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Interpreting Joint Probability Plots

Joint probability plots allow you to compare the likelihood of a specific combination of changes occurring between two variables, relative to any other combination on the same plot.

Interpreting the graphs below

The contours on the diagrams represent a probability that has been multiplied by 1000. So if a relative probability of '2' is indicated on the contour line this relates to a probability of 0.002 that there will be a simultaneous change in a certain amount in variable X and a certain amount in variably Y.

Figure 1 shows how the likelihood of a combination of events (two projected changes) occurring can be identified from a joint probability plot.

Joint probability plots can also be used to show the likelihood of a combination of events occurring in relation to another combination of events, as shown in Figure 2.

In Figure 2, the likelihood of there being a 2.5ºC increase in temperature and a ~4% drop in precipitation, is 2.5 times more likely than a 1.5ºC increase in temperature and a ~7% increase in precipitation.

This is calculated by first identifying the contours where the two different combinations intersect.

  • A 2.5ºC increase in temperature and a ~4% drop in precipitation intersect at the 250 contour.
  • A 1.5ºC increase in temperature and a ~7% increase in precipitation intersect at the 100 contour.

As with the PDF, to find the relative probability, divide the higher value by the lower - in this example divide 250 by 100 to determine that one combination is projected to be 2.5 times more likely to occur than the other.

Joint probability plot

Figure 1

Joint probability plot

Figure 2