Expected Preparations:

  Calculus:
Functions and equations; Polynomial functions, logarithms, trigonometric functions; Integrals and derivatives; Theorem and proof.
   [FND-STA]
Probability 		 
  If you are not already familiar with the prior knowledge listed above, you need to prepare yourself from other information sources.   The units listed above are part of this course and contain important preparatory material.  
Keywords: Nature of a probability distribution; important distributions; comparing observed and simulated probability distributions; Kullback-Leibler divergence; the Kolmogorov-Smirnov test
Objectives:

This unit will …

  • … introduce basic concepts of probability distributions;

  • … demonstrate the Poisson, the uniform, and the normal distribution;

  • … teach how to visually and quantitatively compare them.

 Outcomes:

After working through this unit you …

  • … can interpret observed events in terms of probability distributions;

  • … are familar with the Poisson, the uniform, and the normal distribution;

  • … can compare observed distributions against the normal distribution with qqnorm().

  • … can compare observed distributions against each other with qqplot().

  • … can use Kullback-Leibler divergence for discrete distributions, and ks.test() for continuous distributions to quantify differences.

Deliverables:

Time management: Before you begin, estimate how long it will take you to complete this unit. Then, record in your course journal: the number of hours you estimated, the number of hours you worked on the unit, and the amount of time that passed between start and completion of this unit.

Journal: Document your progress in your Course Journal. Some tasks may ask you to include specific items in your journal. Don’t overlook these.

Insights: If you find something particularly noteworthy about this unit, make a note in your insights! page.

Evaluation:

NA: This unit is not evaluated for course marks.

Contents

Probability distributions are at the core of any statistical analysis, in which modelled distributions are compared with sampled distributions to relate an observation to our theoretical understanding. This unit introduces the principles, discusses Poisson, uniform, and normal distributions, and presents methods to compare distributions with each other and quantify the difference.

 

Task…

  • Open RStudio and load the ABC-units R project. If you have loaded it before, choose File ▸ Recent projects ▸ ABC-Units. If you have not loaded it before, follow the instructions in the RPR-Introduction unit.
  • Choose Tools ▸ Version Control ▸ Pull Branches to fetch the most recent version of the project from its GitHub repository with all changes and bug fixes included. This ensures that your data and code remain up to date when we update, or fix bugs.
  • Type init() if requested.
  • Open the file FND-STA-Probability_distribution.R and follow the instructions.

     

    Note: take care that you understand all of the code in the script. Evaluation in this course is cumulative and you may be asked to explain any part of code.

 

Questions, comments

If in doubt, ask! If anything about this contents is not clear to you, do not proceed but ask for clarification. If you have ideas about how to make this material better, let’s hear them. We are aiming to compile a list of FAQs for all learning units, and your contributions will count towards your participation marks.

Improve this page! If you have questions or comments, please post them on the Quercus Discussion board with a subject line that includes the name of the unit.

References

Page ID: FND-STA-Probability_distribution

Author:
Boris Steipe ( <boris.steipe@utoronto.ca> )
Created:
2017-08-05
Last modified:
2022-09-14
Version:
1.0.01
Version History:
–  1.0.1 2020 Maintenance
–  1.0 New material
Tagged with:
–  Unit
–  Live
–  Links to R course project

 

[END]