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Sanmitra Ghosh Supervisor: Dr Srinandan Dasmahapatra & Dr Koushik Maharatna Electronics and Software Systems, School of Electronics & Computer Science University of Southampton 1

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Outline Introduction Black Box models (System Identification) Modelling plant responses as ODEs Calibration of Models (Parameter Estimation in ODE using ABC-SMC) ABC-SMC using Gaussian processes Future work References 2

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Introduction 3 Experiments Models ???

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Introduction 4 Typical electrical responses Light Ozone (sprayed for 2 minutes)

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Black Box models 5 Generalized least-square estimator {A,B,F,C,D} are rational polynomials Linear estimator

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Black Box models 6 Nonlinear Hammerstein-Wiener model structure System output Cost function This cost function is minimized using optimization

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Black Box models

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Modelling responses as ODEs 8 Proposed model: time Voltage

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Modelling responses as ODEs 9

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ABC 10 Approximate Bayesian Computation Prior Likelihood posterior

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ABC 11

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ABC 12 ABC-Sequential Monte Carlo (Toni et al, 1999) Limitation: extremely slow due to large number of explicit ODE solving for generating simulated data

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ABC 13 Data Gaussian Process The Gaussian process trick

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ABC 14

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ABC 15 Predator-Prayab generated2.10 estimated (ABC-SMC)2.102.07 estimated (ABC-SMC-GPDist)2.102.06 Fitzhugh-Nagumoabc generated0.20 3.00 estimated (ABC-SMC)0.190.202.97 estimated (ABC-SMC- GPDist) 0.210.222.62 Mackay-Glassβnγτ generated2.009.651.002.00 estimated (ABC-SMC)2.079.421.032.01 estimated (ABC-SMC- GPDist) 2.049.161.002.04

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Future work 16 Model needs to be extended to capture the variability seen among different electrical responses. More models are required to represent other stimuli.

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References 17 1. J K Pritchard, M T Seielstad, a Perez-Lezaun, and M W Feldman. Population growth of human Y chromosomes: a study of Y chromosome microsatellites. Mol. Biol. Evol., 16(12):1791–8, December 1999. 2. T. Toni, D. Welch, N. Strelkowa, a. Ipsen, and M. P.H Stumpf. Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J. R. Soc. Interface, 6(31):187–202, February 2009.

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