Applied Statistics - Week 7

Monday the 5th - Friday the 9th of January 2026

The following is a description of what we will go through during this week of the course. The chapter references and computer exercises are considered read, understood, and solved by the beginning of the following class, where I'll shortly go through the exercise solution.

General notes, links, and comments:
  • If last week got you interested in the intersection of statistics and machine learning, then perhaps take a look at some of the talks at the PHYSTAT - Statistics meets ML conference (which I unfortunately could not attend).

    Monday:
    We will start the week beating the sqrt(N) law! This can be done through stratification, which is the process of cleverly dividing data into "strata" (i.e. subparts), which through their homogenity and external knowledge improves sampling precision.
    I will also go through the curriculum, and answer all the possible questions you may have, perhaps sharpened by the problem set handing in.
    In the exercises, we'll try out a (simple?) example of stratification, after which you get to do it yourself and think about how to plan a sampling experiment.
    Reading:
  • You should at this point have read essentially the whole curriculum.
    Lecture(s):
  • Stratification - beating the sqrt(N) law!
  • Afterwards, I'll essentially give very short versions of the last seven week's curriculum, with focus on what you want to hear about.
    Computer Exercise(s):
  • Stratification exercise with (semi-)realistic numbers: Stratification_original.ipynb

    Tuesday:
    The subject of the day will be advanced fitting, moving towards more complicated cases. As stated, fitting is a bit of an artform, and there is little literature on the subject - only (bitter?) experience! I've tried my best in the reading list below.
    Reading:
  • Possibly Barlow page 184, section 10.2.2.
  • Possibly Cowan page 65.
  • Possibly Bevington chapters 6-8 (best of the three!).
  • Curve Fitting (Wikipedia)
    Lecture(s):
  • Advanced Fitting
    Computer Exercise(s):
  • Advanced fitting:
  • FittingTricks_1.XfarFromZero_original.ipynb
  • FittingTricks_2.CombinedParameters_original.ipynb
  • FittingTricks_3.HighCorrelations_original.ipynb

    Friday:
    The day will focus on time series, which is a separate subject, yet fairly straight forward, once you get the hang of the idea. The associated exercise is inspired by biophysics.

    Reading:
  • No reading - logic and reason suffices.
    Lecture(s):
  • Time Series (Mathias)
    Computer Exercise(s):
  • Time series: EstimatingFrequencies_original.ipynb
    Last updated: 2nd of January 2026.