Abstract :
Recent remarkable advances in computer performance have enabled us to estimate parameter values by the huge power of numerical computation, the so-called `Brute force`, resulting in the high-speed simultaneous estimation of a large number of parameter values. However, these advancements have not been fully utilised to improve the accuracy of parameter estimation. Here the authors review a novel method for parameter estimation using symbolic computation power, `Bruno force`, named after Bruno Buchberger, who found the Grobner base. In the method, the objective functions combining the symbolic computation techniques are formulated. First, the authors utilise a symbolic computation technique, differential elimination, which symbolically reduces an equivalent system of differential equations to a system in a given model. Second, since its equivalent system is frequently composed of large equations, the system is further simplified by another symbolic computation. The performance of the authors` method for parameter accuracy improvement is illustrated by two representative models in biology, a simple cascade model and a negative feedback model in comparison with the previous numerical methods. Finally, the limits and extensions of the authors` method are discussed, in terms of the possible power of `Bruno force` for the development of a new horizon in parameter estimation.
