8,940 research outputs found
Perfect Sampling of the Master Equation for Gene Regulatory Networks
We present a Perfect Sampling algorithm that can be applied to the Master
Equation of Gene Regulatory Networks (GRNs). The method recasts Gillespie's
Stochastic Simulation Algorithm (SSA) in the light of Markov Chain Monte Carlo
methods and combines it with the Dominated Coupling From The Past (DCFTP)
algorithm to provide guaranteed sampling from the stationary distribution. We
show how the DCFTP-SSA can be generically applied to genetic networks with
feedback formed by the interconnection of linear enzymatic reactions and
nonlinear Monod- and Hill-type elements. We establish rigorous bounds on the
error and convergence of the DCFTP-SSA, as compared to the standard SSA,
through a set of increasingly complex examples. Once the building blocks for
GRNs have been introduced, the algorithm is applied to study properly averaged
dynamic properties of two experimentally relevant genetic networks: the toggle
switch, a two-dimensional bistable system, and the repressilator, a
six-dimensional genetic oscillator.Comment: Minor rewriting; final version to be published in Biophysical Journa
Interest rate models with Markov chains
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Efficient cyclic reduction for QBDs with rank structured blocks
We provide effective algorithms for solving block tridiagonal block Toeplitz
systems with quasiseparable blocks, as well as quadratic matrix
equations with quasiseparable coefficients, based on cyclic
reduction and on the technology of rank-structured matrices. The algorithms
rely on the exponential decay of the singular values of the off-diagonal
submatrices generated by cyclic reduction. We provide a formal proof of this
decay in the Markovian framework. The results of the numerical experiments that
we report confirm a significant speed up over the general algorithms, already
starting with the moderately small size
Bayesian analysis of DSGE models
This paper reviews Bayesian methods that have been developed in recent years to estimate and evaluate dynamic stochastic general equilibrium (DSGE) models. We consider the estimation of linearized DSGE models, the evaluation of models based on Bayesian model checking, posterior odds comparisons, and comparisons to vector autoregressions, as well as the nonlinear estimation based on a second-order accurate model solution. These methods are applied to data generated from correctly specified and misspecified linearized DSGE models, and a DSGE model that was solved with a second-order perturbation method.Macroeconomics ; Vector autoregression
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