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Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 ABC SMC for parameter estimation and model selection with applications in systems biology Tina Toni Department of Biological Engineering, Massachusetts Institute of

  1. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 ABC SMC for parameter estimation and model selection with applications in systems biology Tina Toni Department of Biological Engineering, Massachusetts Institute of Technology, USA & Theoretical Systems Biology Group, Imperial College London, UK ABC in London, 05/05/2011 Tina Toni ABC in systems biology 05/05/2011 1 / 25

  2. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Motivation Complex biological systems Models often ODE or stochastic master equations High dimensional parameter space Time course, non-equidistant, missing data Interested in Characterization of distributions over parameters rather than point estimates. What dynamic behaviour can reproduce data? Which models represent suitable hypothesis about the system? Tina Toni ABC in systems biology 05/05/2011 2 / 25

  3. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Outline Parameter estimation 1 ABC basics ABC SMC Application: Modeling bacterial stress response Model selection 2 ABC SMC for model selection Application: Epo signaling pathway Application: Phosphorylation dynamics Tina Toni ABC in systems biology 05/05/2011 3 / 25

  4. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC basics Approximate Bayesian Computation basics 1 Sample θ c from P ( θ ). 2 Simulate a data set D c from the model with θ c . 3 If dist ( D , D c ) ≤ ǫ , accept θ c , otherwise reject. 4 Return to 1 . x x x x time Prior Posterior P ( θ ) P ( θ | D )

  5. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC basics Approximate Bayesian Computation basics 1 Sample θ c from P ( θ ). 2 Simulate a data set D c from the model with θ c . 3 If dist ( D , D c ) ≤ ǫ , accept θ c , otherwise reject. 4 Return to 1 . x x x x time Prior Posterior P ( θ ) P ( θ | D )

  6. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC basics Approximate Bayesian Computation basics 1 Sample θ c from P ( θ ). 2 Simulate a data set D c from the model with θ c . 3 If dist ( D , D c ) ≤ ǫ , accept θ c , otherwise reject. 4 Return to 1 . x x x x time Prior Posterior P ( θ ) P ( θ | D )

  7. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC basics Approximate Bayesian Computation basics 1 Sample θ c from P ( θ ). 2 Simulate a data set D c from the model with θ c . 3 If dist ( D , D c ) ≤ ǫ , accept θ c , otherwise reject. 4 Return to 1 . x x x x time Prior Posterior P ( θ ) P ( θ | D )

  8. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC basics Approximate Bayesian Computation basics 1 Sample θ c from P ( θ ). 2 Simulate a data set D c from the model with θ c . 3 If dist ( D , D c ) ≤ ǫ , accept θ c , otherwise reject. 4 Return to 1 . x x x x time Prior Posterior P ( θ ) P ( θ | D )

  9. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC basics Approximate Bayesian Computation basics 1 Sample θ c from P ( θ ). 2 Simulate a data set D c from the model with θ c . 3 If dist ( D , D c ) ≤ ǫ , accept θ c , otherwise reject. 4 Return to 1 . x x x x time Prior Posterior P ( θ ) P ( θ | D ) Tina Toni ABC in systems biology 05/05/2011 4 / 25

  10. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC basics Approximate Bayesian Computation basics 1 Sample θ c from P ( θ ). 2 Simulate a data set D c from the model with θ c . 3 If dist ( D , D c ) ≤ ǫ , accept θ c , otherwise reject. 4 Return to 1 . x x x x time Prior Posterior P ( θ ) P ( θ | D ) Tina Toni ABC in systems biology 05/05/2011 4 / 25

  11. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC basics Approximate Bayesian Computation basics 1 Sample θ c from P ( θ ). 2 Simulate a data set D c from the model with θ c . 3 If dist ( D , D c ) ≤ ǫ , accept θ c , otherwise reject. 4 Return to 1 . x x x x time Prior Posterior P ( θ ) P ( θ | D )

  12. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC basics Approximate Bayesian Computation basics 1 Sample θ c from P ( θ ). 2 Simulate a data set D c from the model with θ c . 3 If dist ( D , D c ) ≤ ǫ , accept θ c , otherwise reject. 4 Return to 1 . x x x x time Prior Posterior P ( θ ) P ( θ | D )

  13. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC basics Approximate Bayesian Computation basics 1 Sample θ c from P ( θ ). 2 Simulate a data set D c from the model with θ c . 3 If dist ( D , D c ) ≤ ǫ , accept θ c , otherwise reject. 4 Return to 1 . x x x x time P ( θ | dist ( D , D c ) ≤ ǫ ) Prior Posterior P ( θ ) P ( θ | D )

  14. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC basics Approximate Bayesian Computation basics 1 Sample θ c from P ( θ ). 2 Simulate a data set D c from the model with θ c . 3 If dist ( D , D c ) ≤ ǫ , accept θ c , otherwise reject. 4 Return to 1 . x x x x time P ( θ | dist ( D , D c ) ≤ ǫ ) Prior Posterior P ( θ ) P ( θ | D )

  15. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC SMC ABC SMC (Sequential Monte Carlo) Prior Posterior (Sisson et al., 2007, PNAS) Tina Toni ABC in systems biology 05/05/2011 5 / 25

  16. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC SMC ABC SMC (Sequential Monte Carlo) Prior Intermediate Distributions Posterior (Sisson et al., 2007, PNAS) Tina Toni ABC in systems biology 05/05/2011 5 / 25

  17. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC SMC ABC SMC (Sequential Monte Carlo) . . . ǫ 1 ǫ 2 ǫ T Prior Intermediate Distributions Posterior (Sisson et al., 2007, PNAS) Tina Toni ABC in systems biology 05/05/2011 5 / 25

  18. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC SMC ABC SMC (Sequential Monte Carlo) . . . ǫ 1 ǫ 2 ǫ T Prior Intermediate Distributions Posterior (Sisson et al., 2007, PNAS) Tina Toni ABC in systems biology 05/05/2011 5 / 25

  19. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC SMC ABC SMC (Sequential Monte Carlo) Population 1 . . . ǫ 1 ǫ 2 ǫ T Prior Intermediate Distributions Posterior (Sisson et al., 2007, PNAS) Tina Toni ABC in systems biology 05/05/2011 5 / 25

  20. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC SMC ABC SMC (Sequential Monte Carlo) Population 1 . . . ǫ 1 ǫ 2 ǫ T Prior Intermediate Distributions Posterior (Sisson et al., 2007, PNAS) Tina Toni ABC in systems biology 05/05/2011 5 / 25

  21. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC SMC ABC SMC (Sequential Monte Carlo) Population 1 . . . ǫ 1 ǫ 2 ǫ T Prior Intermediate Distributions Posterior (Sisson et al., 2007, PNAS) Tina Toni ABC in systems biology 05/05/2011 5 / 25

  22. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC SMC ABC SMC (Sequential Monte Carlo) Population 1 Population 2 . . . ǫ 1 ǫ 2 ǫ T Prior Intermediate Distributions Posterior (Sisson et al., 2007, PNAS) Tina Toni ABC in systems biology 05/05/2011 5 / 25

  23. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC SMC ABC SMC (Sequential Monte Carlo) Population 1 Population 2 Population T . . . ǫ 1 ǫ 2 ǫ T Prior Intermediate Distributions Posterior (Sisson et al., 2007, PNAS) Tina Toni ABC in systems biology 05/05/2011 5 / 25

  24. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC SMC ABC SMC (Sequential Monte Carlo) Population 1 Population 2 Population T . . . ǫ 1 ǫ 2 ǫ T Prior Intermediate Distributions Posterior (Sisson et al., 2007, PNAS) Tina Toni ABC in systems biology 05/05/2011 5 / 25

  25. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation ABC SMC Weights π t ( θ t ) w t ( θ t ) = η t ( θ t ) � η t ( θ t ) = 1 ( π ( θ t ) > 0) 1 ( dist < ǫ t ) π t − 1 ( θ t − 1 ) K t ( θ t | θ t − 1 ) d θ t − 1 π ( θ ( i ) t ) w ( i ) = t � N j =1 w ( j ) t − 1 K t ( θ ( i ) t | θ ( j ) t − 1 ) (Toni et al. , J. R. Soc. Interface, 2009) Tina Toni ABC in systems biology 05/05/2011 6 / 25

  26. Nature Precedings : doi:10.1038/npre.2011.5964.1 : Posted 13 May 2011 Parameter estimation Application: Modeling bacterial stress response Application: Modeling phage shock protein response in Escherichia coli Signal Phage damages the membrane of bacteria (we call this stress). Response Reduced motility Anaerobic respiration Start membrane repair mechanisms etc. Tina Toni ABC in systems biology 05/05/2011 7 / 25

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