39,726 research outputs found
A Statistical Inference Comparison for Measurement Estimation Using Stochastic Simulation Techniques
Auxiliary Likelihood-Based Approximate Bayesian Computation in State Space Models
A computationally simple approach to inference in state space models is
proposed, using approximate Bayesian computation (ABC). ABC avoids evaluation
of an intractable likelihood by matching summary statistics for the observed
data with statistics computed from data simulated from the true process, based
on parameter draws from the prior. Draws that produce a 'match' between
observed and simulated summaries are retained, and used to estimate the
inaccessible posterior. With no reduction to a low-dimensional set of
sufficient statistics being possible in the state space setting, we define the
summaries as the maximum of an auxiliary likelihood function, and thereby
exploit the asymptotic sufficiency of this estimator for the auxiliary
parameter vector. We derive conditions under which this approach - including a
computationally efficient version based on the auxiliary score - achieves
Bayesian consistency. To reduce the well-documented inaccuracy of ABC in
multi-parameter settings, we propose the separate treatment of each parameter
dimension using an integrated likelihood technique. Three stochastic volatility
models for which exact Bayesian inference is either computationally
challenging, or infeasible, are used for illustration. We demonstrate that our
approach compares favorably against an extensive set of approximate and exact
comparators. An empirical illustration completes the paper.Comment: This paper is forthcoming at the Journal of Computational and
Graphical Statistics. It also supersedes the earlier arXiv paper "Approximate
Bayesian Computation in State Space Models" (arXiv:1409.8363
Bayesian inference of biochemical kinetic parameters using the linear noise approximation
Background
Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models requires the deveopment of effective statistical methods to calibrate such models against available data. Given the prevalence of stochasticity and noise in biochemical systems inference for stochastic models is of special interest. In this paper we present a simple and computationally efficient algorithm for the estimation of biochemical kinetic parameters from gene reporter data.
Results
We use the linear noise approximation to model biochemical reactions through a stochastic dynamic model which essentially approximates a diffusion model by an ordinary differential equation model with an appropriately defined noise process. An explicit formula for the likelihood function can be derived allowing for computationally efficient parameter estimation. The proposed algorithm is embedded in a Bayesian framework and inference is performed using Markov chain Monte Carlo.
Conclusion
The major advantage of the method is that in contrast to the more established diffusion approximation based methods the computationally costly methods of data augmentation are not necessary. Our approach also allows for unobserved variables and measurement error. The application of the method to both simulated and experimental data shows that the proposed methodology provides a useful alternative to diffusion approximation based methods
Multi-scale uncertainty quantification in geostatistical seismic inversion
Geostatistical seismic inversion is commonly used to infer the spatial
distribution of the subsurface petro-elastic properties by perturbing the model
parameter space through iterative stochastic sequential
simulations/co-simulations. The spatial uncertainty of the inferred
petro-elastic properties is represented with the updated a posteriori variance
from an ensemble of the simulated realizations. Within this setting, the
large-scale geological (metaparameters) used to generate the petro-elastic
realizations, such as the spatial correlation model and the global a priori
distribution of the properties of interest, are assumed to be known and
stationary for the entire inversion domain. This assumption leads to
underestimation of the uncertainty associated with the inverted models. We
propose a practical framework to quantify uncertainty of the large-scale
geological parameters in seismic inversion. The framework couples
geostatistical seismic inversion with a stochastic adaptive sampling and
Bayesian inference of the metaparameters to provide a more accurate and
realistic prediction of uncertainty not restricted by heavy assumptions on
large-scale geological parameters. The proposed framework is illustrated with
both synthetic and real case studies. The results show the ability retrieve
more reliable acoustic impedance models with a more adequate uncertainty spread
when compared with conventional geostatistical seismic inversion techniques.
The proposed approach separately account for geological uncertainty at
large-scale (metaparameters) and local scale (trace-by-trace inversion)
Statistical Inference for Partially Observed Markov Processes via the R Package pomp
Partially observed Markov process (POMP) models, also known as hidden Markov
models or state space models, are ubiquitous tools for time series analysis.
The R package pomp provides a very flexible framework for Monte Carlo
statistical investigations using nonlinear, non-Gaussian POMP models. A range
of modern statistical methods for POMP models have been implemented in this
framework including sequential Monte Carlo, iterated filtering, particle Markov
chain Monte Carlo, approximate Bayesian computation, maximum synthetic
likelihood estimation, nonlinear forecasting, and trajectory matching. In this
paper, we demonstrate the application of these methodologies using some simple
toy problems. We also illustrate the specification of more complex POMP models,
using a nonlinear epidemiological model with a discrete population,
seasonality, and extra-demographic stochasticity. We discuss the specification
of user-defined models and the development of additional methods within the
programming environment provided by pomp.Comment: In press at the Journal of Statistical Software. A version of this
paper is provided at the pomp package website: http://kingaa.github.io/pom
Uncertainty Updating in the Description of Coupled Heat and Moisture Transport in Heterogeneous Materials
To assess the durability of structures, heat and moisture transport need to
be analyzed. To provide a reliable estimation of heat and moisture distribution
in a certain structure, one needs to include all available information about
the loading conditions and material parameters. Moreover, the information
should be accompanied by a corresponding evaluation of its credibility. Here,
the Bayesian inference is applied to combine different sources of information,
so as to provide a more accurate estimation of heat and moisture fields [1].
The procedure is demonstrated on the probabilistic description of heterogeneous
material where the uncertainties consist of a particular value of individual
material characteristic and spatial fluctuations. As for the heat and moisture
transfer, it is modelled in coupled setting [2]
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