1. A parameter controlling apparatus that controls parameters for adjusting, in a multistage collation apparatus that collates between input data and multiple pieces of registration data at multiple stages with multiple collating devices, refinement precision of the registration data, the parameter controlling apparatus comprising: an inter-different-data-similarity-variation-distribution calculator that calculates distribution of similarity variation of different pieces of data as distribution of occurrence probability of similarity of different pieces of the registration data in the collating devices at multiple stages; an identical-data-similarity-variation-distribution calculator that calculates distribution of similarity variation in identical data as distribution of occurrence probability of similarity in identical data for each of the input data; a collation break-off rate function creator that creates a collation break-off rate function in which the parameters are variables in the collating devices at multiple stages based on the distribution of similarity variation of the different pieces of data calculated by the inter-different-data-similarity-variation-distribution calculator; an error probability function creator that creates an error probability function in which the parameters are variables in the collating devices at multiple stages based on the distribution of similarity variation in the identical data calculated by the identical-data-similarity-variation-distribution calculator; a total collation time function and total error probability function creator that creates a total collation time function and a total error probability function based on the collation break-off rate function, the error probability function, number of pieces of the registration data, and unit collation time information in the collating devices at multiple stages; a constraint equation creator that creates a constraint equation based on the total collation time function, the total error probability function, total collation time constraint parameters corresponding to the total collation time function, and total error probability constraint parameters corresponding to the total error probability function; and an optimum parameter calculator that calculates an optimum parameter group which is a combination of parameters that optimizes an objective function constituted by the collation break-off rate function, the error probability function, the total collation time function, and the total error probability function among combinations of parameters that satisfy the constraint equation created by the constraint equation creator.