7,669 research outputs found
Bayesian estimation of discretely observed multi-dimensional diffusion processes using guided proposals
Estimation of parameters of a diffusion based on discrete time observations
poses a difficult problem due to the lack of a closed form expression for the
likelihood. From a Bayesian computational perspective it can be casted as a
missing data problem where the diffusion bridges in between discrete-time
observations are missing. The computational problem can then be dealt with
using a Markov-chain Monte-Carlo method known as data-augmentation. If unknown
parameters appear in the diffusion coefficient, direct implementation of
data-augmentation results in a Markov chain that is reducible. Furthermore,
data-augmentation requires efficient sampling of diffusion bridges, which can
be difficult, especially in the multidimensional case.
We present a general framework to deal with with these problems that does not
rely on discretisation. The construction generalises previous approaches and
sheds light on the assumptions necessary to make these approaches work. We
define a random-walk type Metropolis-Hastings sampler for updating diffusion
bridges. Our methods are illustrated using guided proposals for sampling
diffusion bridges. These are Markov processes obtained by adding a guiding term
to the drift of the diffusion. We give general guidelines on the construction
of these proposals and introduce a time change and scaling of the guided
proposal that reduces discretisation error. Numerical examples demonstrate the
performance of our methods
Nonequilibrium candidate Monte Carlo: A new tool for efficient equilibrium simulation
Metropolis Monte Carlo simulation is a powerful tool for studying the
equilibrium properties of matter. In complex condensed-phase systems, however,
it is difficult to design Monte Carlo moves with high acceptance probabilities
that also rapidly sample uncorrelated configurations. Here, we introduce a new
class of moves based on nonequilibrium dynamics: candidate configurations are
generated through a finite-time process in which a system is actively driven
out of equilibrium, and accepted with criteria that preserve the equilibrium
distribution. The acceptance rule is similar to the Metropolis acceptance
probability, but related to the nonequilibrium work rather than the
instantaneous energy difference. Our method is applicable to sampling from both
a single thermodynamic state or a mixture of thermodynamic states, and allows
both coordinates and thermodynamic parameters to be driven in nonequilibrium
proposals. While generating finite-time switching trajectories incurs an
additional cost, driving some degrees of freedom while allowing others to
evolve naturally can lead to large enhancements in acceptance probabilities,
greatly reducing structural correlation times. Using nonequilibrium driven
processes vastly expands the repertoire of useful Monte Carlo proposals in
simulations of dense solvated systems
A^2-Net: Molecular Structure Estimation from Cryo-EM Density Volumes
Constructing of molecular structural models from Cryo-Electron Microscopy
(Cryo-EM) density volumes is the critical last step of structure determination
by Cryo-EM technologies. Methods have evolved from manual construction by
structural biologists to perform 6D translation-rotation searching, which is
extremely compute-intensive. In this paper, we propose a learning-based method
and formulate this problem as a vision-inspired 3D detection and pose
estimation task. We develop a deep learning framework for amino acid
determination in a 3D Cryo-EM density volume. We also design a sequence-guided
Monte Carlo Tree Search (MCTS) to thread over the candidate amino acids to form
the molecular structure. This framework achieves 91% coverage on our newly
proposed dataset and takes only a few minutes for a typical structure with a
thousand amino acids. Our method is hundreds of times faster and several times
more accurate than existing automated solutions without any human intervention.Comment: 8 pages, 5 figures, 4 table
Efficient and effective solution procedures for order acceptance and capacity planning.
This paper investigates dynamic order acceptance and capacity planning under limited regular and non-regular resources. Our goal is to maximize the profits of the accepted projects within a finite planning horizon. The way in which the projects are planned affects their payout time and, as a consequence, there investment revenues as well as the available capacity for future arriving projects. In general, project proposals arise dynamically to the organization, and their actual characteristics are only revealed upon arrival. Dynamic solution approaches are therefore most likely to obtain good results. Although the problem can theoretically be solved to optimality as a stochastic dynamic program, real-life problem instances are too difficult to be solved exactly within areas on able amount of time. Efficient and effective heuristics are thus required that supply a response without delay.For this reason, this paper considers both 'single-pass' algorithms as well as approximate dynamic-programming algorithms and investigates their suitability to solve the problem. Simulation experiments compare the performance of our procedures to a firrst-come, first-served policy that is commonly used in practice.Approximate dynamic programming; Capacity planning; multi-project; Order acceptance; Simulation;
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