物理のためのデータサイエンス入門 (Introduction to Data Science for Physics)

植村誠「物理のためのデータサイエンス入門」講談社、2023年3月、amazon

A textbook written in Japanese

目次

第0章 データサイエンス、機械学習・・・何が嬉しいの?

第1章 推定と検定 (Statistical estimation and test)
1.1 データに最適なモデル:尤度、最尤推定、最小二乗法
1.2 モデルの不定性:χ2分布、仮説検定、信頼区間

第2章 高次元のモデルへ (To the world of high-dimensional models)
2.1 モデルの過適合と汎化性能
2.2 最適化と局所解

第3章 ベイズモデリング (Bayesian modeling)
3.1 モデルパラメータを確率変数に
3.2 ベイズの定理
3.3 例題1:新型コロナのPCR検査
3.4 例題2:スパムフィルター
3.5 例題3:滑らかな曲線

第4章 マルコフ連鎖モンテカルロ法 (Markov chain Monte Carlo methods)
4.1 確率分布からのサンプリング
4.2 MCMCの原理
4.3 様々なアルゴリズム
4.4 実践例1:活動銀河核ジェットの物理状態
4.5 実践例2:地震波形の再構成
4.6 MCMCが収束しません!

第5章 正則化とスパースモデリング (Regularization and sparse modeling)
5.1 ブラックホールの夜
5.2 最小二乗法と正則化
5.3 スパースモデリング
5.4 実践例1:変光星の周期解析
5.5 実践例2:電波干渉計とMRIの画像再構成
5.6 実践例3:超新星の明るさを決める変数の選択

第6章 判別モデル (Discrimination models)
6.1 手で境界線を引いたら、ダメですか?
6.2 判別モデルの基本的な考え方
6.3 ロジスティック回帰
6.4 サポートベクトルマシン
6.5 実践例:津波堆積物

第7章 ガウス過程 (Gaussian process)
7.1 頭の良いデータの取り方
7.2 ガウス過程の数理
7.3 実践例1:天体の不規則な光度変化
7.4 実践例2:ダークエミュレータ
7.5 実践例3:自動車エアコン用送風機の設計

第8章 ニューラルネットワーク (Neural network)
8.1 ニューラルネットワークとは
8.2 実践例1:風に煽られる望遠鏡
8.3 実践例2:超新星の捜索

付録 Pythonプログラム

Feature selection for classification of blazars

Uemura, M., Abe, T., Yamada, Y., and Ikeda, S., “Feature selection for classification of blazars based on optical photometric and polarimetric time-series data”, PASJ, 72, 74, 2020

We investigated the differences of two sub-types of blazars, FSRQs, and BL Lac objects, in the variability. We characterize the variability using the Ornstein–Uhlenbeck (OU) process, and search for the features that are discriminative for the two subtypes. We used optical photometric and polarimetric data obtained with the 1.5 m Kanata telescope for 2008–2014. We found that four features, namely the variation amplitude, characteristic timescale, and non-stationarity of the variability obtained from the light curves and the median of the degree of polarization (PD), are essential for distinguishing between FSRQs and BL Lac objects. The characteristics of the variability imply that the nature of the variation in the jets is common in FSRQs and BL Lac objects. We found that BL Lac objects tend to have high PD medians, which suggests that they have a stable polarization component. FSRQs have no such component, possibly because of a strong Compton cooling effect in sub-parsec-scale jets.

Degeneracy of the SED Model of the blazar Mrk 421

Yamada, Y.,  Uemura, M.,  Itoh, R.,  Fukazawa, Y.,  Ohno, M., and Imazato, F., “Variations of the physical parameters of the blazar Mrk 421 based on analysis of the spectral energy distributions”, PASJ, 72, 42, 2020

The MCMC code for the SSC model optimization to the SED data is available at the project page of yysscfit

We report on the variations of the physical parameters of the jet observed in the blazar Mrk 421, and discuss the origin of X-ray flares in the jet, based on analysis of several spectral energy distributions (SEDs). The SEDs are modeled using the one-zone synchrotron self-Compton model, its parameters determined using a Markov chain Monte Carlo method. The lack of data at TeV energies means many of the parameters cannot be uniquely determined and are correlated. These are studied in detail. We find that the optimal solution can be uniquely determined only when we apply a constraint to one of four parameters: the magnetic field, the Doppler factor, the size of the emitting region, and the normalization factor of the electron energy distribution. The result of our SED analysis suggests that, in the X-ray faint state, the emission occurs in a relatively small area with a relatively strong magnetic field. The X-ray bright state shows a tendency opposite to that of the faint state. The presence of two kinds of emitting areas implies that the one-zone model is unsuitable for reproducing at least part of the observed SEDs.

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