13,588 research outputs found
Patterns of Scalable Bayesian Inference
Datasets are growing not just in size but in complexity, creating a demand
for rich models and quantification of uncertainty. Bayesian methods are an
excellent fit for this demand, but scaling Bayesian inference is a challenge.
In response to this challenge, there has been considerable recent work based on
varying assumptions about model structure, underlying computational resources,
and the importance of asymptotic correctness. As a result, there is a zoo of
ideas with few clear overarching principles.
In this paper, we seek to identify unifying principles, patterns, and
intuitions for scaling Bayesian inference. We review existing work on utilizing
modern computing resources with both MCMC and variational approximation
techniques. From this taxonomy of ideas, we characterize the general principles
that have proven successful for designing scalable inference procedures and
comment on the path forward
Active network management for electrical distribution systems: problem formulation, benchmark, and approximate solution
With the increasing share of renewable and distributed generation in
electrical distribution systems, Active Network Management (ANM) becomes a
valuable option for a distribution system operator to operate his system in a
secure and cost-effective way without relying solely on network reinforcement.
ANM strategies are short-term policies that control the power injected by
generators and/or taken off by loads in order to avoid congestion or voltage
issues. Advanced ANM strategies imply that the system operator has to solve
large-scale optimal sequential decision-making problems under uncertainty. For
example, decisions taken at a given moment constrain the future decisions that
can be taken and uncertainty must be explicitly accounted for because neither
demand nor generation can be accurately forecasted. We first formulate the ANM
problem, which in addition to be sequential and uncertain, has a nonlinear
nature stemming from the power flow equations and a discrete nature arising
from the activation of power modulation signals. This ANM problem is then cast
as a stochastic mixed-integer nonlinear program, as well as second-order cone
and linear counterparts, for which we provide quantitative results using state
of the art solvers and perform a sensitivity analysis over the size of the
system, the amount of available flexibility, and the number of scenarios
considered in the deterministic equivalent of the stochastic program. To foster
further research on this problem, we make available at
http://www.montefiore.ulg.ac.be/~anm/ three test beds based on distribution
networks of 5, 33, and 77 buses. These test beds contain a simulator of the
distribution system, with stochastic models for the generation and consumption
devices, and callbacks to implement and test various ANM strategies
An empirical test for cellular automaton models of traffic flow
Based on a detailed microscopic test scenario motivated by recent empirical
studies of single-vehicle data, several cellular automaton models for traffic
flow are compared. We find three levels of agreement with the empirical data:
1) models that do not reproduce even qualitatively the most important empirical
observations,
2) models that are on a macroscopic level in reasonable agreement with the
empirics, and 3) models that reproduce the empirical data on a microscopic
level as well.
Our results are not only relevant for applications, but also shed new light
on the relevant interactions in traffic flow.Comment: 28 pages, 36 figures, accepted for publication in PR
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