# Frequentist and Bayesian Statistical Inference

## Course Description

**Statistical inference** is the process of using data analysis to draw conclusions about populations or scientific truths on the basis of a data sample. Inference can take many forms, but primary inferential aims will often be **point estimation**, to provide a “best guess” of an unknown parameter, and **interval estimation**, to produce ranges for unknown parameters that are supported by the data.

Under the **frequentist** approach, parameters and hypotheses are viewed as unknown but fixed (nonrandom) quantities, and consequently there is no possibility of making probability statements about these unknowns. As the name suggests, the frequentist approach is characterized by a frequency view of probability, and the behaviour of inferential procedures is evaluated under hypothetical repeated sampling of the data.

Under the **Bayesian** approach, a different line is taken. The parameters are regarded as random variables. As part of the model a **prior** distribution of the parameter is introduced. This is supposed to express a state of knowledge or ignorance about the parameters before the data are obtained (*ex ante*). Given the prior distribution, the probability model and the data, it is now possible to calculate the **posterior** (*ex post*) probability of the parameters given the data. From this distribution inferences about the parameters are made.

In modern era statistical inference is facilitated by **probabilistic programming (PP)** languages. The veteran BUGS/WinBUGS/OpenBUGS has been complemented by PyStan and PyMC3; and now PyMC4 is on the horizon.

In this course we will examine both frequentist and Bayesian approaches, explain probabilistic programming (PP) languages, and illustrate their usage with examples.

## Details

## Syllabus

- Classical probability
- Interpretations of probability
- Axiomatic probability
- Frequentist inference
- Bayes’s theorem, its various forms, and examples
- Bayesian inference
- Frequentist and Bayesian approaches to regression
- Probabilistic programming languages

## Schedule

Time | Activity |
---|---|

08:30–09:00 | Registration and welcome |

09:00–09:45 | Lecture 1: Classical probability |

09:45–10:30 | Lecture 2: Interpretations of probability |

10:30–11:00 | Coffee break |

11:00–11:45 | Lecture 3: Axiomatic probability |

11:45–12:30 | Lecture 4: Frequentist inference |

12:30–13:30 | Lunch |

13:30–14:15 | Lecture 5: Bayes's theorem, its various forms, and examples |

14:15–15:00 | Lecture 6: Bayesian inference |

15:00–15:30 | Coffee break |

15:30–16:15 | Lecture 7: Frequentist and Bayesian approaches to regression |

16:15–17:00 | Lecture 8: Probabilistic programming languages |

## Instructor

## Paul Bilokon, PhD

**CEO and Founder of Thalesians Ltd**. Previously served as Director and Head of global credit and core e-trading quants at Deutsche Bank, the **teams that he helped set up** with Jason Batt and Martin Zinkin. Having also worked at Morgan Stanley, Lehman Brothers, and Nomura, Paul **pioneered electronic trading in credit** with Rob Smith and William Osborn at Citigroup.

Paul has graduated from Christ Church, University of Oxford, with a **distinction and Best Overall Performance prize**. He has also graduated twice from Imperial College London.

Paul’s lectures at Imperial College London in machine learning for MSc students in mathematics and finance and **his courses consistently achieve top rankings among the students**.

Paul has made **contributions to mathematical logic, domain theory, and stochastic filtering theory**, and, with Abbas Edalat, has published a prestigious LICS paper. Paul’s books are being published by Wiley and Springer.

Dr Bilokon is a Member of the British Computer Society, Institution of Engineering and Technology, and European Complex Systems Society.

Paul is a **frequent speaker at premier conferences** such as Global Derivatives/QuantMinds, WBS QuanTech, AI, and Quantitative Finance conferences, alphascope, LICS, and Domains.