2 research outputs found
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A Bayesian framework for inverse problems for quantitative biology
In this thesis, we present a Bayesian framework to solve inverse problems in the context of quantitative biology. We present a novel combination of the Bayesian approach to inverse problems, suitable for infinite-dimensional problems, with a parallel, scalable Markov Chain Monte Carlo algorithm to approximate the posterior distribution. Both the Bayesian framework and the parallelised MCMC were already known but they were not used in this context in the past. Our approach puts together existing results in order to provide a tool to easily solve inverse problems. We focus on models given by partial differential equations. Our methodology differs from previous results in its approach: it aims to be as transparent and independent of the model as possible, in order to make it flexible and applicable to a wide range of problems emerging from experimental and physical sciences. We illustrate our methodology with three of such applications in the areas of theoretical biology and cell biology.
The first application deals with parameter and function identification within a Turing pattern formation model. To the best of our knowledge, our results are the first attempt to use Bayesian techniques to study the inverse problem for Turing patterns. In this example, we show how our implementation can deal with both finite- and infinite-dimensional parameters in the context of inverse problems for partial differential equations.
The second example studies the spatio-temporal dynamics in cell biology. The study provides an example that seeks to best-fit a mathematical model to experimental data finding in the process optimal parameters and credible regimes and regions. We present a new derivation of the model, that corrects the short-comings of previous approaches. We provide all the details from techniques for data acquisition to the parameter identification, and we show in particular how the mathematical model can be used as a proxy to estimate parameters that are difficult to measure in the experiments, providing an novel alternative to more indirect estimates that also require more complex experiments.
Finally, our third example illustrates the flexibility of our implementation of the methodology by using it to study traction force microscopy (TFM) data with a solver implemented independent of the Bayesian approach for parameter identification. We limit ourselves to the classical TFM setting, that we model as a two-dimensional linear elasticity problem. The results and methods generalise to more complex settings where quantitative modelling driven by biological observations is a requirement
GPU accelerated novel particle filtering method
In this paper, a graphics processor unit (GPU) accelerated particle filtering algorithm is presented with an introduction to a novel resampling technique. The aim remains in the mitigation of particle impoverishment as well as computational burden, problems which are commonly associated with classical (systematic) resampled particle filtering. The proposed algorithm employs a priori-space dependent distribution in addition to the likelihood, and hence is christened as dual distribution dependent (D3) resampling method. Simulation results exhibit lesser values for root mean square error (RMSE) in comparison to that for systematic resampling. D3 resampling is shown to improve particle diversity after each iteration, thereby affecting the overall quality of estimation. However, computational burden is significantly increased owing to few excessive computations within the newly formulated resampling framework. With a view to obtaining parallel speedup we introduce a CUDA version of the proposed method for necessary acceleration by GPU. The GPU programming model is detailed in the context of this paper. Implementation issues are discussed along with illustration of empirical computational efficiency, as obtained by executing the CUDA code on Quadro 2000 GPU. The GPU enabled code has a speedup of 3 and 4 over the sequential executions of systematic and D3 resampling methods respectively. Performance both in terms of RMSE and running time have been elaborated with respect to different selections for threads per block towards effective implementations. It is in this context that, we further introduce a cost to performance metric (CPM) for assessing the algorithmic efficiency of the estimator, involving both quality of estimation and running time as comparative factors, transformed into a unified parameter for assessment. CPM values for estimators obtained from all such different choices for threads per block have been determined and a final value for the chosen parameter is resolved for generation of a holistic effective estimator