We named the method GDC-0449 MCMC-HFM which can deal with the mixture of qualitative and quantitative fitness measures. We first tested the MCMC-HFM to a kinetic toy model with a positive feedback. Starting with an assumed set of parameters that satisfies qualitative condition, we generated kinetic data with some noise. Using the generated data and qualitative condition, we tried to infer the kinetic parameters mainly related to the positive feedback. As the result, MCMC-HFM could reliably infer the kinetic parameters with use of both qualitative and quantitative fitness measures. Next, we applied the MCMC-HFM to a mathematical model of apoptosis signal transduction network, which was proposed before. We tried to infer the kinetic parameters which are especially related to the implicit positive feedback because it is known to be important for characteristic system properties such as bistability and irreversibility of output. As the result, MCMC-HFM could also reliably infer the kinetic parameters, especially those of which have experimental estimates without using these data and the results were consistent with experiments. We also examined 95% credible intervals of inferred parameter distributions, and tried to gain deeper understanding of the implicit positive feedback for bistability, irreversibility, and characteristic dynamics of output in the apoptosis model. This analysis allowed us to specify the important kinetic parameter and corresponding biochemical process for characteristic system properties. These results indicate that MCMC-HFM is a useful method for parameter inference and system analysis. Toni et al. applied ABC-SMC algorithm for parameter inference of the repressilator model comparing time series data. The idea and manner of ABC-MCMC, which judge the acceptance of parameters by all-or-none manner, might be intuitively applied when an experimental result support the existence of a specific phenomenon. In this case, unknown parameters are judged whether they reproduce the observed experimental phenomenon or not by all-or-none manner. An example is the case that an experimental result supports the existence of some specific bifurcation patterns such as saddle-node bifurcation or Hopf bifurcation in a mathematical model. In this case, existence of a specific bifurcation pattern is judged by all-or-none manner. However, both MCMC and ABC-MCMC algorithms cannot, at least in these forms, deal with a mixture of quantitative and qualitative conditions. Thus, extensions and heuristic assumptions of these algorithms are needed to overcome this problem. For this purpose, firstly, we consider the case that we have qualitatively different experiment data obtained in the same system. In this manner, we can utilize a number of different experimental data. In this study, we want to use both quantitative condition i.e. experimental data represented by histogram and qualitative condition i.e. experimental data which indicate the existence of specific bifurcation pattern. Then, we utilize the above idea, a multiplication of conditional probabilities, and employ an assumption to deal with both quantitative and qualitative conditions. In bifurcation analysis, steady AZ 960 states concentrations of all proteins were calculated by solving the simultaneous equations obtained by setting all the ordinary differential equations equals to zero with the standard Newton-Raphson method. Local stabilities of all the steady states were determined by evaluating eigenvalues of Jacobian matrices which were obtained by linearization of ordinary differential equations. In the present study, we introduced functions to evaluate fitness to experimental results, named fitness measures. Then we formulated Bayesian formula for hybrid fitness measures. We implemented it and developed MCMC-HFM algorithm to deal with a mixture of quantitative and qualitative fitness measures.