This paper proposes a robust tracking method that uses interval analysis. Any single posterior model necessarily includes a modeling uncertainty (error), and thus, the posterior should be represented as an interval of probability. Then, the objective of visual tracking becomes to find the best state that maximizes the posterior and minimizes its interval simultaneously. By minimizing the interval of the posterior, our method can reduce the modeling uncertainty in the posterior. In this paper, the aforementioned objective is achieved by using the M4 estimation, which combines the Maximum a Posterior (MAP) estimation with Minimum Mean-Square Error (MMSE), Maximum Likelihood (ML), and Minimum Interval Length (MIL) estimations. In the M4 estimation, our method maximizes the posterior over the state obtained by the MMSE estimation. The method also minimizes interval of the posterior by reducing the gap between the lower and upper bounds of the posterior. The gap is reduced when the likelihood is maximized by the ML estimation and the interval length of the state is minimized by the MIL estimation. The experimental results demonstrate that M4 estimation can be easily integrated into conventional tracking methods and can greatly enhance their tracking accuracy. In several challenging datasets, our method outperforms state-of-the-art tracking methods.