hamza-sadruddin/uncertainty_course

Principles of Data and Error Analysis in Engineering Measurements

(Topics in Signal Processing)
Instructor: Miodrag Bolic, University of Ottawa, Ottawa, Canada
www.site.uottawa.ca/~mbolic
Time and place: Monday 10:00 - 13:00, MNO E218
Course code: ELG 7172B (EACJ 5600)

Calendar Style Description:

Uncertainty, Uncertainty propagation, Bayesian Inference, Bayesian Filtering, Data fusion, Metrology, Measurement Science, Error Analysis, Measures of Agreement, Data Quality, Data quality index. Case studies will be drawn from various fields including biomedical instrumentation, sensors and signal processing.

Prerequisites: Digital signal processing course We expect participating students to bring basic knowledge and experience in

• Programming using Python
• Elementary Probability
• Elementary Statistics

Grading: For collecting the credits the student are expected to

• assignments (45% of the grade) + optional up 25% bonus points for small projects/literature reviews,
• scribing(15% of the grade)
• final exam (40% of the grade)

Syllabus:

Part I Statistical concepts required to understand uncertainty

• Intro: Definitions and motivation

Uncertainty, data quality, data analysis
Calibration, Precision, Accuracy, traceability, reproducibility, error
Measurement model

• Monte Carlo methods

Random variable generation, Importance sampling, Metropolis-Hastings Algorithm, MCMC

• Bootstrap principles

Principles or resampling, pivoting, bootstrap for time series

• Statistical intervals

Confidence intervals for a Normal distribution, Bootstrap based statistical intervals

• Bayesian analysis and inference

Part II Uncertainty when no data and/or with historical data is available

• Uncertainty in Metrology, GUM

Terminology, uncertainty quantification based on GUM

• Uncertainty propagation

Example of uncertainty propagation for temperature, pressure and other sensors

• Sensitivity analysis

Global sensitivity analysis, variance based method, Monte Carlo approaches, application to exploring sensitivity to parameters in the models in biomedical instrumentation

• Regression analysis

Linear and non-linear fitting, Confidence intervals of the estimates

• Model calibration and parameter estimation

Adjusting model parameters in order to improve the agreement between the model output and collected data, Regression analysis for calibration

Part III Uncertainty for real-time analysis

• Bayesian inference

Bayesian theorem, importance of prior, implementation using Markov Chain Monte Carlo, Prediction and Credible intervals
Model checking
Hierarchical Bayesian models

• Time series and HMM
• Particle filtering

State-space model, Bayesian filtering and Monte Carlo simulations, From complex probabilistic formulas to implementation

• Data and Sensor fusion
• Bayesian neural networks

Links

• This course at Github
  
• Virtual campus at the University of Ottawa

Support or Contact

Miodrag Bolic email