Probability

The probability concept is used in geo-statistics to describe the likelihood (from 0, never occurring, to 1, always happening) that a particular event will take place (Bayesian view).

For instance, the probability of obtaining a six when rolling a theoretically unbiased die is one-of-six ( $p(E)=\frac{1}{6}$), as each side of the die is equally likely to end up on the top (real dice are biased - more dots on the ``6'' side).

Another interpretation of probability is taken by the Frequentist view, where a measure of probability gives the expected number of occurrence for a particular event for a large number of samples (observations).

If the die is thrown 600 times, the expected number of sixes is 100. The expected number is $N \times p(E)$. In this sense, the probability may be viewed as a kind of frequency measure: the higher the probability, the more often the event is expected to take place. Example: climate change cannot be addressed as using ``frequentists'' approach. Can only assign it prior probabilities based on how much we ``believe'' in the models.

Conditional probability: $p(E_2\vert E_1) = p(E_1 \mbox{ and } E_2)/p(E_1)$, the probability that E₂ will happen given that E₁ has occurred.