Short answers, pulled from the story.
Thomas Bayes published his essay An Essay Towards Solving a Problem in the Doctrine of Chances between 1763 and 1764. He died in 1761 before seeing it printed.
Bayesian inference derives the posterior probability as a consequence of two antecedents: a prior probability and a likelihood function derived from statistical models for observed data. The formula calculates this by multiplying the prior estimate with the likelihood of observing evidence given the hypothesis.
Pierre-Simon Laplace introduced what is now called Bayes theorem as Principle VI in his own work during the late eighteenth century. He used it to address problems in celestial mechanics medical statistics reliability and jurisprudence.
A dramatic growth in research occurred in the 1980s mostly attributed to discovery of Markov chain Monte Carlo methods which removed many computational barriers. These techniques enabled complex models to be processed where closed form solutions failed completely.
Spam filtering systems including CRM114 DSPAM Bogofilter SpamAssassin SpamBayes Mozilla XEAMS utilize Bayesian techniques developed since the late 1950s for computerized pattern recognition.