Related papers: Objective Climate Model Predictions Using Jeffreys…
This paper deals with Bayesian inference of a mixture of Gaussian distributions. A novel formulation of the mixture model is introduced, which includes the prior constraint that each Gaussian component is always assigned a minimal number of…
The Yule-Simon distribution is usually employed in the analysis of frequency data. As the Bayesian literature, so far, ignored this distribution, here we show the derivation of two objective priors for the parameter of the Yule-Simon…
Seasonal weather forecasts are crucial for long-term planning in many practical situations and skillful forecasts may have substantial economic and humanitarian implications. Current seasonal forecasting models require statistical…
We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional…
Ensemble forecasts of weather and climate are subject to systematic biases in the ensemble mean and variance, leading to inaccurate estimates of the forecast mean and variance. To address these biases, ensemble forecasts are post-processed…
Uncertainty quantification is crucial to decision-making. A prominent example is probabilistic forecasting in numerical weather prediction. The dominant approach to representing uncertainty in weather forecasting is to generate an ensemble…
We propose a method for estimating the posterior distribution of a standard geostatistical model. After choosing the model formulation and specifying a prior, we use normal mixture densities to approximate the posterior distribution. The…
Earth System Models (ESMs) are the state of the art for projecting the effects of climate change. However, longstanding uncertainties in their ability to simulate regional and local precipitation extremes and related processes inhibit…
The Generalized Pareto (GP) and Generalized extreme value (GEV) distributions play an important role in extreme value analyses, as models for threshold excesses and block maxima respectively. For each of these distributions we consider…
Estimating how uncertain an AI system is in its predictions is important to improve the safety of such systems. Uncertainty in predictive can result from uncertainty in model parameters, irreducible data uncertainty and uncertainty due to…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
We consider Bayesian shrinkage predictions for the Normal regression problem under the frequentist Kullback-Leibler risk function. Firstly, we consider the multivariate Normal model with an unknown mean and a known covariance. While the…
The difference between a model forecast and actual observations is called forecast bias. This bias is due to either incomplete model assumptions and/or poorly known parameter values and initial/boundary conditions. In this paper we discuss…
There are three principle paradigms of statistical inference: (i) Bayesian, (ii) information-based and (iii) frequentist inference. We describe an objective prior (the weighting or $w$-prior) which unifies objective Bayes and…
Statistical modeling of high-dimensional matrix-valued data motivates the use of a low-rank representation that simultaneously summarizes key characteristics of the data and enables dimension reduction. Low-rank representations commonly…
Motivated by the need, in some Bayesian likelihood free inference problems, of imputing a multivariate counting distribution based on its vector of means and variance-covariance matrix, we define a generic multivariate discrete…
Since the prediction of climate is mainly considered as a prediction of second kind, it is indispensable to assess the accuracy with which these boundary conditions can be determined so that we can find a reasonable answer, whether climate…
Probabilistic forecasting of multivariate time series is essential for various downstream tasks. Most existing approaches rely on the sequences being uniformly spaced and aligned across all variables. However, real-world multivariate time…
Inference from limited data requires a notion of measure on parameter space, most explicit in the Bayesian framework as a prior. Here we demonstrate that Jeffreys prior, the best-known uninformative choice, introduces enormous bias when…
In this paper we introduce objective proper prior distributions for hypothesis testing and model selection based on measures of divergence between the competing models; we call them divergence based (DB) priors. DB priors have simple forms…