List of top Geology and Geophysics Questions on Bayesian construction of posterior probabilities asked in GATE GG

While doing Bayesian inference, consider estimating the posterior distribution of the model parameter (m), given data (d). Assume that Prior and Likelihood are proportional to Gaussian functions given by \[ {Prior} \propto \exp(-0.5(m - 1)^2) \] \[ {Likelihood} \propto \exp(-0.5(m - 3)^2) \] 

The mean of the posterior distribution is (Answer in integer)

While doing Bayesian inference, consider estimating the posterior distribution of the model parameter (m), given data (d). Assume that Prior and Likelihood are proportional to Gaussian functions given by \[ {Prior} \propto \exp(-0.5(m - 1)^2) \] \[ {Likelihood} \propto \exp(-0.5(m - 3)^2) \]

The mean of the posterior distribution is (Answer in integer)

A petroleum company estimates that a reservoir holds oil with a prior probability of 60\%. It then acquires petrophysical data that suggests the presence of oil. If the petrophysical analysis is accurate with a probability of 70\%, the posterior probability of the presence of oil in \% is ________ (rounded off to two decimal places).