Bayesian Theory of Decision

Bayesian Theory of Decision

1. Decision Theory

   • Set of alternatives
     • Certainty
       • Linear programming
     • Incertidumbre
       • Processes Stochastic
   • Problem
     • Definition
     • Sampling
       • Event
       • Experiment
     • Model
     • Solution
     • Consequence
   • a Pirori
   • a Posteriori

2. THEORY OF BAYES

   • Let A1, A2, ..., An, events mutually exclusive and of non-zero probability, such that A1∪A2∪ ... ∪An = Ω. If B is a event in Ω probability no void, then:
   • Example
     • The 60% of the screws produced by a factory come from machine A and 40% from machine B. The proportion of defective in A is 0.1 and in B is 0.5 What is the probability that, knowing that a screw is defective, comes from the machine A?
       • A: machine manufactured screw A
         • P(D/A)=0,1P(D/B)=0,5
       • B: screw manufactured by machine B
       • D: defective screw
         • P(Dn/B)=1-P(D/B)=1-0,5=0,5
       • Dn: screw not defective
         • P(Dn/A)=1-P(D/A)=1-0,1=0,9

3. Applications

   • Neural Networks
   • Quantum mechanics
   • Cost analysis
   • Medical Decisions

4. Criteria

   • Maximax
     • Possibility Optimistic
   • Wald (Maximin)
     • Minimize the lost
   • A posteriori
     • Probability estimates with reference to another partner
   • Hurwitz
     • Combines pessimistic and optimistic
   • Savage (Minimax)
     • It is less conservative that Maximin
   • Laplace
     • Evaluate different alternatives

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