Prior probability is defined as...

Prior probability is defined as...

• A. Our belief in a hypothesis or model before considering the data.
• B. The probability of the data under the model.
• C. The posterior probability after data.
• D. The probability of the null hypothesis after data.

Answer: (A)

Prior probability is the probability assigned to a hypothesis or model before observing any data. It reflects your belief about how likely the hypothesis is based on theory, previous research, or subjective judgment. In Bayesian reasoning, this prior is updated with the data through Bayes’ rule to form the posterior, which is your updated belief after seeing the evidence. This distinguishes it from the likelihood, which is the probability of the observed data given the model, and from the posterior, which is the belief after data. It also isn’t the probability of the null after data, which would be a specific posterior assessment.

Prior probability is the probability assigned to a hypothesis or model before observing any data. It reflects your belief about how likely the hypothesis is based on theory, previous research, or subjective judgment. In Bayesian reasoning, this prior is updated with the data through Bayes’ rule to form the posterior, which is your updated belief after seeing the evidence. This distinguishes it from the likelihood, which is the probability of the observed data given the model, and from the posterior, which is the belief after data. It also isn’t the probability of the null after data, which would be a specific posterior assessment.