4,309 research outputs found
Optimal experimental design for mathematical models of haematopoiesis.
The haematopoietic system has a highly regulated and complex structure in which cells are organized to successfully create and maintain new blood cells. It is known that feedback regulation is crucial to tightly control this system, but the specific mechanisms by which control is exerted are not completely understood. In this work, we aim to uncover the underlying mechanisms in haematopoiesis by conducting perturbation experiments, where animal subjects are exposed to an external agent in order to observe the system response and evolution. We have developed a novel Bayesian hierarchical framework for optimal design of perturbation experiments and proper analysis of the data collected. We use a deterministic model that accounts for feedback and feedforward regulation on cell division rates and self-renewal probabilities. A significant obstacle is that the experimental data are not longitudinal, rather each data point corresponds to a different animal. We overcome this difficulty by modelling the unobserved cellular levels as latent variables. We then use principles of Bayesian experimental design to optimally distribute time points at which the haematopoietic cells are quantified. We evaluate our approach using synthetic and real experimental data and show that an optimal design can lead to better estimates of model parameters
Fast Bayesian Optimal Experimental Design for Seismic Source Inversion
We develop a fast method for optimally designing experiments in the context
of statistical seismic source inversion. In particular, we efficiently compute
the optimal number and locations of the receivers or seismographs. The seismic
source is modeled by a point moment tensor multiplied by a time-dependent
function. The parameters include the source location, moment tensor components,
and start time and frequency in the time function. The forward problem is
modeled by elastodynamic wave equations. We show that the Hessian of the cost
functional, which is usually defined as the square of the weighted L2 norm of
the difference between the experimental data and the simulated data, is
proportional to the measurement time and the number of receivers. Consequently,
the posterior distribution of the parameters, in a Bayesian setting,
concentrates around the "true" parameters, and we can employ Laplace
approximation and speed up the estimation of the expected Kullback-Leibler
divergence (expected information gain), the optimality criterion in the
experimental design procedure. Since the source parameters span several
magnitudes, we use a scaling matrix for efficient control of the condition
number of the original Hessian matrix. We use a second-order accurate finite
difference method to compute the Hessian matrix and either sparse quadrature or
Monte Carlo sampling to carry out numerical integration. We demonstrate the
efficiency, accuracy, and applicability of our method on a two-dimensional
seismic source inversion problem
Optimal Experimental Design with R
Abstracts not available for BookReview
Variational Bayesian Optimal Experimental Design
Bayesian optimal experimental design (BOED) is a principled framework for
making efficient use of limited experimental resources. Unfortunately, its
applicability is hampered by the difficulty of obtaining accurate estimates of
the expected information gain (EIG) of an experiment. To address this, we
introduce several classes of fast EIG estimators by building on ideas from
amortized variational inference. We show theoretically and empirically that
these estimators can provide significant gains in speed and accuracy over
previous approaches. We further demonstrate the practicality of our approach on
a number of end-to-end experiments.Comment: Published as a conference paper at the Thirty-third Conference on
Neural Information Processing Systems, Vancouver 2019.
https://papers.nips.cc/paper/9553-variational-bayesian-optimal-experimental-design.pd
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