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Semester timetable

This is the timetable we followed last year. This year at the start we'll interweave learning to program, so the exact details may change especially at the beginning.

Week 1

  • Intro to class and pretest
  • Homework: skills
    • Get set up with Git and GitHub.
  • Homework: reading
    • How algorithms unite data science
  • Structured programming
  • The inter-relation of hypotheses, models, and algorithms
  • 3 algorithm classes: model, training, inference

Week 2

  • Homework: skills
    • Git and GitHub: stage, commit, push, backtrack
  • Homework: reflection/analysis
    • Linear regression workflow
  • Homework: mini lecture
    • Algorithms in data science: 3 classes
  • Analysis workflows
  • Model algorithms intro
    • Simple linear model in math and code
    • Design matrix and parameterization
    • Linear model shorthand
  • Homework: mini lecture
    • Training algorithms intro
  • Class: Code a grid search training algorithm

Week 3

  • Optimization algorithms
    • Nelder-Mead simplex algorithm using optim()
    • SSQ QR decomposition algorithm used in lm()
  • Inference algorithms intro
    • Inference problems/goals
    • Looking back or looking forward
    • Looking back: considering the ways data could have happened
  • Frequentist inference algorithms
    • The sampling distribution algorithm - considering the ways a sample could have happened
    • Plug in principle
    • Inference algorithms for lm() simple linear model
    • Confidence intervals from the sampling distribution
    • Coverage algorithm
    • P-value algorithm
    • Prediction intervals
  • Homework:
    • Coding optimization algorithms
    • Coding confidence and prediction intervals

Week 4

  • Homework: skills
    • Git and GitHub: branch, merge, amend, .gitignore, GUI
    • Using code styles
  • Homework: reading
    • Bootstrap algorithm
  • Bootstrap algorithm
    • Non-parametric, empirical, parametric
    • Bootstrapped confidence interval
    • Bootstrapped p-value
  • Homework:
    • Coding bootstrap algorithms

Week 5

  • Homework: skills

    • Reproducible science
    • Writing markdown documents

  • Homework: reading

    • Pitfalls of p-values
    • Conceptual foundations of likelihood
    • Likelihood inference for the linear model

  • Homework: mini lecture

    • Likelihood

  • Homework: problem set

    • Likelihood problems from McElreath Ch 2

  • Likelihood inference

    • Conditional probability: P(y|theta)
    • Likelihood principle, likelihood function, likelihood ratio
    • Training algorithm: maximum likelihood
    • Inference algorithm: likelihood profiles
    • Pure likelihood intervals

  • Homework:

    • Coding likelihood intervals for the linear model

Week 6

  • Homework: skills
    • Practice git branch and merge with your own code
  • Homework: reading and mini lecture
    • Bayes' theorem, prior, posterior
  • Homework: problem set
    • Bayesian problems from McElreath Ch 2
  • Homework: reading & active coding
    • Bayesian model notation
    • Bayesian inference algorithm
    • Coding problems from McElreath Ch 4
  • Bayesian inference algorithms
    • Posterior sampling
    • Histograms as approximations to posterior distribution
    • Credible intervals: central posterior interval, highest posterior density interval
    • Prediction intervals
    • Inference for linear models

Week 7

  • Homework: skills

    • Reproducible workflow
    • Render an R script to markdown

  • MCMC algorithms for Bayesian training

    • Metropolis-Hastings, Gibbs sampling, Hamiltonian Monte Carlo
    • Stan, rstan, rstanarm
    • MCMC diagnostics

  • Further Bayesian topics

    • Choosing priors
    • Posteriors for derived quantities

  • Homework: coding

    • McElreath Ch 8 problems

  • Class: ant species richness dataset

Week 8

  • Homework: skills

    • Visualization
    • Theory and concepts behind ggplot
    • Using ggplot

  • Model diagnostics

    • Checking model assumptions
    • Assessing training robustness
    • Residuals, influence, leverage, outliers, QQ plots, nonlinearity, non-constant variance
    • Case deletion diagnostics for influence

  • Homework: coding

    • Diagnostics for the naive ants linear model

  • Generalized linear models (GLMs)

    • Link functions
    • Data distributions in the exponential family

Week 9

  • Homework: skills
    • Data manipulation with dplyr
  • GLMs: ant data case study
    • Frequentist/likelihood analysis using glm()
    • Bayesian analysis using stan_glm()

Week 10

  • Homework: skills
    • Tidy data
  • Homework: individual project
    • Preproposal
  • Data visualization
    • Exploratory data analysis of hierarchical data
    • Using dplyr and ggplot
  • Model formulae in R
    • Shorthand notation for linear model design matrix
  • Introduction to multilevel models (Normal, linear)
    • Grouping variables
    • Fixed vs random effects
    • Partial pooling and shrinkage
    • Using lmer() and stan_lmer()
  • Workflow algorithm
    • Sketch the data design
    • Write the equations
    • Linear model syntax

Homework: reading

  • Radon multilevel case study (Gelman & Hill Ch 12)

Week 11

  • Homework: skills
    • R markdown
  • Homework: individual project
    • Project proposal
    • Begin EDA using dplyr and ggplot
  • Radon multilevel case study
    • Likelihood and Bayesian algorithms
    • Predictor variables at different scales
    • Alternative parameterizations
    • Credible and prediction intervals

Week 12

  • Homework: skills
    • Using LaTeX to write equations
  • Homework: individual project
    • Modeling predictors at different scales
      • Scales of grouping & predictor variables
      • Sketch data structure, write math, write R model formulae
  • Multiple nested scales: math and R formulae
  • How multilevel models account for autocorrelation
  • Generalized linear mixed models (GLMM)
  • Accounting for overdispersion using multilevel models
  • Case study: revisiting the ants data as multilevel
    • Math and R formulae
    • Using glmer() and stan_glmer()

Week 13

  • Homework: individual project
    • Fit multilevel model
  • Homework: reading & exercises
    • Experimental design
  • Binomial GLMM
  • Study design: experimental design and sampling design
    • Replication, randomization, control
    • Multiscale experimental and sampling design (randomized blocks, split plots etc)
    • Grouping models for multilevel designs

Week 14

  • Homework: individual project
    • Draft report
  • Homework: reading
    • Cross validation
    • Model selection
  • Model selection from various perspectives (frequentist, Bayesian, IC)
    • CV, AIC, BIC, WAIC, LOOIC
  • Introduction to machine learning
    • Cross validation algorithm
  • Either individual meetings about project or maybe these topics:
    • Priors in multilevel models
    • Zero inflated models

Week 15

  • Fake data simulation of multilevel designs
  • Posterior predictive check in Bayesian (and potentially frequentist) models
  • Leave-one-out influence check
  • Homework: individual project
    • Advanced diagnostics
      • Fake data simulation
      • Posterior predictive check
      • LOO influence check

Where next?

I am currently designing a full two-semester sequence of this course and am writing a textbook Data Science for Ecology. These topics will be covered in the book and a selection in future semesters and seminars:

  • Bayes factors
  • Permutation inference algorithms
  • rstan - beyond GLMMs, general hierarchical models
  • Machine learning (see my course website from Spring 2022)
    • regression trees, random forest, boosting, neural networks & deep learning
  • Time series analysis
  • Spatio-temporal models
  • Structural equation models
  • Unsupervised learning (aka "multivariate statistics")
  • Ecological forecasting (see my course website from Spring 2020)