a large number of potential designs and/or simulated datasets. This can be expensive and prohibit scaling up these methods to…
Bayesian inference can often be sensitive to the choice of hyperparameters of the prior or likelihood, yet defining and quantifying this sensitivity in a principled and computationally feasible way remains challenging in practice.…
Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and…
Bayesian approach, as a useful tool for quantifying uncertainties, has been widely used for solving inverse problems of partial differential equations (PDEs). One of the key difficulties for employing Bayesian approach for the issue is how…
Gaussian latent variable models are a key class of Bayesian hierarchical models with applications in many fields. Performing Bayesian inference on such models can be challenging as Markov chain Monte Carlo algorithms struggle with the…
This note attempts to revisit the classical results on Laplace approximation in a modern non-asymptotic and dimension free form. Such an extension is motivated by applications to high dimensional statistical and optimization problems. The…
Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing…
There is a lack of simple and scalable algorithms for uncertainty quantification. Bayesian methods quantify uncertainty through posterior and predictive distributions, but it is difficult to rapidly estimate summaries of these…
Bayesian posterior approximation has become more accessible to practitioners than ever, thanks to modern black-box software. While these tools provide highly accurate approximations with minimal user effort, certain posterior geometries…
The 21st century has seen an enormous growth in the development and use of approximate Bayesian methods. Such methods produce computational solutions to certain intractable statistical problems that challenge exact methods like Markov chain…