51,870 research outputs found
Split Sampling: Expectations, Normalisation and Rare Events
In this paper we develop a methodology that we call split sampling methods to
estimate high dimensional expectations and rare event probabilities. Split
sampling uses an auxiliary variable MCMC simulation and expresses the
expectation of interest as an integrated set of rare event probabilities. We
derive our estimator from a Rao-Blackwellised estimate of a marginal auxiliary
variable distribution. We illustrate our method with two applications. First,
we compute a shortest network path rare event probability and compare our
method to estimation to a cross entropy approach. Then, we compute a
normalisation constant of a high dimensional mixture of Gaussians and compare
our estimate to one based on nested sampling. We discuss the relationship
between our method and other alternatives such as the product of conditional
probability estimator and importance sampling. The methods developed here are
available in the R package: SplitSampling
The role of learning on industrial simulation design and analysis
The capability of modeling real-world system operations has turned simulation into an indispensable problemsolving methodology for business system design and analysis. Today, simulation supports decisions ranging
from sourcing to operations to finance, starting at the strategic level and proceeding towards tactical and
operational levels of decision-making. In such a dynamic setting, the practice of simulation goes beyond
being a static problem-solving exercise and requires integration with learning. This article discusses the role
of learning in simulation design and analysis motivated by the needs of industrial problems and describes
how selected tools of statistical learning can be utilized for this purpose
Semiconductor manufacturing simulation design and analysis with limited data
This paper discusses simulation design and analysis for Silicon Carbide (SiC) manufacturing operations management at New York Power Electronics Manufacturing Consortium (PEMC) facility. Prior work has addressed the development of manufacturing system simulation as the decision support to solve the strategic equipment portfolio selection problem for the SiC fab design [1]. As we move into the phase of collecting data from the equipment purchased for the PEMC facility, we discuss how to redesign our manufacturing simulations and analyze their outputs to overcome the challenges that naturally arise in the presence of limited fab data. We conclude with insights on how an approach aimed to reflect learning from data can enable our discrete-event stochastic simulation to accurately estimate the performance measures for SiC manufacturing at the PEMC facility
Connecting the Dots: Towards Continuous Time Hamiltonian Monte Carlo
Continuous time Hamiltonian Monte Carlo is introduced, as a powerful
alternative to Markov chain Monte Carlo methods for continuous target
distributions. The method is constructed in two steps: First Hamiltonian
dynamics are chosen as the deterministic dynamics in a continuous time
piecewise deterministic Markov process. Under very mild restrictions, such a
process will have the desired target distribution as an invariant distribution.
Secondly, the numerical implementation of such processes, based on adaptive
numerical integration of second order ordinary differential equations is
considered. The numerical implementation yields an approximate, yet highly
robust algorithm that, unlike conventional Hamiltonian Monte Carlo, enables the
exploitation of the complete Hamiltonian trajectories (hence the title). The
proposed algorithm may yield large speedups and improvements in stability
relative to relevant benchmarks, while incurring numerical errors that are
negligible relative to the overall Monte Carlo errors
Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art
Stochasticity is a key characteristic of intracellular processes such as gene
regulation and chemical signalling. Therefore, characterising stochastic
effects in biochemical systems is essential to understand the complex dynamics
of living things. Mathematical idealisations of biochemically reacting systems
must be able to capture stochastic phenomena. While robust theory exists to
describe such stochastic models, the computational challenges in exploring
these models can be a significant burden in practice since realistic models are
analytically intractable. Determining the expected behaviour and variability of
a stochastic biochemical reaction network requires many probabilistic
simulations of its evolution. Using a biochemical reaction network model to
assist in the interpretation of time course data from a biological experiment
is an even greater challenge due to the intractability of the likelihood
function for determining observation probabilities. These computational
challenges have been subjects of active research for over four decades. In this
review, we present an accessible discussion of the major historical
developments and state-of-the-art computational techniques relevant to
simulation and inference problems for stochastic biochemical reaction network
models. Detailed algorithms for particularly important methods are described
and complemented with MATLAB implementations. As a result, this review provides
a practical and accessible introduction to computational methods for stochastic
models within the life sciences community
Efficient data augmentation for fitting stochastic epidemic models to prevalence data
Stochastic epidemic models describe the dynamics of an epidemic as a disease
spreads through a population. Typically, only a fraction of cases are observed
at a set of discrete times. The absence of complete information about the time
evolution of an epidemic gives rise to a complicated latent variable problem in
which the state space size of the epidemic grows large as the population size
increases. This makes analytically integrating over the missing data infeasible
for populations of even moderate size. We present a data augmentation Markov
chain Monte Carlo (MCMC) framework for Bayesian estimation of stochastic
epidemic model parameters, in which measurements are augmented with
subject-level disease histories. In our MCMC algorithm, we propose each new
subject-level path, conditional on the data, using a time-inhomogeneous
continuous-time Markov process with rates determined by the infection histories
of other individuals. The method is general, and may be applied, with minimal
modifications, to a broad class of stochastic epidemic models. We present our
algorithm in the context of multiple stochastic epidemic models in which the
data are binomially sampled prevalence counts, and apply our method to data
from an outbreak of influenza in a British boarding school
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