An asymptotic Peskun ordering and its application to lifted samplers

A Peskun ordering between two samplers, implying a dominance of one over the other, is known among the Markov chain Monte Carlo community for being a remarkably strong result, but it is also known for being one that is notably difficult to establish. Indeed, one has to prove that the probability to reach a state $\mathbf{y}$ from a state $\mathbf{x}$, using a sampler, is greater than or equal to the probability using the other sampler, and this must hold for all pairs $(\mathbf{x}, \mathbf{y})$ such that $\mathbf{x} \neq \mathbf{y}$. We provide in this paper a weaker version that does not require an inequality between the probabilities for all these states: essentially, the dominance holds asymptotically, as a varying parameter grows without bound, as long as the states for which the probabilities are greater than or equal to belong to a mass-concentrating set. The weak ordering turns out to be useful to compare lifted samplers for partially-ordered discrete state-spaces with their Metropolis--Hastings counterparts. An analysis in great generality yields a qualitative conclusion: they asymptotically perform better in certain situations (and we are able to identify them), but not necessarily in others (and the reasons why are made clear). A thorough study in a specific context of graphical-model simulation is also conducted

Improving multiple-try Metropolis with local balancing

Multiple-try Metropolis (MTM) is a popular Markov chain Monte Carlo method with the appealing feature of being amenable to parallel computing. At each iteration, it samples several candidates for the next state of the Markov chain and randomly selects one of them based on a weight function. The canonical weight function is proportional to the target density. We show both theoretically and empirically that this weight function induces pathological behaviours in high dimensions, especially during the convergence phase. We propose to instead use weight functions akin to the locally-balanced proposal distributions of Zanella (2020), thus yielding MTM algorithms that do not exhibit those pathological behaviours. To theoretically analyse these algorithms, we study the high-dimensional performance of ideal schemes that can be think of as MTM algorithms which sample an infinite number of candidates at each iteration, as well as the discrepancy between such schemes and the MTM algorithms which sample a finite number of candidates. Our analysis unveils a strong distinction between the convergence and stationary phases: in the former, local balancing is crucial and effective to achieve fast convergence, while in the latter, the canonical and novel weight functions yield similar performance. Numerical experiments include an application in precision medicine involving a computationally expensive forward model, which makes the use of parallel computing within MTM iterations beneficial

Quantification of nitrate removal by a flooded alluvial zone in the Ill floodplain (Eastern France)

The nitrate reducing capacity of a flooded system in the Ill floodplain (Eastern France) was investigated for a period of 2 years. The methodology used consisted of a spatio-temporal monitoring of stream flow and nitrate concentrations in the groundwater and surface water, calculation of input and output fluxes and modelling of groundwater fluxes and nitrate transfer through the alluvial area. A comparison of chloride flux (used as hydrological tracer) and nitrate flux was done to determine a floodplain effect on the retention of nitrate. We show that up to 95% of the nitrate load in the groundwater is retained by the system, whereas the retention in the stream network is very low. Ammonium fluxes increased from inputs to outputs in the stream and in the groundwater. The chloride input in the groundwater is higher than the output, whereas in the surface water the output is higher than the input, the amount evacuated in streams corresponding to the losses from groundwater. The nitrate removal rate calculated for the whole modelized surface area (40 km2) represented 559 t N yr-1 or 1397.7 kg N ha-1 yr-1. The ammonium fluxes exported by the system represented 102 kg N ha-1 yr-1 A part of nitrate is reduced and exported by the groundwater and stream network in the form of ammonium. These results can be explained by the duration of floods which controls the equilibrium between the various forms of nitrogen. Thus, long watering periods favour nitrogen removal (denitrification and plant uptake) and limit nitrate production which compensates elimination during the dry period

Linking electricity prices and costs in bottom-up top-down coupling under changing market environments

We couple top-down and bottom-up models to analyse electricity markets. We simulate energy policies under alternative regulatory assumptions. We shows that market liberalisation affects the links between generation costs and user prices. We show that the coupling mechanisms should reflect the nature of electricity market regulation. We show that a tax on electricity is more effective in a liberalized than in a regulated market

Croyance et incroyance dans l’Europe de la Révolution et du XIXe siècle

Philippe Boutry, directeur d’études avec Daniel Couty, maître de conférences à l’Université de Rouen et Catherine Maire, chargée de recherche au CNRS Liens et frontières du religieux : un enjeu politique, une donnée littéraire Quatre séances ont été consacrées à l’examen de questions théologiques, éthiques et philosophiques intéressant les mutations du catholicisme à l’âge du jansénisme et de la philosophie des Lumières. Béatrice Guion (Université de Toulouse-II), dans un séminaire intitulé «..

Croyance et incroyance dans l’Europe de la Révolution et du XIXe siècle

Philippe Boutry, directeur d’étudesCatherine Maire, chargée de recherches au CNRSJean-François Chanet, maître de conférences à l’Institut universitaire de France (Lille-III) Le séminaire, organisé en collaboration avec Catherine Maire, chargée de recherches au CNRS, membre du Centre d’anthropologie religieuse européenne (CARE), et Jean-François Chanet, professeur d’histoire contemporaine à l’Université Lille-III, détaché à l’Institut universitaire de France, a de nouveau porté sur « Liens et ..