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Maximum likelihood estimation

Maximum likelihood estimation. Aim. Find a point estimate for a parameter “best guess about the parameter value” Procedure Based on subjective prior knowledge, define conditional probability of observations given the parameter P(index finger | mean) Observe the data

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Maximum likelihood estimation

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  1. Maximum likelihood estimation

  2. Aim • Find a point estimate for a parameter “best guess about the parameter value” • Procedure • Based on subjective prior knowledge, define conditional probability of observations given the parameter P(index finger | mean) • Observe the data • View P(index finger|mean) as a function of mean once data are observed : “likelihood function” • Find a mean for which P(index finger|mean) is the largest

  3. Example • A person who has a dog has a car with probability P(car | dog)=0.8 • A person who do not have a dog has a car with probability P(car | no dog)=0.5 • Knowing that a person has a car, the maximum likelihood estimate (MLE) is that the person also has a dog

  4. Example • When using frequency probability, the dog-car example does not work : owning is a state of the world that is fixed, it does not vary randomly between sampling

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