Daten werden in allen Bereichen des gesellschaftlichen Lebens erfasst, seien es riesige Datenmengen, die sich in Medizin, Biologie, Bioinformatik, Finanzwesen, Marketing und Soziologie ergeben oder auch weniger umfangreiche Beobachtungen bei naturwissenschaftlichen Experimenten und technischen Qualitätstests. Die Aufgabe der Statistik ist "Learning from data". Dabei geht es darum, Methoden und Konzepte aufzuzeigen, wie man die Informationen, die in diesen Daten stecken, herausfiltert, wie man zugrundeliegende Strukturen erkennt und künftige Tendenzen vorhersagt. Ziel der Vorlesung ist es, ausgehend von ausgewählten Problemstellungen statistische Grundprinzipien zur Analyse von Daten zu vermitteln, um die in Literatur und Softwarepaketen enthaltenen statistischen Verfahren sinnvoll anzuwenden. Daten werden als Werte von zufälligen Größen betrachtet und die Gültigkeit der hergeleiteten Schlüsse wird durch die Angabe von Wahrscheinlich-keiten quantifiziert. Deshalb werden neben Methoden aus der Statistik auch wichtige Grundbegriffe aus der Wahrscheinlichkeitstheorie eingeführt. Folgende Themen werden behandelt:
| Einführung | 01:31:20 | |
|---|---|---|
| Definition of a Confidence Intervall | 00:00:00 | |
| Approximative Confidence Intervall for a Probability | 00:00:00 | |
| What is a test? | 00:00:00 | |
| Possible errors | 00:00:00 | |
| Construction of a test procedur | 00:00:00 |
| t-Test | 01:26:10 | |
|---|---|---|
| Transition | 00:00:00 | |
| Connection: Test and Confidence Interval | 00:00:00 | |
| t-Tests | 00:00:00 | |
| Realization in R | 00:00:00 | |
| Two-sample-t-Test | 00:00:00 | |
| Power of the t-Test | 00:00:00 |
| Binomial-Test | 01:30:11 | |
|---|---|---|
| Transition | 00:00:00 | |
| Table of binomial distribution | 00:00:00 | |
| binomial test for two-sided hypothesis | 00:00:00 | |
| Goodnes of fit test | 00:00:00 | |
| Q-Q-Plots | 00:00:00 |
| Test and distribution for discrete random-values | 01:28:04 | |
|---|---|---|
| Formulation of the problem | 00:00:00 | |
| Stating the problem | 00:00:00 | |
| Testing homogeneity | 00:00:00 | |
| Contingency table | 00:00:00 | |
| Further Example | 00:00:00 |
| Test of autonomy | 01:29:37 | |
|---|---|---|
| Distribution of the number of runs | 00:00:00 | |
| Transition | 00:00:00 | |
| Kendalls Tau | 00:00:00 | |
| run test | 00:00:00 | |
| Excel | 00:00:00 | |
| 2-random sample T-Test | 00:00:00 | |
| Example: Alcohol | 00:00:00 | |
| New Segment | 00:00:00 |
| Parametrische Regression I | 01:30:45 | |
|---|---|---|
| Ermittlung des Median | 00:00:00 | |
| Berechnung des Korrelationsassistenten | 00:00:00 | |
| Aim | 00:00:00 | |
| Approaches for the estimation of f | 00:00:00 | |
| Inputs | 00:00:00 |
| Parametrische Regression I | 01:30:26 | |
|---|---|---|
| Repetition | 00:13:20 | |
| Notation Regression | 00:22:30 | |
| Properties of the l.s.e. | 00:17:22 | |
| Simple linear regression | 00:06:09 | |
| Standart errors | 00:32:07 |
| Parametric regression II | 01:30:36 | |
|---|---|---|
| Linear regression in R | 00:14:33 | |
| Coefficient of determination | 00:13:24 | |
| The normal regression model | 00:20:16 | |
| Example in R | 00:18:30 | |
| Prediction intervall for Ynen | 00:24:52 |
| Parametric regression III | 01:31:49 | |
|---|---|---|
| Confidence ellipsoids | 00:10:14 | |
| F-Test Examples | 00:25:55 | |
| Test procedure | 00:08:44 | |
| F-Distribution | 00:23:21 | |
| Normale Quantile Plot | 00:11:21 | |
| Backward procedure | 00:16:10 |
| Linear regression | 01:28:49 | |
|---|---|---|
| Realization in Excel | 00:17:25 | |
| Example Phosphateindex | 00:22:10 | |
| Weighted least squares estimator | 00:11:21 | |
| Logit model | 00:16:56 | |
| Demonstration | 00:00:00 | |
| Estimation Procedure | 00:10:17 |
| Discussion of exercises | 01:31:42 | |
|---|---|---|
| The model | 00:07:13 | |
| Linear regression | 00:20:32 | |
| Monte Carlo Simulation | 00:12:19 | |
| Exercise 3 | 00:18:14 | |
| Exercise 3 task 2 | 00:10:55 | |
| Exercise 3 mixing music | 00:16:59 | |
| Q-Q-Plot | 00:08:01 |
| Introduction | 01:20:01 | |
|---|---|---|
| Outline | 00:01:50 | |
| Introduction | 00:15:35 | |
| Histograms | 00:27:48 | |
| Nearest neighbor estimation | 00:14:38 | |
| Example | 00:12:50 | |
| Properties of kernel estimators | 00:08:36 |
| Eigenschaften von Kernschätzern | 01:29:04 | |
|---|---|---|
| Start | 00:02:34 | |
| Mean squared error | 00:23:28 | |
| Summarizing | 00:06:01 | |
| Test statistic | 00:19:50 | |
| Normal reference band | 00:09:59 | |
| Estimation | 00:13:43 | |
| Different points of view | 00:14:52 |
| Methods of estimation | 01:30:53 | |
|---|---|---|
| Organisational matters | 00:03:05 | |
| Local constant regression estimator | 00:18:04 | |
| Local linear | 00:10:25 | |
| Nonparametric regression | 00:23:17 | |
| Comparison | 00:09:38 | |
| choice of the bandwidth | 00:12:55 | |
| Plug-in Method | 00:14:56 |
| Adaptive Bestimmung des Glättungsparameters | 01:30:22 | |
|---|---|---|
| Repetition | 00:08:59 | |
| Cross validation | 00:12:27 | |
| Adaptive bandwidth selection in R | 00:22:39 | |
| Local linear estimator | 00:13:59 | |
| Additive model | 00:20:03 | |
| Summarizing Additive model | 00:13:25 |
| Nonparametric logistic models | 01:35:00 | |
|---|---|---|
| Outline | 00:04:01 | |
| Nonparametric logistic models | 00:24:08 | |
| General Nonparametric additive logistic model | 00:11:56 | |
| Testing | 00:24:32 | |
| Exercice I | 00:07:47 | |
| Exercice II | 00:22:49 |
| Cluster analysis | 01:30:39 | |
|---|---|---|
| exercises | 00:12:57 | |
| Logistic regression : Cancer remission | 00:14:02 | |
| Mixture of normal distribution | 00:11:57 | |
| For discussion | 00:12:24 | |
| What is cluster analysis | 00:09:59 | |
| K-means algorithm | 00:18:07 | |
| Example: Illustration | 00:12:37 |
| Linear and quadratic discrimination and classification | 01:31:36 | |
|---|---|---|
| Clustering Approaches | 00:13:04 | |
| Dendrogramm | 00:21:05 | |
| Classification Rules | 00:09:01 | |
| Linear discriminant analysis LDA | 00:20:43 | |
| Probability of misclassification | 00:13:54 | |
| Canonical DA and Fisher\'s LDA | 00:15:02 |
| Discriminant Analysis | 01:31:08 | |
|---|---|---|
| Review | 00:08:01 | |
| Example | 00:22:16 | |
| Quadratic discriminant analysis | 00:16:07 | |
| Linear discriminant analysis | 00:12:59 | |
| Nonparametric discriminant analysis | 00:21:56 | |
| Summary | 00:10:59 |
| Exerciseanalysis of nonparametric regression | 01:32:13 | |
|---|---|---|
| Organisational matters | 00:04:07 | |
| Realization of equal-distributed random-variables | 00:15:15 | |
| Graphs | 00:13:10 | |
| Nonparametric logistic | 00:21:44 | |
| Type of task-formulation | 00:21:22 | |
| Example Clusteranalysis | 00:08:13 | |
| Example discrimination analyse | 00:09:45 |
| Test preparation | 01:39:38 | |
|---|---|---|
| Start | 00:02:51 | |
| Adaptiontest | 00:12:57 | |
| Indipendence- and homogenity-test | 00:24:43 | |
| Linear model | 00:20:03 | |
| Seeding rate | 00:18:39 | |
| Logistic regression | 00:21:39 |
