Course Syllabus for

# Statistical Inference for Partially Observed Stochastic Processes Statistisk inferens för partiellt observerade stokastiska processer

## FMS020F, 7.5 credits

Valid from: Spring 2016
Decided by: FN1/AndersGustafsson
Date of establishment: 2015-12-21

## General Information

Division: Mathematical Statistics
Course type: Third-cycle course
Teaching language: English

## Aim

The main aim lies in enhancing the scope of statistical problems that the doctoral student will be able to solve. The aim is also that the doctoral student shall gain proficiency with modern statistical methods for inference in partially observed stochastic processes. Partially observed processes encompass a broad class of statistical models with applications in, e.g. finance, environment, and biology. The last purpose of the course is to give the doctoral student knowledge and tools for both parameter inference in partially observed stochastic processes, and reconstruction of the unobserved parts of the process. Computational difficulties of the methods and possible solutions will be presented, allowing the students to apply the methods in their own research.

## Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• Be able to describe the principles and methods for conducting inference for partially observed stochastic processes, with focus on continuous time or space domains.
• Be able to describe and highlight potential computational difficulties in inference.
• Be able to identify suitable inferential strategies depending on the given problem formulation and application area.

Competences and Skills

For a passing grade the doctoral student must

• Be able to select and use a suitable inference strategy for the model and data at hand.
• Be able to implement software code for one or more inferential methods. Compare and discuss results.
• Be able to use the developed model for prediction.
• Present the analysis and conclusions of the analysis in a written report.

Judgement and Approach

For a passing grade the doctoral student must

• Be able to describe differences between outcomes resulting from the use of exact and approximate inference strategies.
• Be able to reflect on the considered inference methods and their strengths and limitations for different applications.

## Course Contents

Inference and data imputation for diffusions and other continuos-time stochastic processes; iterated filtering; particle marginal methods for parameter inference; approximate Bayesian computation (ABC); inference for Gaussian Markov random fields.

## Course Literature

The literature will consist of relevant key publications chosen by the lecturer(s).

## Instruction Details

Types of instruction: Lectures, exercises, project

## Examination Details

Examination formats: Written report, written assignments. To pass the course students must present the home assignments and an approved written project report.