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  • Courseware 
    Observation Theory: Estimating the Unknown

    Observation Theory: Estimating the Unknown

    Are you an engineer, scientist or technician? Are you dealing with measurements or big data, but are you unsure about how to proceed? This is the course that teaches you how to find the best estimates of the unknown parameters from noisy observations. You will also learn how to assess the quality of your results. TU Delft’s approach to observation theory is world leading and based on decades of experience in research and teaching in geodesy and the wider geosciences. The theory, however, can be applied to all the engineering sciences where measurements are used to estimate unknown parameters. The course introduces a standardized approach for parameter estimation, using a functional model (relating the observations to the unknown parameters) and a stochastic model (describing the quality of the observations). Using the concepts of least squares and best linear unbiased estimation (BLUE), parameters are estimated and analyzed in terms of precision and significance. The course ends with the concept of overall model test, to check the validity of the parameter estimation results using hypothesis testing. Emphasis is given to develop a standardized way to deal with estimation problems. Most of the course effort will be on examples and exercises from different engineering disciplines, especially in the domain of Earth Sciences. This course is aimed towards Engineering and Earth Sciences students at Bachelor’s, Master’s and postgraduate level.

    Keywords:
    Observers (Control theory) Mathematical statistics
    Resource Type:
    Courseware
     
  • Courseware 
    Math 131B: Introduction to Probability and Statistics

    Math 131B: Introduction to Probability and Statistics

    Second introductory course covering basic principles of probability and statistical inference. Topics: Point estimation, interval estimating, and testing hypotheses, Bayesian approaches to inference.

    Subjects:
    Mathematics and Statistics
    Keywords:
    Probabilities Mathematical statistics
    Resource Type:
    Courseware
     
  • Courseware 
    Math 131A: Introduction to Probability and Statistics

    Math 131A: Introduction to Probability and Statistics

    Introductory course covering basic principles of probability and statistical inference. Topics covered in this course: Axiomatic definition of probability, random variables, probability distributions, expectation.

    Subjects:
    Mathematics and Statistics
    Keywords:
    Probabilities Mathematical statistics
    Resource Type:
    Courseware
     
  • Courseware 
    Statistics for Applications

    Statistics for Applications

    This course offers an in-depth the theoretical foundations for statistical methods that are useful in many applications. The goal is to understand the role of mathematics in the research and development of efficient statistical methods.

    Subjects:
    Mathematics and Statistics
    Keywords:
    Mathematical statistics
    Resource Type:
    Courseware
     
  • Courseware 
    Mathematical Statistics

    Mathematical Statistics

    This course provides students with decision theory, estimation, confidence intervals, and hypothesis testing. It introduces large sample theory, asymptotic efficiency of estimates, exponential families, and sequential analysis.

    Subjects:
    Mathematics and Statistics
    Keywords:
    Mathematical statistics
    Resource Type:
    Courseware