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Statistics and Geodata Analysis using R (SOGA-R)
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Introduction to R
Overview Introduction to R
Getting Started
Contributed Packages
R as a Calculator
Built-in Functions
Variable Assignment
Data Types And Data Structures
Data Types
Data Structures
Data Frame
Functions
Control Flow Structures
Plotting Data
Base R Graphics
Base R Graph Layout
lattice
ggplot2
Walter-Lieth diagram
Plotting Maps
Ternary Diagrams with ggtern
Additional Plotting Libraries
Spatial Data in R
terra and rasterVis
sp
sf
spatstat
Date, time and time series in R
Basics of Statistics
Overview Basics of Statistics
Descriptive Statistics
Measures of Central Tendency
The Mean
The Median
The Mode
Measures of Dispersion
Variance and Standard Deviation
The Range
Measures of Position
Quartiles and Interquartile Range
The Five Number Summary
Percentiles and Percentile Rank
Outliers and Boxplots
Measures of Relation
Covariance
Correlation
The Contingency Coeficient
Discrete Random Variables
Discrete Random Variables - An Example
The Mean and Standard Deviation
The Binomial Distribution
Requirements
The Binomial Distribution
Mean and Standard Deviation
Binomial and Hypergeometric Distribution
The Poisson Distribution
The Poisson Distribution - An Example
Shape, Mean and Standard Deviation
Poisson Approximation to the Binomial Distribution
The Hypergeometric Distribution
The Hypergeometric Distribution in R
The Hypergeometric Distribution - A gender application
The Hypergeometric Distribution - Additional exercises
Continous Random Variables
Probability Density Functions
The Normal Distribution
The Standard Normal Distribution
The Continuous Uniform Distribution
The Continuous Uniform Distribution in R
The Students t-Distribution
The Students t-Distribution in R
The Chi-Square Distribution
The Chi-Square Distribution in R
The F-Distribution
The F-Distribution in R
The Central Limit Theorem
The Central Limit Theorem - Introductory video
The Population Distribution
Population and Sample Statistics
The Sampling Error
The Sampling Distribution
The Standard Error
Normally Distributed Population
Not Normally Distributed Population
Inferential Statistics
The Point Estimate
The Interval Estimate
Precision and Accuracy
Population Mean - The z-Distribution
The One-Mean z-Interval Procedure
Population Mean - The t-Distribution
The One-Mean t-Interval Procedure
Advanced Example using MC-Estimation
Hypothesis Tests
Introduction to Hypothesis Testing
Hypothesis Formulation
Error and Significance Level
Critical Value and the p-Value
One Population Mean
Hypothesis Tests when Sigma Is Known
Hypothesis Tests when Sigma is Unknown
Two Population Means
Standard Deviations Assumed Equal
Standard Deviations Not Assumed Equal
Paired Samples
Population Standard Deviations
One Population Standard Deviation
Two Population Standard Deviations
Example: MC-Estimation of CI's as Test Alternative
Chi-Square Tests
Chi-Square Goodness-of-Fit Test
The Chi-Square Independence Test
Regression and Correlation
Inferences About the Slope
Inferences About the Correlation
Probability Tables
The z-Distribution
The t-Distribution
The Chi Square Distribution
The F-Distribution
Analysis of Variance - ANOVA
One-way ANOVA
One-way ANOVA Hypothesis Test
Multiple Comparisons
Linear Regression
Simple Linear Regression
Paramter Estimation
Simple Linear Regression - An example
Model Diagnostic
Polynomial Regression
Polynomial Regression - An example
Logistic Regression
The Logit Function
The Logistic Regression Model
Logistic Regression in R - An Example
Advanced statistics
Overview Advanced statistics
Feature scales
Reasons for Transformations
Linear Transformations
Non-Linear Transformations
Transformations for double contraint intervals
Real world challenges: Semiquantitative measure on constraint intervals
Zero Missings
Intro to compositional data
Algebraic operations in Aitchison simplex
Compositional Graphics
Logratio Transformations
Descriptive Analysis of compositional data
Multivariate approaches
Multiple linear regression
Parameter estimation
Multiple linear regression analysis - a simple example
Multiple linear regression analysis - an advanced example
Regularization methods
Multiple linear regression - exercises
Principal Component Analysis
Principal Component Analysis - the basics
Principal Component Analysis in R
Principal Component Analysis - An example
Principal Component Analysis for Regression Modelling
Principal Component Analysis - Exercises
Application example: PCA & LDA
Factor Analysis
The Exploratory Factor Model
A simple example of Factor Analysis in R
Factor Analysis - an advanced example
Factor Analysis - Exercises
Compositional PCA - An Example
An Advanced Time Series Modelling Approach
End-member modelling analysis
Time Series Analysis
Basic properties of time series
Date, time and time series in R
Datasets used
Weather station Berlin-Dahlem
Modern carbon dioxide measurement
Earth surface temperature anomalies
Ice core atmospheric carbon dioxide record
Basic operations on time series using R
Subsetting and indexing the data
Summary statistics
Aggregation of time series data
Dealing with missing values
Imputing missing values with zoo and forecast
Smoothing
Smoothing by filtering (moving average)
Kernel smoothing
Smoothing via local polynomials
Lowess
Smoothing Splines
Seasonal decompositon
Working data set
Seasonal and Trend decomposition using Loess (STL)
Trends and seasonal effects
Working data set
Linear trend estimation
Eliminating the seasonal effect
Time series statistical models
White noise models
Random walk models
Moving Average (MA) models
Autoregressive (AR) models
ARMA models
ARIMA models
ARIMA modelling in R
An Advanced Time Series Modelling Approach
Spatial Point Patterns
The Spatial Point Process
Spatial data analysis with R
Berlin City Data
Analysis of Spatial Point Patterns
Intensity
Interactions in Point Pattern Analysis
Simulation Envelopes
Geostatistics
Data sets used
Lake Rangsdorf
DWD Weather Data Germany
DWD Weather Data East Germany
SRTM Digital Elevation Model for Germany
Nearest Neighbor Interpolation
Inverse Distance Weighting (IDW)
IDW Interpolation of Weather Data
Model Selection via Cross-Validation for IDW
Geostatistical Interpolation
Estimation of the Mean Function
Estimation of the Semivariogram
Modeling the Semivariogram
Kriging
Geostatistical Interpolation with R
Mean Annual Rainfall Germany
Lake Rangsdorf - Ordinary kriging in a nutshell
Machine learning
Overview Machine learning
Introduction to machine learning with R
Artifical Neural Networks (ANN)
Widrow Hoff learning rule
Multilayer Perceptron Algorithm
Clustering example
Classification example
k-Nearest Neighbors
Support Vector Machines
A typical machine learning workflow
Application example: Random Forest Regression
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Date, time and time series in R
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