A bayesian approach for predicting with polynomial regresión of unknown degree.

This article presents a comparison of four methods to compute the posterior probabilities of the possible orders in polynomial regression models. These posterior probabilities are used for forecasting by using Bayesian model averaging. It is shown that Bayesian model averaging provides a closer relationship between the theoretical coverage of the high density predictive interval (HDPI) and the observed coverage than those corresponding to selecting the best model. The performance of the different procedures are illustrated with simulations and some known engineering data

A Bayesian Approach for Predicting with Polynomial Regresión of Unknown Degree.

This article presents a comparison of four methods to compute the posterior probabilities of the possible orders in polynomial regression models. These posterior probabilities are used for forecasting by using Bayesian model averaging. It is shown that Bayesian model averaging provides a closer relationship between the theoretical coverage of the high density predictive interval (HDPI) and the observed coverage than those corresponding to selecting the best model. The performance of the different procedures are illustrated with simulations and some known engineering data.

Bayesian estimate of the degree of a polynomial given a noisy data sample

A widely used method to create a continuous representation of a discrete data-set is regression analysis. When the regression model is not based on a mathematical description of the physics underlying the data, heuristic techniques play a crucial role and the model choice can have a significant impact on the result. In this paper, the problem of identifying the most appropriate model is formulated and solved in terms of Bayesian selection. Besides, probability calculus is the best way to choose among different alternatives. The results obtained are applied to the case of both univariate and bivariate polynomials used as trial solutions of systems of thermodynamic partial differential equations.Comment: 10 pages, 5 figures, submitted to Metrologi

Model selection in regression under structural constraints

The paper considers model selection in regression under the additional structural constraints on admissible models where the number of potential predictors might be even larger than the available sample size. We develop a Bayesian formalism as a natural tool for generating a wide class of model selection criteria based on penalized least squares estimation with various complexity penalties associated with a prior on a model size. The resulting criteria are adaptive to structural constraints. We establish the upper bound for the quadratic risk of the resulting MAP estimator and the corresponding lower bound for the minimax risk over a set of admissible models of a given size. We then specify the class of priors (and, therefore, the class of complexity penalties) where for the "nearly-orthogonal" design the MAP estimator is asymptotically at least nearly-minimax (up to a log-factor) simultaneously over an entire range of sparse and dense setups. Moreover, when the numbers of admissible models are "small" (e.g., ordered variable selection) or, on the opposite, for the case of complete variable selection, the proposed estimator achieves the exact minimax rates.Comment: arXiv admin note: text overlap with arXiv:0912.438

The Challenge of Machine Learning in Space Weather Nowcasting and Forecasting

The numerous recent breakthroughs in machine learning (ML) make imperative to carefully ponder how the scientific community can benefit from a technology that, although not necessarily new, is today living its golden age. This Grand Challenge review paper is focused on the present and future role of machine learning in space weather. The purpose is twofold. On one hand, we will discuss previous works that use ML for space weather forecasting, focusing in particular on the few areas that have seen most activity: the forecasting of geomagnetic indices, of relativistic electrons at geosynchronous orbits, of solar flares occurrence, of coronal mass ejection propagation time, and of solar wind speed. On the other hand, this paper serves as a gentle introduction to the field of machine learning tailored to the space weather community and as a pointer to a number of open challenges that we believe the community should undertake in the next decade. The recurring themes throughout the review are the need to shift our forecasting paradigm to a probabilistic approach focused on the reliable assessment of uncertainties, and the combination of physics-based and machine learning approaches, known as gray-box.Comment: under revie