Consistency of the posterior distribution and MLE for piecewise linear regression

We prove the weak consistency of the posterior distribution and that of the Bayes estimator for a two-phase piecewise linear regression mdoel where the break-point is unknown. The non-differentiability of the likelihood of the model with regard to the break- point parameter induces technical difficulties that we overcome by creating a regularised version of the problem at hand. We first recover the strong consistency of the quantities of interest for the regularised version, using results about the MLE, and we then prove that the regularised version and the original version of the problem share the same asymptotic properties

On particle filters applied to electricity load forecasting

We are interested in the online prediction of the electricity load, within the Bayesian framework of dynamic models. We offer a review of sequential Monte Carlo methods, and provide the calculations needed for the derivation of so-called particles filters. We also discuss the practical issues arising from their use, and some of the variants proposed in the literature to deal with them, giving detailed algorithms whenever possible for an easy implementation. We propose an additional step to help make basic particle filters more robust with regard to outlying observations. Finally we use such a particle filter to estimate a state-space model that includes exogenous variables in order to forecast the electricity load for the customers of the French electricity company \'Electricit\'e de France and discuss the various results obtained

Construction of an informative hierarchical prior for a small sample with the help of historical data and application to electricity load forecasting

We are interested in the estimation and prediction of a parametric model on a short dataset upon which it is expected to overfit and perform badly. To overcome the lack of data (relatively to the dimension of the model) we propose the construction of an informative hierarchical Bayesian prior based upon another longer dataset which is assumed to share some similarities with the original, short dataset. We illustrate the performance of our prior on simulated dataset from three standard models. Then we apply the methodology to a working model for the electricity load forecasting on real datasets, where it leads to a substantial improvement of the quality of the predictions

Transition to Chaos in an acoustically-driven cavity flow

We consider the unsteady regimes of an acoustically-driven jet that forces a recirculating flow through successive reflections on the walls of a square cavity. The specific question being addressed is to know whether the system can sustain states of low-dimensional chaos when the acoustic intensity driving the jet is increased, and, if so, to characterise the pathway and underlying physical mechanisms. We adopt two complementary approaches, both based on data extracted from numerical simulations: (i) We first characterise successive bifurcations through the analysis of leading frequencies. Two successive phases in the evolution of the system are singled out in this way, both leading to potentially chaotic states. The two phases are separated by a drastic simplification of the dynamics that immediately follows the emergence of intermittency. The second phase also features a second intermediate state where the dynamics is simplified due to frequency-locking. (ii) Nonlinear time series analysis enables us to reconstruct the attractor of the underlying dynamical system, and to calculate its correlation dimension and leading Lyapunov exponent. Both these quantities bring confirmation that the state preceding the dynamic simplification that initiates the second phase is chaotic. Poincar\'e maps further reveal that this chaotic state in fact results from a dynamic instability of the system between two non-chaotic states respectively observed at slightly lower and slightly higher acoustic forcing.Comment: 28 pages, 19 figure

BLOOM: A 176B-Parameter Open-Access Multilingual Language Model

Large language models (LLMs) have been shown to be able to perform new tasks based on a few demonstrations or natural language instructions. While these capabilities have led to widespread adoption, most LLMs are developed by resource-rich organizations and are frequently kept from the public. As a step towards democratizing this powerful technology, we present BLOOM, a 176B-parameter open-access language model designed and built thanks to a collaboration of hundreds of researchers. BLOOM is a decoder-only Transformer language model that was trained on the ROOTS corpus, a dataset comprising hundreds of sources in 46 natural and 13 programming languages (59 in total). We find that BLOOM achieves competitive performance on a wide variety of benchmarks, with stronger results after undergoing multitask prompted finetuning. To facilitate future research and applications using LLMs, we publicly release our models and code under the Responsible AI License

Лапаротомия в системе лечения перитонитов

ПЕРИТОНИТ /ХИРБРЮШИНЫ БОЛЕЗНИ /ХИРЛАПАРОТОМИЯХИРУРГИЧЕСКИЕ ОПЕРАЦИИ /МЕТОДЫРЕЛАПАРОТОМИ

COVID-19 symptoms at hospital admission vary with age and sex: results from the ISARIC prospective multinational observational study

Background: The ISARIC prospective multinational observational study is the largest cohort of hospitalized patients with COVID-19. We present relationships of age, sex, and nationality to presenting symptoms. Methods: International, prospective observational study of 60 109 hospitalized symptomatic patients with laboratory-confirmed COVID-19 recruited from 43 countries between 30 January and 3 August 2020. Logistic regression was performed to evaluate relationships of age and sex to published COVID-19 case definitions and the most commonly reported symptoms. Results: ‘Typical’ symptoms of fever (69%), cough (68%) and shortness of breath (66%) were the most commonly reported. 92% of patients experienced at least one of these. Prevalence of typical symptoms was greatest in 30- to 60-year-olds (respectively 80, 79, 69%; at least one 95%). They were reported less frequently in children (≤ 18 years: 69, 48, 23; 85%), older adults (≥ 70 years: 61, 62, 65; 90%), and women (66, 66, 64; 90%; vs. men 71, 70, 67; 93%, each P < 0.001). The most common atypical presentations under 60 years of age were nausea and vomiting and abdominal pain, and over 60 years was confusion. Regression models showed significant differences in symptoms with sex, age and country. Interpretation: This international collaboration has allowed us to report reliable symptom data from the largest cohort of patients admitted to hospital with COVID-19. Adults over 60 and children admitted to hospital with COVID-19 are less likely to present with typical symptoms. Nausea and vomiting are common atypical presentations under 30 years. Confusion is a frequent atypical presentation of COVID-19 in adults over 60 years. Women are less likely to experience typical symptoms than men

Méthodes bayésiennes pour la prévision de consommation l'électricité

In this manuscript, we develop Bayesian statistics tools to forecast the French electricity load. We first prove the asymptotic normality of the posterior distribution (Bernstein-von Mises theorem) for the piecewise linear regression model used to describe the heating effect and the consistency of the Bayes estimator. We then build a a hierarchical informative prior to help improve the quality of the predictions for a high dimension model with a short dataset. We typically show, with two examples involving the non metered EDF customers, that the method we propose allows a more robust estimation of the model with regard to the lack of data. Finally, we study a new nonlinear dynamic model to predict the electricity load online. We develop a particle filter algorithm to estimate the model et compare the predictions obtained with operationnal predictions from EDF.Dans ce manuscrit, nous développons des outils de statistique bayésienne pour la prévision de consommation d'électricité en France. Nous prouvons tout d'abord la normalité asymptotique de la loi a posteriori (théorème de Bernstein-von Mises) pour le modèle linéaire par morceaux de part chauffage et la consistance de l'estimateur de Bayes. Nous décrivons ensuite la construction d'une loi a priori informative afin d'améliorer la qualité des prévisions d'un modèle de grande dimension en situation d'historique court. A partir de deux exemples impliquant les clients non télérelevés de EDF, nous montrons notamment que la méthode proposée permet de rendre l'évaluation du modèle plus robuste vis-à-vis du manque de données. Nous proposons enfin un nouveau modèle dynamique, non-linéaire, pour prévoir la consommation d'électricité en ligne. Nous construisons un algorithme de filtrage particulaire afin d'estimer ce modèle et comparons les prévisions obtenues aux prévisions opérationnelles utilisées au sein d'EDF