Fundamentals of Statistics
contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics...
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Overview
Index P...
p values
Interpreting p values
p-chart
p- and c-Charts
paired differences
Wilcoxon Test for Paired Differences
paired experiments
Paired Experiments
parameter
Parameters
parametric tests
Parametric and Non-Parametric Tests
pareto distribution
Pareto Distribution
parsimonious model
Modeling
partial derivative
Partial Derivative
partial least squares
Modeling with latent variables
PLS - Partial Least Squares Regression
PCA
Literature References - Factor Analysis, Principal Components
Principal Component Analysis
Application Example of PCA - Classification of Wine
Data Compression by PCA
PCA - Loadings and Scores
PCA - Different Forms
PCA - Model Order
Exercise - Dependence of PC scores on scaling of data
Exercise - Classification of unknown wine samples by PCA
Exercise - Detection of mixtures of two different wines by PCA
Relations between Loadings, Scores and Original Data
PCA of Transposed Matrices
PCR
Principal Component Regression
Exercise - Perform a PCR by successive application of PCA and MLR
Modeling with latent variables
Pearson
Karl Pearson
Significance of Outliers
Pearson's contingency coefficient
Contingency Coefficient
Pearson's correlation coefficient
Pearson's Correlation Coefficient
perceptron
Multi-layer Perceptron
permutation
Matrix Determinant
Counting Rules
phase angle
Fourier Series
phase space
Phase Space
physical dimension
Data Set - Physical Dimension of Fishes
pink noise
Types of Noise
platykurtic distribution
Kurtosis
PLS
Modeling with latent variables
PLS - Partial Least Squares Regression
PLS Discriminant Analysis
Evaluating the performance of PLS-DA
pocket calculator
Decimal Places and Precision
Poisson distribution
Poisson Distribution
Relationship Between Various Distributions
polynomial filter
Savitzky-Golay Filter - Mathematical Details
polynomial fit
Exercise - Calculate a polynomial fit by means of MLR
Data Set - Polynomial Fit
Curve Fitting by Polynomials
population
Population and Sample
positive predictive value
Classifier Performance
power
Types of Error
Power of a Test
precision
The Data
Decimal Places and Precision
Definitions of Quality Control
Random and Systematic Errors
Classifier Performance
Determination Limit
prediction of future values
Regression - Confidence Interval
MLR - Estimation of New Observations
predictive ability
Predictive Ability
predictor
Modeling
PRESS
PCA - Model Order
Predictive Ability
Validation of Models
principal component regression
Principal Component Regression
Exercise - Perform a PCR by successive application of PCA and MLR
Modeling with latent variables
principal components
Literature References - Factor Analysis, Principal Components
Principal Component Analysis
Data Compression by PCA
PCA - Different Forms
Principal Component Regression
Exercise - Estimation of Boiling Points from Chemical Structure
Exercise - Dependence of PC scores on scaling of data
Exercise - Classification of unknown wine samples by PCA
Exercise - Detection of mixtures of two different wines by PCA
The NIPALS Algorithm
Relations between Loadings, Scores and Original Data
PCA of Transposed Matrices
principal diagonal
Matrix Algebra - Fundamentals
probability
Algebra of Probabilities
Bayesian Rule
Conditional Probability
Counting Rules
Events and Sample Space
Independent Events
Probability - Introduction
Probability Theory
Exercise - Probability of Observations
Exercise - Probability of a train being delayed
Summation of Probabilities
Additivity Rule
Complementary Sets and Subsets
Union and Intersection
probability density function
Exercise - Design a data set showing a bimodal probability density function
Exercise - Design a data set showing a normal probability density function
probability plot
Probability Plot
process control
Control Charts
p- and c-Charts
x- and R-Charts
process stability
Control Charts
process variability
Variability
processing unit
ANN - Single Processing Unit
propagation of errors
Error Propagation
pruning
Variable Selection - Pruning
pseudo random numbers
Random Number Generators
pseudo-inverse matrix
Moore-Penrose Pseudo-Inverse Matrix