Hui Hu Ph.D.
Department of Epidemiology
College of Public Health and Health Professions & College of Medicine
April 3, 2019
Data
Prior Belief
Decision
Frequentist
Bayesian
Frequentist |
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Data are repeatable random sample: there is a frequency |
Underlying parameters remain constant during this repeatable process |
Parameters are fixed |
Bayesian |
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Data are observed from the realized sample |
Parameters are unknown and described probabilistically |
Data are fixed |
Posterior:
The probability of parameter given the data is collected
Likelihood:
The probability of collecting this data given the parameter
Prior:
The probability of the parameter before collecting data
Marginal Likelihood:
The probability of collecting this data under all possible parameters
Posterior:
The probability of parameter given the data is collected
Likelihood:
The probability of collecting this data given the parameter
Prior:
The probability of the parameter before collecting data
Marginal Likelihood:
The probability of collecting this data under all possible parameters
Posterior:
The probability of parameter given the data is collected
Likelihood:
The probability of collecting this data given the parameter
Prior:
The probability of the parameter before collecting data
Marginal Likelihood:
The probability of collecting this data under all possible parameters
Posterior:
The probability of parameter given the data is collected
Likelihood:
The probability of collecting this data given the parameter
Prior:
The probability of the parameter before collecting data
Marginal Likelihood:
The probability of collecting this data under all possible parameters
The posterior is proportional to the likelihood times the prior