In this thesis, we propose a Monte Carlo method for Hilbert space embeddings of conditional distributions. This approach enables us to compute the kernelized sum rule by directly handling specified conditional distributions. Combining the Monte Carlo method with kernel Bayes' rule, we design a novel semi-nonparametric filter called the kernel Monte Carlo filter for state-space models. We apply the kernel Monte Carlo filter to a difficult vision-based mobile robot localization task to show the potential of our method for a wide range of applications in practical settings. We expect that our approach will be extended to develop semi-nonparametric inference methods beyond state-space filters.