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We propose a novel portfolio selection approach that manages to ease some of the problems that characterise standard expected utility maximisation. The optimal portfolio is no longer defined as the extremum of a suitably chosen utility…

Monte Carlo methods are essential tools for Bayesian inference. Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning, and statistics, employed to draw samples from…

Monte Carlo sampling techniques have broad applications in machine learning, Bayesian posterior inference, and parameter estimation. Often the target distribution takes the form of a product distribution over a dataset with a large number…

Adaptive importance sampling is a class of techniques for finding good proposal distributions for importance sampling. Often the proposal distributions are standard probability distributions whose parameters are adapted based on the…

A key quantity of interest in Bayesian inference are expectations of functions with respect to a posterior distribution. Markov Chain Monte Carlo is a fundamental tool to consistently compute these expectations via averaging samples drawn…

This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…

Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…

Practitioners of Bayesian statistics have long depended on Markov chain Monte Carlo (MCMC) to obtain samples from intractable posterior distributions. Unfortunately, MCMC algorithms are typically serial, and do not scale to the large…

A simple and efficient adaptive Markov Chain Monte Carlo (MCMC) method, called the Metropolized Adaptive Subspace (MAdaSub) algorithm, is proposed for sampling from high-dimensional posterior model distributions in Bayesian variable…

Importance sampling (IS) is commonly used for cross validation (CV) in Bayesian models, because it only involves reweighting existing posterior draws without needing to re-estimate the model by re-running Markov chain Monte Carlo (MCMC).…

We propose a new computationally efficient sampling scheme for Bayesian inference involving high dimensional probability distributions. Our method maps the original parameter space into a low-dimensional latent space, explores the latent…

There is a tension between robustness and efficiency when designing Markov chain Monte Carlo (MCMC) sampling algorithms. Here we focus on robustness with respect to tuning parameters, showing that more sophisticated algorithms tend to be…

Importance sampling is a Monte Carlo method that introduces a proposal distribution to sample the space according to the target distribution. Yet calibration of the proposal distribution is essential to achieving efficiency, thus the resort…

The Metropolis-Hastings (MH) algorithm is one of the most widely used Markov Chain Monte Carlo schemes for generating samples from Bayesian posterior distributions. The algorithm is asymptotically exact, flexible and easy to implement.…

We propose an adaptive importance sampling scheme for Gaussian approximations of intractable posteriors. Optimization-based approximations like variational inference can be too inaccurate while existing Monte Carlo methods can be too slow.…

We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We…

Performing reliable Bayesian inference on a big data scale is becoming a keystone in the modern era of machine learning. A workhorse class of methods to achieve this task are Markov chain Monte Carlo (MCMC) algorithms and their design to…

Sequential optimization methods are often confronted with the curse of dimensionality in high-dimensional spaces. Current approaches under the Gaussian process framework are still burdened by the computational complexity of tracking…

Frequentist and likelihood methods of inference based on the multivariate skew-normal model encounter several technical difficulties with this model. In spite of the popularity of this class of densities, there are no broadly satisfactory…

Achieving robust uncertainty quantification for deep neural networks represents an important requirement in many real-world applications of deep learning such as medical imaging where it is necessary to assess the reliability of a neural…