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

LCA modelling of cement concrete waste management

Recycling of Construction and Demolition Waste (CDW) could be seen as a proper solution to improve environmental performances and conserve natural resources. Keeping a balance between economic pressures and environmentally friendly practices would play an important role in a circular economy with local material recovery and a recycling industry sector. This balance would ensure a sustainable future to this industry as well as essential quality improvements and developments of market for value added products, which are needed to make recycled materials economically viable. Therefore, environmental assessment of circular economy through life cycle assessment has given rise to further research questions, which have to be answered. Replacing natural resources with recycled materials may cause some indirect environmental impacts (either positive or negative) on other products’ life cycles through economic market mechanisms. In fact, according to Ekvall (2000) “indirect effects depend on how the market for recycled materials reacts to a change in supply or demand for the recycled materials, this in turn depends on political constraints, price elasticities, etc. in the market for recycled materials.” Different system models have been developed to assess environmental effects of recycling, through markets mechanisms, using partial equilibrium economic models. However, they are generally applied to global markets, such as metals or fuels. Construction materials are usually managed and handled at local scale. At this scale, market equilibrium will not follow general market equilibrium rules, but will highly depend on local regulations and local technical practices and recycling facilities. Our general aim is to develop a LCA model of cement concrete waste management at local level including market mechanisms in order to identify action levers for both economic and environmental improvements. In this presentation, through a simple example we compare environmental performances between two scenarios of cement concrete waste management: recycling into road construction or inert landfill. For recycling, we use two system modeling. One system model will use a classical substitution assumption without market mechanism. A second one will take into account a simple market mechanism based on qualities requirements, and thus further existing usage of natural and recycled aggregates. This study will serve setting the basic assumptions to develop a more generic conceptual model, based on material flow analysis, qualities of materials, and economic market mechanisms. This model is applied to the case study of Loire-Atlantique in France, using local economic and flow data

Understanding the progenitor formation galaxies of merging binary black holes

With nearly a hundred gravitational wave detections, the origin of black hole mergers has become a key question. Here, we focus on understanding the typical galactic environment in which binary black hole mergers arise. To this end, we synthesize progenitors of binary black hole mergers as a function of the redshift of progenitor formation, present-day formation galaxy mass, and progenitor stellar metallicity for $240$ star formation and binary evolution models. We provide guidelines to infer the formation galaxy properties and time of formation, highlighting the interplay between the star formation rate and the efficiency of forming merging binary black holes from binary stars, both of which strongly depend on metallicity. We find that across models, over 50% of BBH mergers have a progenitor metallicity of a few tenths of Solar metallicity, however, inferring formation galaxy properties strongly depends on both the binary evolution model and global metallicity evolution. The numerous, low-mass black holes ($\mathrm{\lesssim 15\,M_{\odot}}$) trace the bulk of the star formation in galaxies heavier than the Milky Way ($M_\mathrm{Gal}$ $\mathrm{\gtrsim 10^{10.5}\,M_{\odot}}$). In contrast, heavier BBH mergers typically stem from larger black holes forming in lower metallicity dwarf galaxies ($M_\mathrm{Gal}$ $\mathrm{\lesssim 10^{9}\,M_{\odot}}$). We find that the progenitors of detectable binary black holes tend to arise from dwarf galaxies at a lower formation redshift ($\lesssim \, 1$). We also produce a posterior probability of the progenitor environment for any detected gravitational wave signal. For the massive GW150914 merger, we show that it likely came from a very low metallicity ($Z$ $\mathrm{\lesssim}\,0.025\,\mathrm{Z_{\odot}}$) environment.Comment: 17 pages, 15 figures, 1 table, Accpeted for publication by MNRA