Type of Work:

bachelor

Supervisor:

Affiliation/Phone:

ÚTIA AV ČR, v.v.i., oddělení AS, 266052274

Tasks:

1. Learn about Bayesian parameter estimation.

2. Familiarize yourself with the concept of recursive Bayesian estimation.

3. Learn about assigning a priori probability to hypotheses.

4. Design an estimation algorithm that at each step: i) generates a new sample of parameters; ii) assigns a priori probability to all samples; iii) correct those probabilities with the Bayes relation; iv) excludes the least suitable parameter sample.

5. Program the result for a simple useful model and compare the quality of your algorithm with a suitable standard.

Recursive estimation of model parameters is a key part of adaptive systems predicting or influencing their complex random environment. Most models do not allow us to use the desired exact Bayesian estimation. Therefore it is necessary to implement them approximately. Monte Carlo procedures allow this, but their efficiency is not great. The work will be focused on an attempt to develop an original variant of the Monte Carlo methodology based on the use of: i) the recently proposed assignment of a priori probability to a new hypothesis; ii) Bayesian rules for estimating confidence in individual parameter samples; iii) linear reduction of the number of considered samples.

Bibliography:

Recommended literature (parts selected after agreement with the supervisor)

1. V. Peterka, Bayesian System Identification, in P. Eykhoff "Trends and Progress in System Identification", Pergamon Press, Oxford, 239-304, 1981.

2. A. Doucet, V.B. Tadic, Parameter estimation in general state-space models using particle methods, Annals of the institute of Statistical Mathematics,55(2),409-422,2003.

3. A. Doucet, M. Johansen, A tutorial on particle filtering and smoothing: 15 years later, In: Handbook of Nonlinear Filtering, Oxford Univ. Press, UK, 2011.

4. M. Kárný, On Assigning Probabilities to New Hypotheses, Pattern Recognition Letters, 150(1), 170-175, 2021.