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Details for Course FMS092F Monte Carlo Methods for Statistical Inference

General
• FMS092F
• Active
Course Name
• Monte Carlo Methods for Statistical Inference
Course Extent
• 7.5
Type of Instruction
• Course given jointly for second and third cycle
• 7152 (Centre of Mathematical Sciences / Mathematical Statistics)
•  -01-13
• FN1/Anders Gustafsson

Current Established Course Syllabus

General
• English
• Every spring semester
Aim
• The aim is that doctoral student shall gain proficiency with modern computer intensive statistical methods and use these to estimate quantities and parameters in complex models that arise in different applications (e.g. economics, signal processing, biology, climate, and environmental statistics). The purpose of the course is to give the doctoral student tools and knowledge to handle complex statistical problems and models in order to be able to use these in the doctoral student's own research. Further, the doctoral student should be able to assess the uncertainty of these estimates. The main aim lies in enhancing the scope of statistical problems that the doctoral student will be able to solve.
Contents
• Simulation based methods of integration and statistical analysis. Monte Carlo methods for sequential problems. Markov chain methods, e.g. Gibbs sampling and the Metropolis-Hastings algorithm, for simulation and inference. Bayesian modelling and inference. The re-sampling principle, both non-parametric and parametric. Methods for constructing confidence intervals using re-sampling. Simulation based tests as an alternative to asymptotic parametric tests.
Knowledge and Understanding
• For a passing grade the doctoral student must
• Be able to describe fundamental principles of Monte Carlo integration and random variable generation.
Be able to explain and use the concept of statistical uncertainty from a frequentist perspective as well as from a Bayesian perspective.
Be able to describe fundamental principles of parametric and non-parametric resampling.
Competences and Skills
• For a passing grade the doctoral student must
• Given a stochastic model and problem formulation, be able to choose relevant quantities in a way that permits approximation using Monte Carlo methods.
Given a (possibly multivariate) probability distribution, be able to suggest and implement in a computer program, a method for generation of random variables from this distribution.
Given a large number of generated random variables from a probability distribution, be able to approximate relevant probabilities and expectations as well as estimate the uncertainty in the approximated quantities.
Given a model description and a statistical problem, be able to suggest a simple permutation test and implement it in a computer program.
Given a model description and a statistical problem, be able to suggest a resampling procedure and implement it in a computer program.
Be able to present the course of action taken and conclusions drawn in the solution of a given statistical problem.
Judgement and Approach
• For a passing grade the doctoral student must
• Be able to identify and problemise the possibilities and limitations of statistical inference.
Types of Instruction
• Lectures
• Laboratory exercises
• Project
Examination Formats
• Written report
• Oral project presentation
• Failed, pass
Assumed Prior Knowledge
Selection Criteria
Literature
• Sköld, M.: Computer Intensive Statistical Methods.
Further Information
Course code
• FMS092F
•  -01-13
• FN1/Anders Gustafsson

All Established Course Syllabi

1 course syllabus.

Valid from First hand in Second hand in Established
Spring 2014 2014‑01‑13 11:49:59 2014‑01‑13 11:59:25 2014‑01‑13

Current or Upcoming Published Course Occasion

No matching course occasion was found.

All Published Course Occasions

7 course occasions.

Course code ▽ Course Name ▽ Division ▽ Established ▽ Course syllabus valid from ▽ Start Date ▽ End Date ▽ Published ▽
FMS092F Monte Carlo Methods for Statistical Inference Mathematical Statistics 2014‑01‑28 Spring 2014 2014‑01‑21 2014‑03‑21 2014‑01‑28
FMS092F Monte Carlo Methods for Statistical Inference Mathematical Statistics 2014‑11‑13 Spring 2014 2015‑01‑20 2015‑03‑21 2014‑11‑13
FMS092F Monte Carlo Methods for Statistical Inference Mathematical Statistics 2017‑12‑20 Spring 2014 2018‑01‑15 2018‑03‑10 2017‑12‑20
FMS092F Monte Carlo Methods for Statistical Inference Mathematical Statistics 2018‑10‑18 Spring 2014 2019‑01‑21 2019‑03‑10 2018‑10‑18
FMS092F Monte Carlo Methods for Statistical Inference Mathematical Statistics 2019‑12‑06 Spring 2014 2020‑01‑21 2020‑03‑18 2019‑12‑06
FMS092F Monte Carlo Methods for Statistical Inference Mathematical Statistics 2020‑11‑30 Spring 2014 2021‑01‑18 2021‑03‑20 2020‑11‑30
FMS092F Monte Carlo Methods for Statistical Inference Mathematical Statistics 2022‑01‑19 Spring 2014 2022‑01‑18 2022‑03‑22 2022‑01‑19