Short-Course on Analytical Paleobiology
Preface
1
Managing and Processing Data From the Paleobiology Database
1.1
Objectives
1.2
Reading
1.3
Introduction
1.4
Getting data
1.5
Processing data
1.6
Binning observations
1.7
Sharing data
1.8
Summary
2
Introduction to Bayesian data analysis
2.1
Objectives
2.2
Reading
2.3
Learning from data
2.3.1
Counting and plausibility
2.4
Building a model
2.4.1
A data story
2.4.2
Bayesian updating
2.4.3
Evaluate
2.5
Terms and theory
2.6
Bayes’ Theorem
2.7
But how does it
work
?
2.7.1
Grid approximation
2.7.2
Markov chain Monte Carlo
2.7.3
Aside on Interpreting Probabilities
2.8
Working with samples
2.8.1
Intervals of defined boundaries
2.8.2
Intervals of defined mass
2.8.3
Point estimates
2.9
Summary
3
Introduction to linear regression
3.1
Objectives
3.2
Reading
3.3
Linear regression
3.3.1
Talking about models
3.3.2
Growing a regression model
3.3.3
Sampling from the model
3.4
Adding a predictor to the mix
3.4.1
Aside: Dummy coding
3.5
Interpreting the model fit
3.5.1
Linear predictor
3.5.2
Posterior prediction
3.5.3
Posterior predictive tests
3.6
Summary
4
Continuing with regression with continuous predictors
4.1
Objectives
4.2
Reading
4.3
Our first example
4.4
A single continuous predictor
4.4.1
Aside: Centering
4.4.2
Checking model fit
4.5
Summary
5
Multiple predictors in linear regression
5.1
Objectives
5.2
Reading
5.3
More than one predictor
5.3.1
Categorical predictor
5.4
Defining our model
5.5
Fitting model in
brms
5.6
Aside: Standardizing
5.7
Checking model fit
5.8
Aside: Matrix Notation
5.9
Summary
6
Interactions
6.1
Objectives
6.2
Reading
6.3
Introduction
6.4
Data and inital model
6.5
How to specify an interaction
6.5.1
Symmetry of interactions
6.6
Fitting a model with an interaction
6.7
Interpreting our model
6.8
Have we improved on our previous model?
6.9
Continuous–Continuous interactions
6.10
Summary
7
Logistic regression
7.1
Objectives
7.2
Reading
7.3
Introduction
7.4
Foram coiling
7.5
Writing out a model
7.5.1
Interpreting logistic regression coefficients
7.6
Priors for our model
7.7
Fitting our model
7.8
Checking model adequacy
7.9
Summary
8
Poisson regression and others GLMs
8.1
Outline
8.2
Poisson distribution
9
Varying-intercept models
9.1
Objectives
9.2
Reading
9.3
Introduction
9.4
A basic model with categorical predictor
9.5
Notation for multilevel models
9.6
From categorical predictors to varying-intercept
9.7
Fitting a multilevel model
9.8
Understanding our multilevel model
9.9
A more complex varying-intercept model
9.10
Summary
10
Varying slopes and intercepts
11
Model Comparison
11.1
Bias-Variance Trade-off
11.1.1
RMSE
11.2
Regularization
11.3
Information Criteria and WAIC
11.4
LOO(IC)
12
Time Series
12.1
Objectives
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Analytical Paleobiology
10
Varying slopes and intercepts