University:
Massachusetts Institute of Technology
Course:
15.501/516 | Accounting
Academic year:

2023
Views:

338

Pages:

23
Author:

tiftstruthfully

Click to edit Master title style Methods of Uncertainty Analysis • Click to edit Master text styles • • • • Second level Third level Fourth level Fifth level “Persons to forecast the Click topretending edit Master title style future shall be considered disorderly •under Click to edit Master text subdivision 3, styles section 901 of •the Second level code and liable to a fine criminal • Third level of $250 and/or six months in • Fourth level prison.” • Fifth level 2 ClickLecture to edit Master Highlights title style • • • •• • • How Clickto touse editDecision Master text Trees styles Second How to level read PDFs (and make one from a histogram) Third level Understanding Fourth level mean vs. median, standard deviations, etc. Fifth level The role of uncertainty in climate change science 3 Elements of a Decision Tree Click to edit Master title style Uncertainty Node: Shows different possible outcomes foredit an uncertain event, and the respective • Click to Master text styles probabilities for each outcome • Second level p • Third level • Fourth level 1-p • Fifth Node: level possible actions at a choice point Decision act BAU 4 Example: Biking in the Rain Decision tree without Memory Click to edit Master title style Period 1 Decision Outcome • • • • • Period 2 Period 3 Click to H edit Master text H styles R R Second level L L Third Hlevel H R FourthRlevel L L Fifth level H R L H R L No connection between periods 6 Decision Tree with Memory Period 1 Period 2 Period 3 Click to edit Master title style Decision Outcome H • • • • • Click to edit Master text styles Second level H R Third level L Fourth level H H R Fifth levelR L H R L R L H R L L Depends on the path 7 Emissions Scenarios Click to edit Master title style • • • • • Growth AEEI Shorthand for Click to edit Master text styles Emissions H H Second level R R Third levelL L Growth H Fourth level R Fifth level L AEEI H R L H R L H R L 8 Climate Scenarios Click to edit Master title style Growth AEEI Kv S • Click to edit Master text styles H L L H • Second level R R R • LThird level H H L • Fourth level Collapse into RR, HL, LH • Fifth level In Homework Economic Uncertainty Faer L H Climate Uncertainty Probability distribution 9 Why ClickWorry to editabout Master Uncertainty? title style • To identify important and assumptions Click to edit Masterfactors text styles underlying disagreements • Second level • To know where more information is needed • Third level • To attach a range to model forecasts •• To Fourth level attitudes toward risk understand •• To Fifth levelfor learning over time account (Attaching uncertainty to predictions might be as natural as attaching cost/benefit to climate targets) 10 ofMaster Uncertainty ClickTypes to edit title style • • • • • • •• Parametric Uncertainty Click to edit Master text styles – Uncertainty in the value of a quantity Second level Model or Structural Uncertainty Third level – Uncertainty in the form of a model Fourth level vs. Quadratic relationship – e.g. Linear Fifth level Surprise/Indeterminacy – Don’t know what we don’t know 11 Describing an Uncertainty Quantity Click to edit Master title style ∞ μ x = ∫ xf x ( x)dx = E[ x] • Mean −∞ • Click to edit Master text styles •• •• • •• ∞ 2 Variance σ = ( x − μ x ) fx ( x)dx = Var[ x] Second level ∫−∞ Third level σ x = Var (x) Standard Deviation Fourth level Covariance cov( X 1 , X 2 ) = E [X 1 ∗ X 2 ] (if E[x]=0) Fifth level 2 x 12 Describing an Uncertain Quantity Click to edit Master title styleII •• Mode: value (peak) Click toMost editlikely Master text styles • Median: Value of x such that • •• • • • Second level – Prob (xx0) = 0.50 Third level Fractile: The p fractile is the value x0 such that – Prob (x