Preface
Why this book?
About this book
How to contribute?
Acknowledgments
I BASIC STATISTICS FOR ECOLOGISTS
1
Introduction to PART I
1.1
Further reading
2
Basics of statistics
2.1
Variables and observations
2.2
Displaying and summarizing data
2.2.1
Histogram
2.2.2
Location and scatter
2.2.3
Correlations
2.2.4
Principal components analyses PCA
2.3
Inferential statistics
2.3.1
Uncertainty
2.3.2
Standard error
2.4
Bayes theorem and the common aim of frequentist and Bayesian methods
2.4.1
Bayes theorem for discrete events
2.4.2
Bayes theorem for continuous parameters
2.4.3
Estimating a mean assuming that the variance is known
2.4.4
Estimating the mean and the variance
2.5
Classical frequentist tests and alternatives
2.5.1
Nullhypothesis testing
2.5.2
Comparison of a sample with a fixed value (one-sample t-test)
2.5.3
Comparison of the locations between two groups (two-sample t-test)
2.6
Summary
3
Data analysis step by step
3.1
Plausibility of Data
3.2
Relationships
3.3
Data Distribution
3.4
Preparation of Explanatory Variables
3.5
Data Structure
3.6
Define Prior Distributions
3.7
Fit the Model
3.8
Check Model
3.9
Model Uncertainty
3.10
Draw Conclusions
Further reading
4
Probability distributions
4.1
Introduction
4.2
Discrete distributions
4.2.1
Bernoulli distribution
4.2.2
Binomial distribution
4.2.3
Poisson distribution
4.2.4
Negative-binomial distribution
4.3
Continuous distributions
4.3.1
Beta distribution
4.3.2
Normal distribution
4.3.3
Gamma distribution
4.3.4
Cauchy distribution
4.3.5
t-distribution
4.3.6
F-distribution
5
Important R-functions
5.1
Data preparation
5.2
Figures
5.3
Summary
6
Reproducible research
6.1
Summary
6.2
Further reading
7
Further topics
7.1
Bioacoustic analyse
7.2
Python
II BAYESIAN DATA ANALYSIS
8
Introduction to PART II
Further reading
9
The Bayesian paradigm
9.1
Introduction
9.2
Summary
10
Prior distributions
10.1
Introduction
10.2
How to choose a prior
10.2.1
Priors for variance parameters
10.3
Prior sensitivity
11
Normal Linear Models
11.1
Linear regression
11.1.1
Background
11.1.2
Fitting a Linear Regression in R
11.1.3
Drawing Conclusions
11.1.4
Interpretation of the R summary output
11.2
Linear model with one categorical predictor (one-way ANOVA)
11.3
Other variants of normal linear models: Two-way anova, analysis of covariance and multiple regression
11.3.1
Linear model with two categorical predictors (two-way ANOVA)
11.3.2
A linear model with a categorical and a numeric predictor (ANCOVA)
11.4
Partial coefficients and some comments on collinearity
11.5
Ordered Factors and Contrasts
11.6
Quadratic and Higher Polynomial Terms
12
Assessing Model Assumptions
12.1
Model Assumptions
12.2
Independent and Identically Distributed
12.3
The QQ-Plot
12.4
Temporal Autocorrelation
12.5
Spatial Autocorrelation
12.6
Heteroscedasticity
13
Linear Mixed Effect Models
13.1
Background
13.1.1
Why Mixed Effects Models?
13.1.2
Random Factors and Partial Pooling
13.2
Fitting a normal linear mixed model in R
13.3
Restricted maximum likelihood estimation (REML)
14
Generalized linear models
14.1
Introduction
14.2
Summary
15
Generalized linear mixed models
15.1
Introduction
15.1.1
Binomial Mixed Model
15.2
Summary
16
Posterior predictive model checking
16.1
Introduction
16.2
Summary
17
Model comparison and multimodel inference
17.1
Introduction
17.2
Summary
18
MCMC using Stan
18.1
Background
18.2
Install
rstan
18.3
Writing a Stan model
18.4
Run Stan from R
Further reading
19
Ridge Regression
19.1
Introduction
20
Structural equation models
20.1
Introduction
21
Modeling spatial data using GLMM
21.1
Introduction
21.2
Summary
III ECOLOGICAL MODELS
22
Introduction to PART III
22.1
Model notations
23
Zero-inflated Poisson Mixed Model
23.1
Introduction
23.2
Example data
23.3
Model
24
Daily nest survival
24.1
Background
24.2
Models for estimating daily nest survival
24.3
Known fate model
24.4
The Stan model
24.5
Prepare data and run Stan
24.6
Check convergence
24.7
Look at results
24.8
Known fate model for irregular nest controls
Further reading
25
Capture-mark recapture model with a mixture structure to account for missing sex-variable for parts of the individuals
25.1
Introduction
25.2
Data description
25.3
Model description
25.4
The Stan code
25.5
Call Stan from R, check convergence and look at results
26
What sample size?
26.1
Introduction
IV APPENDICES
Referenzen
Bayesian Data Analysis in Ecology with R and Stan
5
Important R-functions
THIS CHAPTER IS UNDER CONSTRUCTION!!!
5.1
Data preparation
5.2
Figures
5.3
Summary