Related papers: Summary Statistics in Approximate Bayesian Computa…
Max-plus based methods have been recently developed to approximate the value function of possibly high dimensional optimal control problems. A critical step of these methods consists in approximating a function by a supremum of a small…
Sparse estimation of the precision matrix under high-dimensional scaling constitutes a canonical problem in statistics and machine learning. Numerous regression and likelihood based approaches, many frequentist and some Bayesian in nature…
Likelihood-free inference for simulator-based statistical models has developed rapidly from its infancy to a useful tool for practitioners. However, models with more than a handful of parameters still generally remain a challenge for the…
The development of statistical methods and numerical algorithms for model choice is vital to many real-world applications. In practice, the ABC approach can be instrumental for sequential model design; however, the theoretical basis of its…
We are often interested in identifying the feasible subset of a decision space under multiple constraints to permit effective design exploration. If determining feasibility required computationally expensive simulations, the cost of…
The goal of this thesis is twofold; introduce the fundamentals of Bayesian inference and computation focusing on astronomical and cosmological applications, and present recent advances in probabilistic computational methods developed by the…
Background: When conducting a meta-analysis of a continuous outcome, estimated means and standard deviations from the selected studies are required in order to obtain an overall estimate of the mean effect and its confidence interval. If…
This paper is on Bayesian inference for parametric statistical models that are defined by a stochastic simulator which specifies how data is generated. Exact sampling is then possible but evaluating the likelihood function is typically…
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…
Consider scene understanding problems such as predicting where a person is probably reaching, or inferring the pose of 3D objects from depth images, or inferring the probable street crossings of pedestrians at a busy intersection. This…
Bayes factors are an increasingly popular tool for indexing evidence from experiments. For two competing population models, the Bayes factor reflects the relative likelihood of observing some data under one model compared to the other. In…
This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems.…
Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively…
A common problem in natural sciences is the comparison of competing models in the light of observed data. Bayesian model comparison provides a statistically sound framework for this comparison based on the evidence each model provides for…
A new recalibration post-processing method is presented to improve the quality of the posterior approximation when using Approximate Bayesian Computation (ABC) algorithms. Recalibration may be used in conjunction with existing…
The frequentist method of simulated minimum distance (SMD) is widely used in economics to estimate complex models with an intractable likelihood. In other disciplines, a Bayesian approach known as Approximate Bayesian Computation (ABC) is…
Astronomers are often confronted with funky populations and distributions of objects: brighter objects are more likely to be detected; targets are selected based on colour cuts; imperfect classification yields impure samples. Failing to…
In this dissertation we study the tractability of the information-based complexity $n(\varepsilon,d)$ for $d$-variate function approximation problems. In the deterministic setting for many unweighted problems the curse of dimensionality…
In generative models with obscured likelihood, Approximate Bayesian Computation (ABC) is often the tool of last resort for inference. However, ABC demands many prior parameter trials to keep only a small fraction that passes an acceptance…
The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure. It is key to understand how many samples are required in order to guarantee…