Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-10T15:22:38.236Z Has data issue: false hasContentIssue false
  • English
  • Français

Maximum likelihood estimation for stochastic rth -order reactions

Published online by Cambridge University Press:  14 July 2016

John P. Mullooly
John P. Mullooly*
Affiliation:
Oregon State University
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we derive the probability distributions of the number of molecules and of the lifetime of a molecule in a stochastic rth-order system by direct evaluation of probabilities, avoiding the use of differential-difference equations. Maximum likelihood estimation of the rate constant is based on an observation of the level of the system at time t > 0. We find the asymptotic solution of the likelihood equation for a large initial number of molecules. By comparison with the numerical solution of the likelihood equation, the asymptotic estimator is shown to be a satisfactory approximation for second order reactions which are far from completion.

Keywords

STOCHASTIC KINETICSPARAMETER ESTIMATIONSURVIVAL TIME DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 1 , March 1972 , pp. 32 - 42
Copyright
Copyright © Applied Probability Trust 1972 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Bartholomay, A. F. (1959) Stochastic models for chemical reactions: II. The unimolecular rate constant. Bull. Math. Biophys. 21, 363–373.CrossRefGoogle Scholar
[2] Ishida, K. (1964) Stochastic models for bimolecular reaction. J. Chem. Phys. 41, 2472–2478.CrossRefGoogle Scholar
[3] Mcquarrie, D. A. (1967) Stochastic approach to chemical kinetics. J. Appl. Prob. 4, 413–478.Google Scholar
[4] Mullooly, J. P. (1971) Maximum likelihood estimation for stochastic first order reactions. Bull. Math. Biophys. 33, 83–96.Google Scholar
[5] Rényi, A. (1954) Treatment of chemical reactions by means of the theory of stochastic processes. (In Hungarian). Magyar Tud. Akad. Alkalm. Math. Int. Közl. 2, 93–101.Google Scholar
[6] Tallis, G. M. and Leslie, R. T. (1969) General models for r-molecular reactions. J. Appl. Prob. 6, 74–87.Google Scholar