Models for Ecological Data

題名Models for Ecological Data: An Introduction

著者James S. Clark

出版社 Princeton Univ. Press (発行2007.03)

ISBN 978-0691121789




別の本(上記の本に沿ったRの使い方)もあるので、注意。ページ数は約1/4(上記の本が600ページくらいなのに対してこちらは150ページくらい)で、上記の本のペーパーバックではない(AmazonではModels for Ecological Data という題名になっていて表紙もほとんど同じ)。

題名Statistical Computation for Environmental Sciences in R

副題Lab Manual for Models for Ecological Data

出版社 Princeton Univ. Press (発行2007.05)

ISBN 0-978-0691122625

目次 1基本的な確率モデル. 2.最尤推定値 3.最尤法の例 4.古典的な推論の例 5.事後分布をシミュレート 6.時系列の例

Models for Ecological Data: An Introductionの目次

I. はじめにIntroduction

Chapter 1: Models in Context 1.1 Complexity and Obscurity in Nature and in Models 1.2 Making the Connections: Data, Inference, and Decision

1.3 モデルの2つの要素:既知のものと未知のものTwo Elements of Models: Known and Unknown 1.4 Learning with Models: Hypotheses and Quantification 1.5 Estimation versus Forward Simulation

1.6 統計的実用主義Statistical Pragmatism

2: モデルの要素:個体群成長の例Model Elements: Application to Population Growth

2.1 モデルとデータの例A Model and Data Example

2.2 モデルの状態と時間Model State and Time

2.3 未知のものの確率性Stochasticity for the Unknown

2.4 Additional Background on Process Models

II. 推論の構成要素Elements of Inference

3: 点推定:最尤法とモーメント法Point Estimation: Maximum Likelihood and the Method of Moments

3.1 はじめにIntroduction

3.2 尤度Likelihood

3.3 二項モデルA Binomial Model

3.4 Combining the Binomial and Exponential

3.5 正規分布の最尤推定値Maximum Likelihood Estimates for the Normal Distribution

3.6 個体群の成長Population Growth



3.7 Application: Fecundity

3.8 最尤法による生存の分析Survival Analysis Using Maximum Likelihood

3.8.1 指数分布のモデルにおける尤度The Likelihood for an Exponential Model


3.9 計画行列Design Matrixes

3.10 最尤法の数値的方法Numerical Methods for MLE

3.11 Moment Matching 71

3.12 Common Sampling Distributions and Dispersion

3.13 仮定と次のステップAssumptions and Next Steps

4: ベイズ的アプローチの基本要素Elements of the Bayesian Approach

4.1 ベイズ的アプローチThe Bayesian Approach

4.2 正規分布The Normal Distribution

4.2.1 分散が既知のときの平均The Mean with Known Variance

4.2.2 1つの観察An Observation

4.2.3 1つのデータセットAn Data Set

4.2.4 1つの正規分布の分散The Variance of a Normal Distribution

4.3 主観確率と事前分布の役割Subjective Probability and the Role of the Prior 91

Chapter 5: Confidence Envelopes and Prediction Intervals 93

5.1 古典的な区間推定Classical Interval Estimation

5.1.1 統計の授業で習う信頼区間A Confidence Interval Learned in Statistical Class

5.2 ベイズ的な確信区間Bayesian Credible Intervals

5.3 Likelihood Profile for Multiple Parameters

5.4 複数のパラメーターの信頼区間:線形回帰Confidence Intervals for Several Parameters: Linear Regression

5.5 Which Confidence Envelope to Use

5.6 Predictive Intervals

5.7 Uncertainty and Variability

5.8 When Is It Bayesian?

Chapter 6: Model Assessment and Selection

6.1 モデルの評価に統計を使うUsing Statistics to Evaluate Models

6.2 仮説検定の役割The Role of Hypothesis Tests

6.3 入れ子になった(階層的な)モデルNested Models

6.4 古典的なモデル選択についてさらに考えるAdditional Considerations for Classical Model Selection

6.5 Bayesian Model Assessment

6.6 Additional Thoughts on Bayesian Model Assessment

III. もっと大きなモデルLarger Models

Chapter 7: Computational Bayes: Introduction to Tools Simulation

7.1 事後分布を得るためのシミュレーションSimulation to Obtain the Posterior

7.2 いくつかの基本的なシミュレーションの技術Some Basic Simulation Techniques

7.3 マルコフ連鎖モンテカルロ・シミュレーションMarkov Chain Monte Carlo Simulation

7.4 例:回帰のベイズ的解析Application: Bayesian Analysis for Regression

7.4.1 事後分布を得るObtaining the Posterior Distribution

7.5 MCMCを使うUsing MCMC

7.6 ベイズ的モデル選択のための計算Computation for Bayesian Model Selection

7.7 Priors on the Response

7.8 The Basics Are Now Behind Us

Chapter 8: A Closer Look at Hierarchical Structures

8.1 Hierarchical Models for Context

8.2 混合および一般化線形モデルMixed and Generalized Linear Models






8.3 適用例:二酸化炭素に対する成長の反応Application: Growth Responses to CO2



8.4 条件的に考えるThinking Conditionally

8.4.1 条件的なモデリング Conditional Modeling

8.4.2 Unrecognized Caveats for Observational Data

8.5 Two Applications to Trees

8.6 階層的な場合における無情報事前分布Noninformative Priors in Hierarchical Settings

8.7 From Simple Models to Graphs

IV. さらに進んだモデルMore Advance Methods

9: 時間Time

9.1 なぜ時間が重要なのか?Why Is Time Important?

9.2 時系列の用語Time Series Terminology

9.3 時系列モデルの記述的な要素Descriptive Elements of Time Series Models







9.3.7 自己相関過程Autoregressive process


9.3.9 自己共分散と自己相関 Autocovariance and autocorrelation

9.4 周波数領域The Frequency Domain

9.5 例:個体数の時系列データにおける密度依存性の検出Application: Detecting Density Dependence in Population Time Series

9.6 ベイズ的状態空間モデルBayesian State Space Models

9.7 例:へロン島のヒメクロアジサシApplication: Black Noddy on Heron Island

9.8 非線形状態空間モデルNonlinear State Space Models 9.9 Lags 9.10 Regime Change 9.11 時系列データへの制約Constraints on Time Series Data 9.12 Additional Sources of Variablity 301 9.13 ギブズサンプラーに代わるものAlternatives to the Gibbs Sampler 9.14 縦断的なデータ構造についての追加More on Longitudinal Data Structures 9.15 Intervention and Treatment Effects 9.16 標識再捕獲法Capture-Recapture Studies 9.17 Structured Models as Matrixes 9.18 Structure as Systems of Difference Equations 9.19 Time Series, Population Regulation, and Stochasticity

10: 空間−時間Space-Time

10.1 確率論的な空間的過程の決定論的モデルA Deterministic Model for a Stochastic Spatial Process 10.2 Classical Inference on Population Movement 359

10.3 島の生物地理学とメタ個体群Island Biogeography and Metapopulations

10.4 受動的な分散の推定Estimation of Passive Dispersal

10.5 ベイズ的な枠組みA Bayesian Framework 10.6 Models for Explicit Space 10.7 Point-Referenced Data 10.8 Block-Referenced Data and Misalignment 10.9 空間に関する階層的な取り扱いHierarchical Treatment of Space 10.10 Application: A Spatio-Temporal Model of Population Spread 10.11 空間の扱い方How to Handle Space

11: Some Concluding Perspectives

11.1 モデル、データ、決定Models, Data, and Decision

11.2 The Promise of Graphical Models, Improved Algorithms, and Faster Computers

11.3 Predictions and What to Do with Them

11.4 ソフトウェアについてSome Remarks on Software

Appendix A テイラー級数Taylor Series

Appendix B 微分方程式と差分方程式についての注意Some Notes on Differential and Difference Equations

Appendix C 行列計算の基本Basic Matrix Algebra

Appendix D 確率モデルProbability Models

Appendix E 基本的な生活史の計算Basic Life History Calculations

Appendix F よく使われる確率分布Common Distributions

Appendix G Common Conjugate Likelihood-Prior Pairs