Editing Student's t-distribution (section)

===In Bayesian statistics===
The Student's {{mvar|t}}&nbsp;distribution, especially in its three-parameter (location-scale) version, arises frequently in [[Bayesian statistics]] as a result of its connection with the normal distribution. Whenever the [[variance]] of a normally distributed [[random variable]] is unknown and a [[conjugate prior]] placed over it that follows an [[inverse gamma distribution]], the resulting [[marginal distribution]] of the variable will follow a Student's {{mvar|t}}&nbsp;distribution. Equivalent constructions with the same results involve a conjugate [[scaled-inverse-chi-squared distribution]] over the variance, or a conjugate gamma distribution over the [[Precision (statistics)|precision]]. If an [[improper prior]] proportional to {{sfrac| 1 | {{mvar|σ}}² }} is placed over the variance, the {{mvar|t}}&nbsp;distribution also arises. This is the case regardless of whether the mean of the normally distributed variable is known, is unknown distributed according to a [[conjugate prior|conjugate]] normally distributed prior, or is unknown distributed according to an improper constant prior.

Related situations that also produce a {{mvar|t}}&nbsp;distribution are:
* The [[marginal distribution|marginal]] [[posterior distribution]] of the unknown mean of a normally distributed variable, with unknown prior mean and variance following the above model.
* The [[prior predictive distribution]] and [[posterior predictive distribution]] of a new normally distributed data point when a series of [[independent identically distributed]] normally distributed data points have been observed, with prior mean and variance as in the above model.