Related papers: Distribution Preserving Multiple Hypotheses Predic…
Predictive uncertainty in hydrological modelling is quantified by using post-processing or Bayesian-based methods. The former methods are not straightforward and the latter ones are not distribution-free (i.e. assumptions on the probability…
Multi-dimensional Hawkes process (MHP) is a class of self and mutually exciting point processes that find wide range of applications -- from prediction of earthquakes to modelling of order books in high frequency trading. This paper makes…
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…
We consider the multiple hypothesis testing (MHT) problem over the joint domain formed by a graph and a measure space. On each sample point of this joint domain, we assign a hypothesis test and a corresponding $p$-value. The goal is to make…
A novel solution to the smoothing problem for multi-object dynamical systems is proposed and evaluated. The systems of interest contain an unknown and varying number of dynamical objects that are partially observed under noisy and corrupted…
Hyper-differential sensitivity analysis with respect to model discrepancy was recently developed to enable uncertainty quantification for optimization problems. The approach consists of two primary steps: (i) Bayesian calibration of the…
Predictions and forecasts of machine learning models should take the form of probability distributions, aiming to increase the quantity of information communicated to end users. Although applications of probabilistic prediction and…
We present a theoretical framework of probabilistic learning derived by Maximum Probability (MP) Theorem shown in the current paper. In this probabilistic framework, a model is defined as an event in the probability space, and a model or…
This paper considers Bayesian parameter estimation of dynamic systems using a Markov Chain Monte Carlo (MCMC) approach. The Metroplis-Hastings (MH) algorithm is employed, and the main contribution of the paper is to examine and illustrate…
Data with missing values is ubiquitous in many applications. Recent years have witnessed increasing attention on prediction with only incomplete data consisting of observed features and a mask that indicates the missing pattern. Existing…
Particle Marginal Metropolis-Hastings (PMMH) is a general approach to Bayesian inference when the likelihood is intractable, but can be estimated unbiasedly. Our article develops an efficient PMMH method that scales up better to higher…
In this article, a multiple split method is proposed that enables construction of multidimensional probabilistic forecasts of a selected set of variables. The method uses repeated resampling to estimate uncertainty of simultaneous…
Statisticians often face the choice between using probability models or a paradigm defined by minimising a loss function. Both approaches are useful and, if the loss can be re-cast into a proper probability model, there are many tools to…
This paper introduces HuLP, a Human-in-the-Loop for Prognosis model designed to enhance the reliability and interpretability of prognostic models in clinical contexts, especially when faced with the complexities of missing covariates and…
The paper presents a new perspective on the mixture of Dirichlet process model which allows the recovery of full and correct uncertainty quantification associated with the full model, even after having integrated out the random distribution…
We present a new antithetic multilevel Monte Carlo (MLMC) method for the estimation of expectations with respect to laws of diffusion processes that can be elliptic or hypo-elliptic. In particular, we consider the case where one has to…
Trajectory prediction is an important task, especially in autonomous driving. The ability to forecast the position of other moving agents can yield to an effective planning, ensuring safety for the autonomous vehicle as well for the…
Probabilistic forecasting provides a principled framework for uncertainty quantification in dynamical systems by representing predictions as probability distributions rather than deterministic trajectories. However, existing forecasting…
Event data consisting of time of occurrence of the events arises in several real-world applications. Recent works have introduced neural network based point processes for modeling event-times, and were shown to provide state-of-the-art…
There is a lack of methodological results for continuous time change detection due to the challenges of noninformative prior specification and efficient posterior inference in this setting. Most methodologies to date assume data are…