Contents

• Contents
• Introduction
  • Purpose of this course
  • Brief history of statistics
  • What is statistics ?
  • General philosophy
  • Statistical software
  • Further reading
  • Exercises
• Descriptive statistics
  • Tabulation and the data matrix
  • Summary measures for univariate data
  • Resistant measures
  • Graphical representation
  • Transformation of data
  • Further reading
  • Exercises
• Probability Distributions
  • Probability distribution and density functions
    • What is probability distribution and why use it?
  • Normal/Gaussian distribution
  • Binomial distribution
    • Example Coin-flipping
  • Gamma distribution
  • Poisson distribution
  • Higher order moments: skewness, kurtosis, etc.
    • Skewness
    • The Kurtosis
  • Further reading
  • Exercises
• Outliers and Extremes
  • Robustness and Resistance
  • Location, Spread and Quantiles
    • Location
    • Spread
    • Example: outliers in the September temperature in Bergen
  • Rank correlation
  • Extreme values
  • Further reading
  • Exercises
• Statistical inference
  • The Null and alternative hypotheses
    • Some definitions
  • Confidence intervals for rejection
  • Student's t-test
  • F-statistics
  • Wilcoxon-Mann-Whitney type tests
  • Chi-squared test
    • Kolmogorov-Smirnov tests^*
    • The Chi-squared distribution^*
  • Monte Carlo tests
  • Test for trends^*
    • Trend testing based on Spearman rank coefficient^*
    • Mann-Kendall rank correlation statistics^*
    • Trend testing based on student's t-test^*
  • Further reading
  • Exercises
• Linear Regression I: Introduction
  • A few words on modelling strategy ...
  • Linear regression
  • ANalysis Of VAriance (ANOVA)
  • Model fit validation using residual diagnostics
  • Weighted and robust regression
  • Further sources of information
  • Exercises
• Linear Regression II: Extensions
  • Multiple regression
  • Multivariate regression
  • Non-linear response
  • Parametric and non-parametric regression
  • Further sources of information
  • Exercises
• Multivariate methods
  • The geographical distribution of correlation
    • Hovmöller plots
  • Problem of multiplicity^*
  • The data matrix and SVD
    • S-mode
    • T-mode^*
  • Empirical Orthogonal Function analysis
    • Geographical weighting
    • Rotated EOFs^*
    • Complex and frequency-domain EOFs^*
    • Extended EOFs^*
  • CCA, SVD and Multivariate regression^*
    • Classical CCA^*
    • Barnett-Preisendorfer CCA^*
    • SVD^*
    • MVR^*
  • Common EOFs^*
  • Cluster analysis^*
  • Further reading
  • Exercises
• Time series I: time-domain
  • Introduction
  • Time series components
  • Filtering and smoothing
  • Serial correlation
  • ARIMA(p,d,q) time series models
  • Further sources of information
  • Exercises
• Time series analysis II: frequency-domain
  • Fourier and Fast Fourier Transforms
    • FT and filtering^*
    • FT and Monte Carlo testing^*
  • Estimating power spectra
  • Red and white noise characteristics
    • FT and the problem of multiplicity^*
  • Advanced topics
    • Multi-taper, maximum entropy, and SSA^*
    • Coherence and Cross-spectra^*
    • Singular Spectrum Analysis^*
    • Wavelet analysis^*
    • 2-D FT^*
  • Further reading
  • Exercises
• Bibliography