Datenanalyse und Stochastische Modellierung

0. Predictions

## Data Analysis and Stochastic Modeling

Dr. Philipp Meyer, University of Potsdam
WS 2022/2023

### What is the best prediction?

#### ...for the next movement without further information

Chapter 1
#### ...for a random movement in a potential

Chapter 2
#### ...for a directed movement given two time points

Chapter 7
#### ...for a directed movement given two time points and additional information

Chapter 13
#### ...for a directed movement given two time points and additional information

Chapter 13
#### ...for a dice throw?

source:wikipedia.org
### Mean squared error

**Evaluating predictions **\[\hat{X}\]
\[\mathrm{MSE}=\frac{1}{N}\sum_{n+1}^N (x_n-\hat{x}_n)^2\]
- The mean squared error is a commonly used metric (loss function)
- Dice throw: best guess is x=3.5

### Data-driven models

- Models can be built from first principles (bottom up) or from observations (top down)
**Here:** we start from data and construct models from observations
- This is necessary if the system is very complex and/or most parameters of the system are unknown
- Starting from general stochastic models encoding only essential information towards complex machine learning models with many parameters

### What data can we describe?

#### Air pressure and Temperature

#### Financial asset values

#### Movement of animals

#### ... or any given time series!