1
Introduction
1.1
Motivation: Data-driven decision-making
1.2
The general form of the problems we’ll take up
1.3
Building decision models
2
Formalism for statistical decision models
2.1
Actions
2.1.1
Example
2.2
States
2.2.1
Example
2.2.2
Representing uncertain states as random variables
2.2.3
Random variables
2.2.4
Random states
2.3
Parameters
2.4
Payoffs
2.4.1
Payoffs as a function of action and state
3
Statistical decision theory
3.1
Formalism for statistical decision models
4
Review
4.1
Big picture: How to make optimal choices under statistical uncertainty?
4.2
Uncertainty
4.3
Optimal choice
4.3.1
Optimization: Defining objectives
4.4
Integrating predictive and inferential tools into the decision calculus
4.5
Payoff functions: Define in terms of
\(x\)
(state) or
\(\theta\)
(parameter value)?
4.5.1
Parameter-dependent payoffs as reduced form of state-dependent payoffs
5
Prediction
5.1
Big picture: data-driven decision-making
5.2
Predictive models
6
Bayesian Methods
6.1
Reminder example: conditional probabilities
6.2
Bayesian methods: Introduction via simple example
6.2.1
Sampling model
6.2.2
Prior information
6.2.3
The Beta distribution
6.2.4
6.2.5
6.3
Bayes Theorem
6.3.1
6.3.2
6.4
Sensitivity analysis
6.5
Building a predictive model
6.5.1
6.5.2
6.5.3
6.6
Prediction via the predictive distribution
7
Forecast evaluation
7.1
Evaluating forecasting systems: Scoring rules
7.2
Q: “How good is your forecasting system?”
7.3
But is it really?
8
The Value of Information
9
Example decision problem: Whether to buy refrigeration
9.1
Formalism for the refrigeration example
9.1.1
Action set
9.1.2
Payoffs: The loss function
9.1.3
Uncertainty
9.1.4
Decision criterion
9.2
Statistical forecasting model
9.2.1
Historical data
9.2.2
Model of the data generating process
9.2.3
Comments on this statistical model: The risk of model mis-specification
9.2.4
Simulation of the prediction process, no covariates
9.2.5
Using a forecast
9.2.6
Simulation of the prediction process, one covariate
10
The Decision Tool Project
10.1
Assignment 1: Concept Note
Decision Analysis: Semi-organized notes
8
The Value of Information
Idea: Score your forecasting system in terms of how much value it adds to your decision system.