0655'122B Bayesian Statistics

1
0655.122B Bayesian Statistics

• If you scored 65 or higher in Bursary Mathematics
  with Statistics
• And you scored 65 or higher in Bursary Calculus
• Then, you might like to enrol in 0655.122B
  Bayesian Statistics instead of 121.
• Bayesian Statistics is important in
• The Law
• Artificial Intelligence
• Neural Networks
• Probabilistic expert systems and computer aided
  reasoning

2
What is Statistics?

• The subject matter of statistics is the process
  of found oout more about the real world by
  collecting and making sense out of data.
• This course
• is not just about doing statistical calculations
• it is also about non-mathematical ideas
• Non-mathematical ideas are at least as important
  as technical skills for
• Successful completion of statistical studies in
  real life
• Success in this course

3
The Cycle of Statistical Investigation
4
Polls and Surveys

• A poll or a survey is the process of collecting a
  sample of data from a population in order to
  determine information about the whole population
• Examples
• A market researcher may telephone 500 people and
  ask which brand of toothpaste and soap they use
• A company which has just bought a consignment of
  steel rods may measure a sample and keep or
  return the consignment depending on the results
• A team of forensic scientists may collect gym
  clothes from students and look for fragments of
  glass

5
Terminology

• What is a population?
• What is a sample?
• Why do we need a sample?

6

• There are 60 circles in the picture to the left
• The diameters of the circles are 0.5cm, 1cm,
  1.5cm, 2cm, 2.5cm and 3.5cm
• Scale has not been preserved so dont measure
  them!
• Choose a sample of 5 circles and work out the
  mean (average) diameter

7
2 19 18 17 16 15 14 13 12 11 10 09 08 07 06 05 0-
8

• Now choose a sample of 5 circles using the table
  of numbers below

• 71578 81355 39007 60764
• 87652 50354 22183
• 14935 09519 97820 86085

• Take the last digit of your telephone number
  (e.g. 7)
• Take pairs of digits to get the circle number
• Calculate the average