Involved in the response to external challenges, such as a temporal change in food availability. In computational systems biology, mathematical models of gene regulatory networks or signal transduction networks are often represented by ordinary and partial differential equations. In these equations, there are kinetic parameters which characterize strengths of interactions or rates of biochemical reactions. However, all the values of kinetic parameters in the model are not always available from previous experiments and literatures. In these cases, unknown kinetic parameters need to be inferred so that the model simulation reproduces the known experimental phenomena. Parameter inference is very important for the mathematical modeling of biological phenomena, because it is known that network structures alone do not always determine the response or function of that network. To infer unknown parameters, there are various methods used in systems biology. Evolutionary strategy is one of the methods for parameter inference by iterative computation and has already been used to estimate kinetic parameters of the mathematical models of metabolic pathway, circadian clock system of Arabidopsis and mammal. Simulated annealing is an optimization algorithm and has already been used for parameter estimation of a biochemical pathway. Although these methods are useful, they do not give us the information about credibility and uncertainty of unknown parameters with the distributions of unknown parameters. In this respect, Bayesian statistics is a powerful method for parameter inference giving us the information about credibility and uncertainty of unknown parameters as a credible interval of INCB18424 JAK inhibitor posterior distribution. However, posterior distributions in Bayesian statistics are often difficult to obtain analytically. In these cases, Markov chain Monte Carlo methods can be used to obtain samples from posterior distributions. In conventional MCMC, LY2109761 explicit evaluation of a likelihood function is needed to evaluate a posterior distribution. Otherwise, when the likelihood function is analytically or computationally intractable, approximate Bayesian computation MCMC can be used. ABC-MCMC can evaluate posterior distribution without explicit evaluation of a likelihood function, but with simulation-based approximations in its algorithm. ABC was implemented not only in MCMC but also in sequential Monte Carlo methods. ABC-SMC has already been applied for parameter inference and model selection in systems biology. Biological experiments are often performed with cell population, and the results are represented by histograms. For example, delay time and switching time of caspase activation after TRAIL treatment in apoptosis signal transduction pathway were represented by histograms. Here, we call this kind of experimental result or data as a quantitative condition. On another front, experiments or observations sometimes indicate the existence of a specific bifurcation pattern. For example, experiments about RBE2F pathway in cell cycle regulatory system and mitochondrial apoptosis signal transduction pathway indicate that those pathway work as bistable switches. Bistability indicates the existence of saddle-node bifurcation in mathematical modeling. Here, we call this kind of experimental result or data as a qualitative condition. In this study, to utilize those conditions for parameter inference, we introduce and call the functions which can evaluate the fitness to those conditions as quantitative and qualitative fitness measures respectively. Although conventional MCMC and ABCMCMC evaluate posterior distribution with and without explicit evaluation of a likelihood function, respectively, none of these MCMC algorithms evaluate posterior distribution in the case that the experiments for parameter inference are a mixture of quantitative.