20,168 research outputs found
Adaptive System Identification using Markov Chain Monte Carlo
One of the major problems in adaptive filtering is the problem of system
identification. It has been studied extensively due to its immense practical
importance in a variety of fields. The underlying goal is to identify the
impulse response of an unknown system. This is accomplished by placing a known
system in parallel and feeding both systems with the same input. Due to initial
disparity in their impulse responses, an error is generated between their
outputs. This error is set to tune the impulse response of known system in a
way that every change in impulse response reduces the magnitude of prospective
error. This process is repeated until the error becomes negligible and the
responses of both systems match. To specifically minimize the error, numerous
adaptive algorithms are available. They are noteworthy either for their low
computational complexity or high convergence speed. Recently, a method, known
as Markov Chain Monte Carlo (MCMC), has gained much attention due to its
remarkably low computational complexity. But despite this colossal advantage,
properties of MCMC method have not been investigated for adaptive system
identification problem. This article bridges this gap by providing a complete
treatment of MCMC method in the aforementioned context
A multi-resolution, non-parametric, Bayesian framework for identification of spatially-varying model parameters
This paper proposes a hierarchical, multi-resolution framework for the
identification of model parameters and their spatially variability from noisy
measurements of the response or output. Such parameters are frequently
encountered in PDE-based models and correspond to quantities such as density or
pressure fields, elasto-plastic moduli and internal variables in solid
mechanics, conductivity fields in heat diffusion problems, permeability fields
in fluid flow through porous media etc. The proposed model has all the
advantages of traditional Bayesian formulations such as the ability to produce
measures of confidence for the inferences made and providing not only
predictive estimates but also quantitative measures of the predictive
uncertainty. In contrast to existing approaches it utilizes a parsimonious,
non-parametric formulation that favors sparse representations and whose
complexity can be determined from the data. The proposed framework in
non-intrusive and makes use of a sequence of forward solvers operating at
various resolutions. As a result, inexpensive, coarse solvers are used to
identify the most salient features of the unknown field(s) which are
subsequently enriched by invoking solvers operating at finer resolutions. This
leads to significant computational savings particularly in problems involving
computationally demanding forward models but also improvements in accuracy. It
is based on a novel, adaptive scheme based on Sequential Monte Carlo sampling
which is embarrassingly parallelizable and circumvents issues with slow mixing
encountered in Markov Chain Monte Carlo schemes
Model Selection and Adaptive Markov chain Monte Carlo for Bayesian Cointegrated VAR model
This paper develops a matrix-variate adaptive Markov chain Monte Carlo (MCMC)
methodology for Bayesian Cointegrated Vector Auto Regressions (CVAR). We
replace the popular approach to sampling Bayesian CVAR models, involving griddy
Gibbs, with an automated efficient alternative, based on the Adaptive
Metropolis algorithm of Roberts and Rosenthal, (2009). Developing the adaptive
MCMC framework for Bayesian CVAR models allows for efficient estimation of
posterior parameters in significantly higher dimensional CVAR series than
previously possible with existing griddy Gibbs samplers. For a n-dimensional
CVAR series, the matrix-variate posterior is in dimension , with
significant correlation present between the blocks of matrix random variables.
We also treat the rank of the CVAR model as a random variable and perform joint
inference on the rank and model parameters. This is achieved with a Bayesian
posterior distribution defined over both the rank and the CVAR model
parameters, and inference is made via Bayes Factor analysis of rank.
Practically the adaptive sampler also aids in the development of automated
Bayesian cointegration models for algorithmic trading systems considering
instruments made up of several assets, such as currency baskets. Previously the
literature on financial applications of CVAR trading models typically only
considers pairs trading (n=2) due to the computational cost of the griddy
Gibbs. We are able to extend under our adaptive framework to and
demonstrate an example with n = 10, resulting in a posterior distribution with
parameters up to dimension 310. By also considering the rank as a random
quantity we can ensure our resulting trading models are able to adjust to
potentially time varying market conditions in a coherent statistical framework.Comment: to appear journal Bayesian Analysi
Global parameter identification of stochastic reaction networks from single trajectories
We consider the problem of inferring the unknown parameters of a stochastic
biochemical network model from a single measured time-course of the
concentration of some of the involved species. Such measurements are available,
e.g., from live-cell fluorescence microscopy in image-based systems biology. In
addition, fluctuation time-courses from, e.g., fluorescence correlation
spectroscopy provide additional information about the system dynamics that can
be used to more robustly infer parameters than when considering only mean
concentrations. Estimating model parameters from a single experimental
trajectory enables single-cell measurements and quantification of cell--cell
variability. We propose a novel combination of an adaptive Monte Carlo sampler,
called Gaussian Adaptation, and efficient exact stochastic simulation
algorithms that allows parameter identification from single stochastic
trajectories. We benchmark the proposed method on a linear and a non-linear
reaction network at steady state and during transient phases. In addition, we
demonstrate that the present method also provides an ellipsoidal volume
estimate of the viable part of parameter space and is able to estimate the
physical volume of the compartment in which the observed reactions take place.Comment: Article in print as a book chapter in Springer's "Advances in Systems
Biology
Improving Simulation Efficiency of MCMC for Inverse Modeling of Hydrologic Systems with a Kalman-Inspired Proposal Distribution
Bayesian analysis is widely used in science and engineering for real-time
forecasting, decision making, and to help unravel the processes that explain
the observed data. These data are some deterministic and/or stochastic
transformations of the underlying parameters. A key task is then to summarize
the posterior distribution of these parameters. When models become too
difficult to analyze analytically, Monte Carlo methods can be used to
approximate the target distribution. Of these, Markov chain Monte Carlo (MCMC)
methods are particularly powerful. Such methods generate a random walk through
the parameter space and, under strict conditions of reversibility and
ergodicity, will successively visit solutions with frequency proportional to
the underlying target density. This requires a proposal distribution that
generates candidate solutions starting from an arbitrary initial state. The
speed of the sampled chains converging to the target distribution deteriorates
rapidly, however, with increasing parameter dimensionality. In this paper, we
introduce a new proposal distribution that enhances significantly the
efficiency of MCMC simulation for highly parameterized models. This proposal
distribution exploits the cross-covariance of model parameters, measurements
and model outputs, and generates candidate states much alike the analysis step
in the Kalman filter. We embed the Kalman-inspired proposal distribution in the
DREAM algorithm during burn-in, and present several numerical experiments with
complex, high-dimensional or multi-modal target distributions. Results
demonstrate that this new proposal distribution can greatly improve simulation
efficiency of MCMC. Specifically, we observe a speed-up on the order of 10-30
times for groundwater models with more than one-hundred parameters
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