# Tech Talks: Bayesian Decision Theory & Gaussians

Bayesian Decision Theory establishes how prior and posterior probabilities factor into decision making in the presence of uncertainty. It can therefore be thought of as one of the most essential and versatile tools of any data scientist.

Say you have an action that may or may not have some desired outcome. From a Bayesian perspective, the objective of decision-making should be to take an action if, and only if, the expected utility of taking the action, if the desired outcome occurs, is greater than the expected disutility of taking the action, if the desired outcome does not occur. Such an expected utility is captured by the utility of the outcome weighted by the probability of the outcome, given that the action has been taken. This probability is often unobservable, but can be derived, through application of Bayes’ rule, from observable ingredients.

In particular, there are two ingredients. The first is the relative frequency with which the action has been taken, among cases where the outcome has been observed, i.e. the probability of the action, given the outcome. The second ingredient is the relative frequency with which the outcome has been observed, among the total number of observations, i.e. the prior probability of the outcome.

At PANOPTICOM, Bayesian Decision Theory, among other theoretical tools, is one of the primary building blocks, for our self-learning media monitoring solution.

For example, whereas a disproportionately large number of tweets on Twitter are about Justin Bieber, we have found that our clients never regard these as relevant. A Bayesian framework allows for the low prior probability of relevance, in cases like that, to become highly dominant. Given the presence of the keyword “Bieber” in a tweet, we quickly arrive at the conclusion that it is irrelevant.

PDF download(Reproduced here, courtesy of PANOPTICOM).