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

FMS020F, 7.5 högskolepoäng

Gäller från och med: Spring 2016
Beslutad av: FN1/AndersGustafsson
Datum för fastställande: 2015-12-21

Allmänna uppgifter

Avdelning: Mathematical Statistics
Kurstyp: Ren forskarutbildningskurs
Undervisningsspråk: English

Syfte

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.

Mål

Kunskap och förståelse

För godkänd kurs skall doktoranden

• 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.

Färdighet och förmåga

För godkänd kurs skall doktoranden

• 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.

Värderingsförmåga och förhållningssätt

För godkänd kurs skall doktoranden

• 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.

Kursinnehåll

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.

Kurslitteratur

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

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, övningar, projekt

Kursens examination

Examinationsformer: Skriftlig rapport, inlämningsuppgifter. To pass the course students must present the home assignments and an approved written project report.
Betygsskala: Underkänd, godkänd
Examinator:

Antagningsuppgifter

Förkunskapskrav: Basics of inference for stochastic processes, Bayesian methods and Monte Carlo methods (e.g. Markov Chain Monte Carlo, Metropolis-Hastings method). For example having taken the courses Time series analysis (FMS051/MASM17) and Monte Carlo and Empirical Methods for Stochastic Inference (FMS091/MASM11).

Kurstillfällesinformation

Kontaktinformation och övrigt

Kursansvariga:
Hemsida: http://www.maths.lu.se/index.php?id=110381