Advanced Statistical Methods and Optimization
Preface
This is the script for the lecture “Advanced Statistical Methods and Optimization” at the DIT/Campus Cham. I do realize, that this body of knowledge has been repeated over and over, but have decided to do my own nonetheless so I can add my own flavor to the realms of statistics. This work is heavily inspired by (Wickham and Grolemund 2016). Please note that this material is copyrighted, you are not allowed to copy, at least ask for permission - you are likely to get it.
Tim Weber, Oct. 2024
Glossary
Text Abbreviations
- ANOVA
-
Analysis of Variance
- CI
-
Confidence Interval
- CL
-
Confidence Level
- CDF
-
cumulative function
- CLT
-
Central Limit Theorem
- CTQ
-
Critical To Quality
- dof
-
degree of freedom
- DoE
-
Design of Experiments
- EDA
-
Exploratory Data Analysis
- FN
-
false negative
- FP
-
false positive
- gof
-
goodness of fit
- H0
-
Null Hypothesis
- Ha
-
Alternative Hypothesis
- IQR
-
Interquartile Range
- KPI
-
Key Performance Indicator
- KS
-
Kolmogorov Smirnov
- LLN
-
Law of Large Numbers
- MLE
-
Maximum Likelihood Estimation
- MSA1
-
Measurement System Analysis Type I
- UCL
-
Upper Control Limit
- LCL
-
Lower Control Limit
- UWL
-
Upper Warning Limit
- LWL
-
Lower Warning Limit
- PCC
-
Pearson Correlation Coefficient
-
Probability Density Function
- PMF
-
Probability Mass Function
- PoI
-
Parameter of Interest
- p
-
Population proportion
- ppm
-
parts per million
- QC
-
Quality Control
-
Quantile-Quantie
- SE
-
Standard Error
- TTF
-
Time to failure
- TN
-
true negative
- TP
-
true positive
- .w.r.t
-
with respect to
- Z
-
Z-standardization
Symbol Abbreviations
- \(\alpha\)
-
significance level
- \(\beta\)
-
false negative risk
- \(\epsilon\)
-
residuals
- \(\mu_0\)
-
the true mean of a population
- \(\varphi(x)\)
-
probability density function
- \(\phi(x)\)
-
cumulative probability density function or cumulative distribution function
- \(\sigma_0^2\)
-
the true variance of a population
- \(\sigma_0\)
-
the true standard deviation of a population
- \(C_g\)
-
potential Measurement System Capability Index
- \(C_{gk}\)
-
Measurement Capability Index with systematic error
- \(C_p\)
-
potential process capability
- \(C_{pk}\)
-
actual process capability including centering
- \(k\)
-
number of predictors in a model
- \(MSE\)
-
mean squared errors
- \(n\)
-
number of data points/observations in the sample
- \(N\)
-
number of datapoints/observations in the population
- \(P\)
-
Probabilities
- \(r^2\)
-
Coefficient of determination
- \(r^2_{adjusted}\)
-
adjusted Coefficient of determination
- \(sd\)
-
the standard deviation of a dataset
- \(SSE\)
-
Sum of squared errors as calculated by
- \(x_i\)
-
the individual datapoints
- \(\bar{x}\)
-
the mean value of the datas
- \(X\)
-
Predictor Variable
- \(Y\)
-
Response Variable
- \(\hat{y}\)
-
predicted value
- \(y_i\)
-
true value