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  • 1
    Electronic Resource
    Electronic Resource
    Maximum likelihood estimation for stochastic first order reactions (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 83-96 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Small sample properties of the maximum likelihood estimator for the rate constant of a stochastic first order reaction are investigated. The approximate bias and variance of the maximum likelihood estimator are derived and tabulated. If observations of the system are made at timesiτ,i=1, 2, ...,N; τ〉0, the observational spacing τ which minimizes the approximate variance of the maximum likelihood estimator is found. The non-applicability of large sample theory to confidence interval derivation is demonstrated by examination of the relative likelihood. Bartlett’s method is employed to derive approximate confidence limits, and is illustrated by using simulated kinetic runs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476667
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  • 2
    Electronic Resource
    Electronic Resource
    Stochastic kinetic models for small reversible systes; The equilibrium distribution (1975)
    Springer
    Bulletin of mathematical biology 37 (1975), S. 127-138 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The equilibrium probability distribution of the process level is studied for a general class of reversible stochastic reactions. A calculationally convenient approximation for equilibrium probabilities is derived and its accuracy is investigated over a range of values of the equilibrium constant. A method of approximating the equilibrium means and variance is developed and illustrated forQ th-order processes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02470619
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  • 3
    Electronic Resource
    Electronic Resource
    Stochastic equilibria for multivariate reaction systems (1976)
    Springer
    Bulletin of mathematical biology 38 (1976), S. 597-622 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The equilibrium distribution for a generalQth-order multivariate reaction system is studied. The state transition intensity matrix is developed and examples are given for small numbers of reaction components. A closed-form expression for the equilibrium distribution for systems which are symmetric with respect to the order of component reactions is presented. Numerical examples for three component systems are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458636
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  • 4
    Electronic Resource
    Electronic Resource
    Stochastic kinetic models for small irreversible systems (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 219-227 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The probability distribution of the process level is derived for a general class of irreversible reaction systems. A method of approximating the mean and variance of the process level is developed and shown to be more accurate for small irreversible systems than other approximations used in the stochastic approach to kinetics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461325
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