Bayes' theorem can tell us the probability of a hypothesis (that you have PF), given an event (that you tested positive for PF), which we can write as follows.
                                                                                                                                                                    \(P\left(PF\ |\ +\right)\)
To calculate this we need to take the prior probability that the hypothesis is true before you took the test, which is the likelihood that you have the disease at all (a good estimate for this is the frequency of PF sufferers in the population, 1%) and multiply that by the probability of a positive test given the hypothesis is true (which is our 95% ie out of a population of 10,000, we would expect 100 people to have PF, and we would expect 95 of them to test positive on the test.  ). 

Bayesian phylogenetics & polynesian migration

Bayesian phylogenetics are particularly useful in the field of Polynesian language evolution due to the unique migratory lifestyle of the polynesian peoples. Contact between distal islands was sporadic, and in the case of Rapa Nui, non existent. This largely eliminates the comparative method criticism of linguistic Current theories of Polynesian people's origin fall into two main camps: Express Train theory and the Entangled Bank theory \cite{Kayser_2000}. The more popular theory, Express Train, first put forward by Jared Diamond \cite{Diamond1988}posits that Polynesian migration originated in Taiwan and started relatively recently 3000-1000BCE, and migrating via the Philippines and New Guinea and reaching Melanesia by roughly 1400BCE and reaching Samoa by 900BCE. Entangled Bank theory however puts forward that there was no single 'express train' to Polynesia, it emphasises smaller migration as well as the long cultural and genetic interactions between the Polynesians, Melanesians and East Asians. Newer theories such as Kayser et al.'s Slow Boat theory attempts to marry these two ideas, while supporting a Tawainese origin and rapid migration to Melanesia, then suggests that upon reaching Melanesia migration slowed, and there was a long delay (leading to cultural and genetic admixture) before migration to Polynesia. 
Contemporary linguists have attempted to solve these competing theories using Bayesian inference, an important paper being Language Phylogenies Reveal Expansion Pulses and Pauses in Pacific Settlement , which focuses on how (timewise) the migration took place, both this and Language trees support the express-train sequence of Austronesian expansion.

Criticism of Bayesian Phylogenetics

Bayesian phenogenetics is by no means perfect though, despite uncertainty is present in your result, you have to be state your prior probability; and in situations where that is unknowable (for example language phylogenies) you have to invent a prior probability, which can skew your result if it's poorly picked. While these unknowns can be aided by using a prior distribution as opposed to a prior probability,
\cite{churchill1912} \cite{Walker_2010} \cite{Diamond_2003}\cite{Greenhill_2010}\cite{churchill1911}\cite{Gray_2009}\cite{2013}\cite{Gray_2000}

Conclusion