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Statistical Thinking

This repository is housing material for the course ETC2420/ETC5242 Statistical Thinking using Randomisation and Simulation taught in Spring 2017 in the Department of Econometrics and Business Statistics at Monash University.

Tentative outline

  • Topic 1: Simulation of games for decision strategies (2 weeks):

    • Week 1, Class 1. Case studies in randomization using Australian election. What is randomness? (Include the draw vs flip coin tosses)

    • Week 1, Class 2. Case studies in randomization (Ch 2, Diez, Barr, Cetinkaya-Rundel). Hypothesis testing I.

    • Lab 1: Introduction to R, functions, permutation, random number generation

    • Week 2, Class 1. Case studies in randomization (Ch 2, Diez, Barr, Cetinkaya-Rundel). Hypothesis testing II.

    • Week 2, Class 2. Decision theory. Computing probabilities of outcomes. Zero-sum two-person: adding reward and loss, saddle points, domination. Criteria for making decisions: minimax, Bayes.

    • Lab 2: Simulate Monty Hall in R

Vocabulary: permutation, association, hypothesis, p-value, pseudo-random number generator, simulation, event, probability, zero-sum two-person game, saddle point, domination, minimax, Bayes criterion

  • Topic 2: Statistical distributions for decision theory (1.5 weeks)

    • Week 3, Class 1: Random numbers Mapping random numbers to events for simulation Statistical distributions READING: CT6, Section 1.3-1.9

    • Lab 3: Hypothesis testing using permutation

    • Week 3, Class 2: Random variables Central limit theorem Density functions Quantiles Estimation Goodness of fit

    • Week 4, Class 1:

    • Lab 4: Finding the best distribution to model olympic medals, estimate number of medals Australia will earn?

  • Topic 3: Linear models for credibility theory (1.5 weeks) (Linear models)

  • review of regression
  • weighted regression
  • resampling methods for assessing parameter estimates: bootstrap
  • repeated measures, mixed effects models
  • Topic 4: Compiling data to problem solve (2 weeks)
  • types of data: sampling, survey, observational, experimental
  • working with temporal data, dates, times, seasonality, covariates
  • longitudinal data
  • working with maps and spatial data: chloropleth, point processes

Vocabulary: Data, information; population, sample; case, subject, sample, variable, feature; quantitative, integer, real-valued, categorical, ordinal, temporal, spatial,

  • Topic 5: Bayesian statistical thinking (1.5 weeks) - Charpentier Ch 3

    (i) Introduction to Bayesian methods (ii) Conjugate priors, small sample examples (iii) MCMC (iv) Bayesian regression, and credibility

  • Topic 6: Temporal data and time series models (1.5 weeks)

    • Modeling time, autocorrelation, cross-correlation
    • Prospective life tables (Charpentier Ch 8)
  • Topic 7: Modeling risk and loss, with data and using randomization to assess uncertainty (2 weeks)

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