Objectives
The element of uncertainty permeates many facets of nature and life. For instance, we may not be certain about the traffic condition for your trip to an important job interview, or the level of a stock index on the next day, or when a natural disaster will strike us, or how receptive is the market about a new product. Whether the uncertainty is inherent in the situation or arises from the lack of complete knowledge about the situation, it is fortuitous that it is amenable to the same theoretical treatment through the use of probabilistic modeling. To be of practical value, such treatment often involves the judicious use of quantitative inputs and entails the ability to acquire, process, evaluate and analyze the inputs that are pertinent to the situation. Quantitative reasoning is a reliable tool, and often the only meaningful tool, by which we gain insights into a situation, draw sound conclusions and make optimal decisions on the basis of available information.
The Uncertainty Module UQR2202 aims to motivate the concepts of quantitative analysis through examples gleaned from encounters in daily life, scientific endeavors, news reports, and opinion polls, … Besides acquiring the proficiency to use quantitative data in making cogent and logical arguments and inference, it is hoped that the students would gain an appreciation of the probabilistic underpinnings that provide a window to the fascinating microcosm of nature's laws.
This module helps students:
- Understand information from surveys and scientific studies and to sift the useful and the accurate from the useless and the misleading;
- Become more informed and critical consumers of statistical data;
- Develop an understanding of chance phenomena.
Course outline
Finding data in life situation
Controlled experiments and Observational studies; Measurements; Surveys and sampling
Finding life in data
Numerical summary; Graphical visualization; Bell-curves; Association versus Causation
Understanding uncertainty in life
Different approaches to probability; Axiomatic approach; Conditional probability; Independent events; Bayes formulas; Law of Large Numbers; Central Limit Theorem
Coincidences, Surprises and Paradoxes
Monty Hall problem and its variations; Birthday problems; Simpson’s Paradox; Prisoner’s dilemma
Textbooks and References
Main text: “Seeing Through Statistics” by Jessica Utts.
A very useful supplementary text: “Statistics” by Freedman, Pisani and Purves.
Other useful reading materials include “The Statistical Sleuth” by R Schafer; and “Statistics: A guide to the unknown” by J Tanur et al.
Related Web Resources
Teaching and Assessment
- Limited to 35 students.
- 2 h/week of lectures, with a 10 minutes break
- 2 h/ week of tutorials where the students take turns in leading the discussion on the reading assignments and problems in assignment sheets.
- Assessment
- Semester Project (in groups of not more than 3) 35%
- Tutorial facilitator/participation 15%
- Mid-term test 15 %
- Final Exam 35%
A term paper (between 10 to 20 pages) on the semester project is required. Possible topics would be provided in due course. The topics aim to reinforce or extend the materials covered in the module.
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