Editing Mathematical model (section)

====Subjective information====

Sometimes it is useful to incorporate subjective information into a mathematical model.  This can be done based on [[Intuition (knowledge)|intuition]], [[experience]], or [[expert opinion]], or based on convenience of mathematical form. [[Bayesian statistics]] provides a theoretical framework for incorporating such subjectivity into a rigorous analysis: we specify a [[prior probability distribution]] (which can be subjective), and then update this distribution based on empirical data.

An example of when such approach would be necessary is a situation in which an experimenter bends a coin slightly and tosses it once, recording whether it comes up heads, and is then given the task of predicting the probability that the next flip comes up heads.  After bending the coin, the true probability that the coin will come up heads is unknown; so the experimenter would need to make a decision (perhaps by looking at the shape of the coin) about what prior distribution to use. Incorporation of such subjective information might be important to get an accurate estimate of the probability.