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Parameter estimation in stochastic differential equations with Markov chain Monte Carlo and non-linear Kalman filtering
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Often, the volume is treated as a constant in CSTR studies.
“Often, the volume is treated as a constant [4,25,38,39], however, in reality the tanks may expand and lead to variable volume.”
From Markov Chain Monte Carlo Analysis of the Variable-Volume Exothermic Model for a Continuously Stirred Tank Reactor (2021) · cites this paper as [25]
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- Aït-Sahalia Y (2002) Maximum likelihood estimation of discretely sampled diffusions: a closed-form approximation approach. Econometrica 70(1):223–262 · DOI
- Aït-Sahalia Y (2008) Closed-form expansion for multivariate diffusions. Ann Stat 36(2):906–937 · DOI
- Andrieu C, Thoms J (2008) A tutorial on adaptive MCMC. Stat Comput 18(4):343–373 · DOI
- Andrieu C, Doucet A, Holenstein R (2010) Particle Markov chain Monte Carlo methods. R Stat Soc Ser B Stat Methodol 72(3):269–342 · DOI
- Berg EVD, Heemink AW, Lin HX, Schoenmakers J (2006) Probability density estimation in stochastic environmental models using reverse representations. Stoch Environ Res Risk Assess 20(1–2):126–139 · DOI
- Berger JO (1985) Statistical decision theory and Bayesian analysis. Springer, Berlin · DOI · Paper page
- Beskos A, Papaspiliopoulos O, Roberts G, Fearnhead P (2006) Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes (with discussion). J R Stat Soc Ser B Stat Methodol 68(3):333–382 · DOI
- Beskos A, Papaspiliopoulos O, Roberts G (2009) Monte Carlo maximum likelihood estimation for discretely observed diffusion processes. Ann Stat 37(1):223–245 · DOI
- Bishop CM (1996) Neural networks for pattern recognition. Oxford University, Oxford
- Brandt M, Santa-Clara P (2002) Simulated likelihood estimation of diffusions with an application to exchange rate dynamics in incomplete markets. J Financ Econ 63(2):161–210 · DOI
- Butcher JC (2003) Numerical methods for ordinary differential equations. Wiley, New York · DOI
- Cappé O, Moulines E, Rydén T (2005) Inference in Hidden Markov models. Springer, Berlin · DOI
- Chen L, Qin Z, Liu JS (2001) Exploring hybrid Monte Carlo in Bayesian computation. In: Proceedings of ISBA
- Doucet A, Godsill SJ, Andrieu C (2000) On sequential Monte Carlo sampling methods for Bayesian filtering. Stat Comput 10(3):197–208 · DOI
- Duane S, Kennedy AD, Pendleton BJ, Roweth D (1987) Hybrid Monte Carlo. Phys Lett B 195(2):216–222 · DOI
- Elerian O (1998) A note on the existence of a closed form conditional transition density for the Milstein scheme. Working paper, Nuffield College, Oxford University
- Elerian O, Chib S, Shephard N (2001) Likelihood inference for discretely observed non-linear diffusions. Econometrica 69(4):959–993 · DOI
- Eraker B (2001) MCMC analysis of diffusion models with application to finance. J Bus Econ Stat 19(2):177–191 · DOI
- Gelman A, Carlin JB, Stern HS, Rubin DB (2004) Bayesian data analysis. CRC/Chapman and Hall, London
- Geyer CJ (1992) Practical Markov chain Monte Carlo. Stat Sci 7(4):473–483 · DOI · Paper page
- Gilks WR, Richardson S, Spiegelhalter DJ (1996) Markov chain Monte Carlo in practice. Chapman and Hall/CRC, London
- Golightly A, Wilkinson DJ (2006) Bayesian sequential inference for nonlinear multivariate diffusions. Stat Comput 16(4):323–338 · DOI
- Golightly A, Wilkinson DJ (2008) Bayesian inference for nonlinear multivariate diffusion models observed with error. Comput Stat Data Anal 52(3):1674–1693 · DOI
- Grewal MS, Andrews AP (2001) Kalman filtering, theory and practice using MATLAB. Wiley-IEEE Press, New York
- Holder T, Leimkuhler B, Reich S (2001) Explicit variable step-size and time-reversible integration. Appl Numer Math 39(3–4):367–377 · DOI
- Hurn AS, Lindsay KA (1999) Estimating the parameters of stochastic differential equations. Mathe Comput Simul 48(4–6):373–384 · DOI
- Hurn AS, Lindsay KA, Martin VL (2003) On the efficacy of simulated maximum likelihood for estimating the parameters of stochastic differential equations. J Time Ser Anal 24(1):45–63 · DOI
- Jazwinski AH (1970) Stochastic processes and filtering theory. Academic Press, Edinburgh
- Jeisman J (2005) Estimation of the Parameters of stochastic differential equations. Doctoral dissertation, Queensland University of Technology
- Jensen B, Poulsen R (2002) Transition densities of diffusion processes: numerical comparison of approximation techniques. J Deriv 9(4):18–32 · DOI
- Jones CS (1998) A simple Bayesian method for the analysis of diffusion processes. Working paper, University of Pennsylvania · DOI
- Julier SJ, Uhlmann JK (2004) Unscented filtering and nonlinear estimation. Proc IEEE 92(3):401–422 · DOI
- Karatzas I, Shreve SE (1991) Brownian motion and stochastic calculus. Springer, Berlin
- Kloeden PE, Platen E (1999) Numerical solution to stochastic differential equations. Springer, Berlin
- Liang F, Liu C, Carroll RJ (2010) Advanced Markov chain Monte Carlo methods: learning from past samples. Wiley, Chichester · DOI
- Najfeld I, Havel TF (1995) Derivatives of the matrix exponential and their computation. Adv Appl Math 16(3):321–375 · DOI
- Neal RM (2011) MCMC using Hamiltonian dynamics. In: Brooks S, Gelman A, Jones GL, Meng XL (eds) Handbook of Markov chain Monte Carlo, chap 5. Chapman& Hall/CRC, London
- Nielsen JN, Madsen H, Young PC (2000) Parameter estimation in stochastic differential equations: an overview. SIAM J Numer Anal 24:83–94
- Ninness B, Henriksen S (2010) Bayesian system identification via Markov chain Monte Carlo techniques. Automatica 46(1):40–51 · DOI
- Øksendal B (2003) Stochastic differential equations: an introduction with applications. Springer, Berlin · DOI
- Ornstein LS, Uhlenbeck GE (1930) On the theory of the Brownian motion. Phys Rev 36(5):823–841 · DOI
- Pedersen AR (1995) A new approach to maximum likelihood estimation for stochastic differential equations based on discrete observations. Scand J Stat 22(1):55–71
- Särkkä S (2006) Recursive Bayesian inference on stochastic differential equations. Doctoral dissertation, Helsinki University of Technology
- Särkkä S (2007) On unscented Kalman filtering for state estimation of continuous-time nonlinear systems. IEEE Trans Autom Control 52(9):1631–1641 · DOI
- Särkkä S, Vehtari A, Lampinen J (2007) Rao-Blackwellized particle filter for multiple target tracking. Inf Fusion J 8(1):2–15 · DOI
- Shoji I, Ozaki T (1998) Estimation for nonlinear stochastic differential equations by a local linearization method. Stoch Anal Appl 16(4):733–752 · DOI
- Singer H (2002) Parameter estimation of nonlinear stochastic differential equations: simulated maximum likelihood versus extended Kalman filter and Itô-Taylor expansion. J Comput Graph Stat 11(4):972–995 · DOI
- Singer H (2004) A survey of estimation methods for stochastic differential equastions. In: Proceedings of 6th international conference on social science methodology, Amsterdam
- Singer H (2011) Continuous-discrete state-space modeling of panel data with nonlinear filter algorithms. AStA Adv Stat Anal 95(4):375–413 · DOI
- Sørensen H (2004) Parametric inference for diffusion processes observed at discrete points in time: a survey. Int Stat Rev 72(3):337–354 · DOI
- Stramer O, Bognar M (2011) Bayesian inference for irreducible diffusion processes using the pseudo-marginal approach. Bayesian Anal 6(2):231–258 · DOI
- Stramer O, Bognar M, Schneider P (2010) Bayesian inference for discretely sampled Markov processes with closed-form likelihood expansions. J Financ Econ 8(4):450–480
- Young P (1980) Parameter estimation for continuous-time models: a survey. Automatica 17(1):23–39 · DOI
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Muhirwa, J. P., Mbalawata, S. I., & Masanja, V. G. (2021) · Engineering, Technology & Applied Science Research · doi:10.48084/etasr.3962 · Cited by 9
Metadata
- Authors
- Mbalawata, I. S., Särkkä, S., & Haario, H.
- Affiliations
- Lappeenranta-Lahti University of Technology (FI)
- Aalto University (FI)
- Corresponding author
- Mbalawata, Isambi S.
- Venue
- Computational Statistics
- Published
- 2012-08-03
- Volume
- 28
- Issue
- 3
- Pages
- 1195-1223
- ISSN
- 0943-4062 (ISSN-L)
- 1613-9658
- OpenAlex
- W2060182299
- Cited by
- 77
- References
- 0
- Citations by year
- 2026: 2 · 2025: 5 · 2024: 1 · 2023: 4 · 2022: 2 · 2021: 5 · 2020: 6 · 2019: 21 · 2018: 5 · 2017: 6 · 2016: 3 · 2015: 5 · 2014: 6 · 2013: 6
- FWCI
- 5.20
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Computational Statistics (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Funders
- Academy of Finland
- Aalto-Yliopisto
- Lappeenranta University of Technology
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Physical Sciences › Computer Science › Artificial Intelligence › Target Tracking and Data Fusion in Sensor Networks
- Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
- Keywords
- parameter estimation, stochastic differential equations, Itô processes, Markov chain Monte Carlo, Metropolis-Hastings algorithm, Hamiltonian Monte Carlo, gradient computation, linear stochastic differential equations
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