# Blog thought

#### Nature of Continuity for Measure & Probability Theory – Part I

Introduction There are many textbooks, posts, videos and papers about continuity. However, it is hard to find a cohesive introduction ...

#### Fundamentals of Topology

In this brief post, we investigate the topological foundations of analysis and give some of its first applications. We limit ...

#### Probability Integral Transform & Quantile Function Theorem

Introduction We present simple illustrations, explanations and proofs for two very important theorems,
• the probability integral transformation, and,
• the quantile ...

#### Inner Products, Norms and Metrics

Most people do have an intuitive understanding of the real number system: it is the number system that should be ...

#### Conditional Probability & Bayes Rule

Conditional Probabilities Let us consider a probability measure $P: \mathcal{A} \rightarrow \mathbb{R}$ of a measurable space $(\Omega, \mathcal{A})$. Further, let ...

#### Uncertainty and Capacities in Finance

Monotone Set Functions and the Choquet Integral The quote of the famous statistician George E. P. Box that "all models ...

#### Decision Problems, Risk and Uncertainty

In this post, an introduction to decision-making under risk and uncertainty is provided. To this end, basic concepts and components ...

#### Binomial- and Poisson-Mixture Model

Introduction The assumption of independent and identically distributed random variables, short i.i.d., my be quite handy since it simplifies several ...

#### Poisson Distribution

Poisson distributions are very important not only for counting events during a fixed period of time but also for different ...

#### GPU TensorFlow Installation Guide for Windows

Before we actually start the installation process of the GPU-accelerated Python API of TensorFlow on a Windows platform, we shortly ...

#### What is an Empirical Copula?

Introduction Copulas are an important concept in statistics and beyond to describe dependency structures of continuous distributions. However, what can ...