@book{CTT100780898,
  author = {SUMIO WATANABE},
  title = {Mathematical theory of Bayesian statistics},
  publisher = {CRC Press},
  year = 2018,
}

@article{CTT100780897,
  author = {SUMIO WATANABE},
  title = {Higher Order Equivalence of Bayes Cross Validation and  WAIC},
  journal = {Springer Proceedings in Mathematics and Statistics,  Information Geometry and Its Applications},
  year = 2018,
}

@inproceedings{CTT100780902,
  author = {Natsuki Kariya and SUMIO WATANABE},
  title = {混合正規分布の均一性検定におけるベイズ検定統計量の漸近挙動},
  booktitle = {},
  year = 2018,
}

@inproceedings{CTT100780901,
  author = {SUMIO WATANABE},
  title = {構造学習理論と代数幾何学},
  booktitle = {},
  year = 2018,
}

@inproceedings{CTT100780900,
  author = {SUMIO WATANABE},
  title = {ベイズ事後分布の相転移について},
  booktitle = {},
  year = 2018,
}

@inproceedings{CTT100780887,
  author = {SUMIO WATANABE},
  title = {Cross Validation and WAIC in layered neural networks},
  booktitle = {},
  year = 2018,
}

@inproceedings{CTT100780893,
  author = {SUMIO WATANABE},
  title = {統計力学と統計学の形式的な相違点を考えることに物理学の課題があるだろうか},
  booktitle = {},
  year = 2018,
}

@inproceedings{CTT100780891,
  author = {Naoki Hayashi and SUMIO WATANABE},
  title = {ハミルトニアンモンテカルロ法を用いた確率行列分解における実対数閾値の実験的考察},
  booktitle = {},
  year = 2018,
}

@inproceedings{CTT100780890,
  author = {Kenji Sato and SUMIO WATANABE},
  title = {混合ポアソン分布の実対数閾値とベイズ汎化誤差について},
  booktitle = {},
  year = 2018,
}

@misc{CTT100780899,
  author = {SUMIO WATANABE},
  title = {機械学習の数学入門},
  year = 2018,
}