Your calculations apply to an exponential distribution. Do we have reasons to choose an exponential prior over a uniform/​loguniform prior for the location of the existential tipping point? I guess one possible disadvantage of the exponential prior is the lack of a maximum (which should arguably be assumed given our knowledge about moisture greenhouse), but this could be solved by using a truncated exponential.
I use exponential prior to illustrate the example with a car. For other catastrophes, I take the tail of normal distribution, there the probability declines very quickly, even hyperexponentially. The math there is more complicated. But it does not affect the main result: if we have anthropic shadow, the expected survival time is around 0.1 of the past time in the wide range of initial parameters.
And in the situation of anthropic shadow we have very limited information about the type of distribution. Exponential and normal seems to be two most plausible types for catastrophes. There is also semi-periodic ones, but they could be described as a sum of periodic plus normal.
Thanks for the reply!
Your calculations apply to an exponential distribution. Do we have reasons to choose an exponential prior over a uniform/​loguniform prior for the location of the existential tipping point? I guess one possible disadvantage of the exponential prior is the lack of a maximum (which should arguably be assumed given our knowledge about moisture greenhouse), but this could be solved by using a truncated exponential.
I use exponential prior to illustrate the example with a car. For other catastrophes, I take the tail of normal distribution, there the probability declines very quickly, even hyperexponentially. The math there is more complicated. But it does not affect the main result: if we have anthropic shadow, the expected survival time is around 0.1 of the past time in the wide range of initial parameters.
And in the situation of anthropic shadow we have very limited information about the type of distribution. Exponential and normal seems to be two most plausible types for catastrophes. There is also semi-periodic ones, but they could be described as a sum of periodic plus normal.
But obviously there is more to dig here.