example.md

title	subtitle	author	date
What is a Good Forecast?	An Essay on the Nature of Goodness in Weather Forecasting (Allan H. Murphy)	Are Frode Kvanum	05.11.2021

There are three types of Goodness in Weather Forecasts

1. Consistency

2. Quality

3. Value

Type 1 Goodness : Consistency

• A forecaster's internal assessment is the Judgement
• A forecaster's external assessment is the Forecast
• Forecasts should correspond with the best Judgement

Type 2 Goodness : Quality

• Correspondence between Forecasts and Observations
• Observations are not controllable

Type 3 Goodness : Value

• Benefits realized/expenses incurred by using the forecast
• ex-ante forecast value

Relating the three types of Goodness

For both Type 2 and Type 3 Goodness to be maximized, the best a forecaster can do is to provide forecasts consistent with the Judgement

• Consistency feeds directly into Quality and Value

Consistency and Quality

• The Brier score $$ BS = (f - x)^2 $$ The MSE of probabilistic forecasts

• Expected Brier score $$ EBS = p(1 - p) + (f - p)^2 $$

• Differentiated with respect to $f$ $$= 2f - 2p$$

Consistency and value

$EE(protect) = rC + (1 - r)C = C$
$EE(\text{do not protect}) = rL + (1 - r)0 = rL$

Cost-Loss ratio
$\text{C/L} \ll 1$, Low cost, easy to take measure
C/L ~ 1, Cost close to Loss, measure may not be worth it

Quality and Value

• Value is multivalued for a given skill

Questions?