Related papers: Fast Likelihood-Free Parameter Estimation for L\'e…

The task of quantifying the inherent uncertainty associated with neural network predictions is a key challenge in artificial intelligence. Bayesian neural networks (BNNs) and deep ensembles are among the most prominent approaches to tackle…

Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…

Bayesian Neural Networks (BNNs) offer a principled and natural framework for proper uncertainty quantification in the context of deep learning. They address the typical challenges associated with conventional deep learning methods, such as…

Deep learning algorithms have recently shown to be a successful tool in estimating parameters of statistical models for which simulation is easy, but likelihood computation is challenging. But the success of these approaches depends on…

We present Sequential Neural Variational Inference (SNVI), an approach to perform Bayesian inference in models with intractable likelihoods. SNVI combines likelihood-estimation (or likelihood-ratio-estimation) with variational inference to…

Bayesian neural networks (BNNs) have been long considered an ideal, yet unscalable solution for improving the robustness and the predictive uncertainty of deep neural networks. While they could capture more accurately the posterior…

We propose a new, two-step empirical Bayes-type of approach for neural networks. We show in context of the nonparametric regression model that the procedure (up to a logarithmic factor) provides optimal recovery of the underlying functional…

We present Causal Posterior Estimation (CPE), a novel method for Bayesian inference in simulator models, i.e., models where the evaluation of the likelihood function is intractable or too computationally expensive, but where one can…

Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data.…

In the gravitational-wave analysis of pulsar-timing-array datasets, parameter estimation is usually performed using Markov Chain Monte Carlo methods to explore posterior probability densities. We introduce an alternative procedure that…

Modeling uncertainty in heavy-tailed time series remains a critical challenge for deep probabilistic forecasting models, which often struggle to capture abrupt, extreme events. While L\'evy stable distributions offer a natural framework for…

In this paper we study the problem of recovering a structured but unknown parameter ${\bf{\theta}}^*$ from $n$ nonlinear observations of the form $y_i=f(\langle {\bf{x}}_i,{\bf{\theta}}^*\rangle)$ for $i=1,2,\ldots,n$. We develop a…

In this paper we present an algorithm for rapid Bayesian analysis that combines the benefits of nested sampling and artificial neural networks. The blind accelerated multimodal Bayesian inference (BAMBI) algorithm implements the MultiNest…

In Hezaveh et al. 2017 we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational lensing systems. Here we demonstrate a method for…

We propose a doubly subordinated Levy process, NDIG, to model the time series properties of the cryptocurrency bitcoin. NDIG captures the skew and fat-tailed properties of bitcoin prices and gives rise to an arbitrage free, option pricing…

Recent advances in computing power and the potential to make more realistic assumptions due to increased flexibility have led to the increased prevalence of simulation models in economics. While models of this class, and particularly…

In this paper, we study nonparametric estimation of the L\'{e}vy density for L\'{e}vy processes, with and without Brownian component. For this, we consider $n$ discrete time observations with step $\Delta$. The asymptotic framework is: $n$…

This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…

Gaussian processes are rich distributions over functions, with generalization properties determined by a kernel function. When used for long-range extrapolation, predictions are particularly sensitive to the choice of kernel parameters. It…

L\'evy processes are widely used in financial mathematics to model return data. Price processes are then defined as a corresponding geometric L\'evy process, implying the fact that returns are independent. In this paper we propose an…