References
- Andrieu, C., Doucet, A., and Holenstein, R. (2010), “Particle Markov Chain Monte Carlo Methods,” Journal of the Royal Statistical Society, Series B, 72, 269–342.
- Berger, J. (2006), “The Case for Objective Bayesian Analysis,” Bayesian Analysis, 1, 385–402.
- Beskos, A., Papaspiliopoulos, O., and Roberts, G.O. (2006a), “Retrospective Exact Simulation of Diffusion Sample Paths With Applications,” Bernoulli, 12, 1077–1098.
- Beskos, A., Papaspiliopoulos, O., Roberts, G.O., and Fearnhead, P. (2006b), “Exact and Computationally Efficient Likelihood-Based Estimation for Discretely Observed Diffusion Processes” (with discussion), Journal of the Royal Statistical, Series B, 68, 333–382.
- Bortot, P., Coles, S.G., and Sisson, S.A. (2007), “Inference for Stereological Extremes,” Journal of the American Statistical Association, 477, 84–92.
- Bretó, C., He, D., Ionides, E.L., and King, A.A. (2009), “Time Series Analysis via Mechanistic Models,” The Annals of Applied Statistics, 3, 319–348.
- Brooks, S., Gelman, A., Jones, G.L., and Meng, X. L. (eds.) (2011), Handbook of Markov Chain Monte Carlo, Boca Raton, FL: CRC Press.
- Chopin, N., Jacob, P.E., and Papaspiliopoulos, O. (2012), “SMC2: An Efficient Algorithm for Sequential Analysis of State Space Models,” Journal of the Royal Statistical Society, Series B, 75, 397–426.
- Donnet, S., and Samson, A. (2008), “Parametric Inference for Mixed Models Defined by Stochastic Differential Equations,” ESAIM: Probability and Statistics, 12, 196–218.
- Doucet, A., De Freitas, N., and Gordon, N. J. eds. (2001), Sequential Monte Carlo Methods in Practice, New York: Springer-Verlag.
- Fearnhead, P., and Prangle, D. (2012), “Constructing Summary Statistics for Approximate Bayesian Computation: Semi-Automatic Approximate Bayesian Computation” (with discussion), Journal of the Royal Statistical Society, Series B, 74, 419–474.
- Friedman, J., Hastie, T., and Tibshirani, R. (2010), “Regularization Paths for Generalized Linear Models via Coordinate Descent,” Journal of Statistical Software, 33, 1–22.
- Gillespie, D.T. (1977), “Exact Stochastic Simulation of Coupled Chemical Reactions,” Journal of Physical Chemistry, 81, 2340–2361.
- Golightly, A., and Wilkinson, D.J. (2010), “Markov Chain Monte Carlo Algorithms for SDE Parameter Estimation,” in Learning and Inference for Computational Systems Biology, Cambridge, MA: MIT Press, pp. 253–276.
- ——— (2011), “Bayesian Parameter Inference for Stochastic Biochemical Network Models Using Particle Markov Chain Monte Carlo,” Interface Focus, 1, 807–820.
- Haario, H., Saksman, E., and Tamminen, J. (2001), “An Adaptive Metropolis Algorithm,” Bernoulli, 7, 223–242.
- Higham, D.J. (2008), “Modeling and Simulating Chemical Reactions,” SIAM Review, 50, 347–368.
- Hurn, A.S., Jeisman, J.I., and Lindsay, K.A. (2007), “Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations,” Journal of Financial Econometrics, 5, 390–455.
- Iacus, S.M., and Yoshida, N. (2012), “Estimation for the Change Point of Volatility in a Stochastic Differential Equation,” Stochastic Processes and their Applications, 122, 1068–1092.
- Ionides, E.L., Bretó, C., and King, A.A. (2006), “Inference for Nonlinear Dynamical Systems,” Proceedings of the National Academy of Sciences, 103, 18438–18443.
- Kloeden, P.E., and Platen, E. (1992), Numerical Solution of Stochastic Differential Equations, New York: Springer.
- Liepe, J., Barnes, C., Cule, E., Erguler, K., Kirk, P., Toni, T., and Stumpf, M. P.H. (2010), “ABC-SysBio—Approximate Bayesian Computation in Python With GPU Support,” Bioinformatics, 26, 1797–1799.
- Marin, J.-M., Pudlo, P., Robert, C.P., and Ryder, R. (2012), “Approximate Bayesian Computational Methods,” Statistics and Computing, 22, 1167–1180.
- Marjoram, P., Molitor, J., Plagnol, V., and Tavaré, S. (2003), “Markov Chain Monte Carlo Without Likelihoods,” Proceedings of the National Academy of Sciences (vol. 100), pp. 15324–15328.
- Murray, L.M. (2013), “Bayesian State-Space Modelling on High-Performance Hardware Using LibBi,” available as arXiv:1306.3277.
- Neal, R.M. (1996), “Sampling From Multimodal Distributions Using Tempered Transitions,” Statistics and Computing, 6, 353–366.
- Øksendal, B. (2003), Stochastic Differential Equations: An Introduction With Applications (6th ed.), New York: Springer.
- Pinheiro, J., and Bates, D. (1995), “Approximations to the Log-Likelihood Function in the Nonlinear Mixed-Effects Model,” Journal of Computational and Graphical Statistics, 4, 12–35.
- Plummer, M., Best, N., Cowles, K., and Vines, K. (2006), “CODA: Convergence Diagnosis and Output Analysis for MCMC,” R News, 6, 7–11.
- Prangle, D. (2011), “Summary Statistics and Sequential Methods for Approximate Bayesian Computation,” Ph.D. thesis, UK: Lancaster University.
- Sisson, S.A., and Fan, Y. (2011), “Likelihood-Free MCMC” Chapter 12, in Handbook of Markov Chain Monte Carlo, Boca Raton, FL: CRC Press, pp. 313–333.
- Solonen, A., Ollinaho, P., Laine, M., Haario, H., Tamminen, J., and Järvinen, H. (2012), “Efficient MCMC for Climate Model Parameter Estimation: Parallel Adaptive Chains and Early Rejection,” Bayesian Analysis, 7, 1–22.
- Sørensen, H. (2004), “Parametric Inference for Diffusion Processes Observed at Discrete Points in Time: A Survey,” International Statistical Review, 72, 337–354.
- Tibshirani, R. (1996), “Regression Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society, Series B, 58, 267–288.
- Toni, T., Welch, D., Strelkowa, N., Ipsen, A., and Stumpf, M. P.H. (2009), “Approximate Bayesian Computation Scheme for Parameter Inference and Model Selection in Dynamical Systems,” Journal of the Royal Society Interface, 6, 187–202.
- Wilkinson, D.J. (2012), Stochastic Modelling for Systems Biology (2nd ed.), Boca Raton, FL: CRC Press.