We will look at actual theories and methods used by the experts to assign a probability of global nuclear war. We will utilize the frequentist inference, the Bayesian inference, and even superforecasting, which holds that the more degrees of uncertainty you can distinguish, the better poker player you are likely to be.
NASA National Aeronautics and Space Administration
This approach does not seem to provide a workable model that results in a probability because the two primary assumptions are that the process is repeatable and that the underlying parameter remains constant. While there is no requirement for prior knowledge about the parameter of interest, the parameter value is estimated from the sample data. Since we do not have any sample data other than Hiroshima and Nagasaki, this approach will be rejected.
Complicated Mathematical Model
Bayesian inference is a method of statistical inference in which Bayes’ theorem (see below) is used to update the probability for a hypothesis as more evidence or information becomes available. As the summer offensive by the Ukrainian Army takes shape in the eastern part of the country and they experience more success than expected, the possibility of the Russians using tactical nuclear weapons increases. So really this is a heads-I-win-tails-you-lose situation for Ukraine. Bayesian statistics in layman's terms is about using your prior beliefs—called priors—to make assumptions on everyday problems and continuously updating those beliefs with the data you gather through experience. So, if the Russians use tactical nuclear weapons and NATO responds by sinking the Russian Black Fleet, which they can do in about half an hour, the likelihood of nuclear war rises exponentially.
The most important thing to remember about Superforecasting is “base rate neglect." A good example of base rate neglect is the prediction of the occupation of a nerd bookworm. You are given three foils—librarian, salesman, or farmer. Most would choose librarian even though only 17 percent of librarians are female. The base case is that Russia will not use nuclear weapons. A recognition of bias and noise will result in better decision-making.
I believe there is less than a 10 percent chance of a global strategic nuclear war even if Russia uses TNWs in the Ukraine. Far more likely is a war resulting from a technical mistake, especially as artificial intelligence is utilized in weapons control.