Sensitivity analysis
Objective. Measure parameter influence and uncertainty.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Sensitivity analysis measures how much a model's output changes in response to changes in its input parameters, identifying which assumptions most affect conclusions. The simplest measure is the partial derivative of output with respect to a parameter, often normalised as an elasticity (∂y/y)/(∂p/p), which compares relative rather than absolute changes across parameters of different units. Example: if population model P=P₀e^(rt) is evaluated at t=10, the sensitivity ∂P/∂r = P₀te^(rt) shows that uncertainty in growth rate r has a rapidly growing effect on predicted population as t increases. Identifying high-sensitivity parameters tells modellers where better data collection would most improve reliability.
Worked example
A model gives output y = 3x² with x = 2. Use sensitivity analysis to find ∂y/∂x at this point.
- 1Differentiate the model: ∂y/∂x = 6x
- 2Substitute x = 2
- 3Compute: ∂y/∂x = 6×2
- 4Simplify: ∂y/∂x = 12
Answer: 12
Concept mastery
Based on your past attempts at this lesson — the question types to practise again come first.
Complete a practice set to see your concept breakdown here.
Practice
Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.
Start practisingCommon mistake. Students treat all parameters as equally important sources of uncertainty without computing their actual sensitivity; a parameter with near-zero ∂y/∂p barely affects predictions even if poorly known.
Your progress
Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.
0 of 5 steps complete
Your place saves automatically as you read.