Not to be too pedantic but your back of the envelope probabilities are based on inaccurate assumptions and probably several orders of magnitude off. Specifically, your not just assuming uniform but also independent from one day to the next. A more accurate treatment would be to assume conditional dependence from one day to the next (the Markov property). Once you have a record hot day, you are significantly more likely to have another record hot day following it.
That said, it’s still low probability, just not as low as what you’re saying.
If we stick with your 1/44 assumption, we can then assume 50% chance that the following day will also be a record setting day (probably too low still but the math is easier). Your one week estimate would be (1/44)*(1/2)^6.
If we stick with your 1/44 assumption, we can then assume 50% chance that the following day will also be a record setting day (probably too low still but the math is easier). Your one week estimate would be (1/44)*(1/2)^6.
While @[email protected] is right about me not being right, I’m not sure their implementation is correct either. I grabbed the data sheet from here, and have calculated the following probabilities. Now that I’m invested I really want to get this ‘right’.
I think its most fair to calculate this using the marginal probability of the next day being warmer for a given month. Some months are generally warming, some generally cooling, so it makes sense to base the marginal probability of the next day being warmer for a specific month (rather than all months). The probability of a given day in July being warmer than the previous day is 0.615. So pretty close to 50/50, but better to be precise. I think if we’re going to go this way, we can also give ourselves the liberty of not starting on July first, but rather then trend can start any time in July.
So now the math becomes:
State one is defined as the probability of having a record warm day in July: 1/44 *days in July
State two is defined as the probability the next day being warmer than the previous in July : 0.615
Which when I put it into this calculator, we get… .9981? This seems extremely low. So much so, I think either the markov chain is implemented wrong, or that the markov principal doesn’t apply here.
This would put the probability of a summer like the one as a one in 500-ish year occurrence. My understanding and read of the news is that this is an event that is on the scale of ‘has never happened before’.
Update:
So I am still not confident in the markov implementation but I put together another approach. I did a one sided T-test of this July versus all the previous Julys.
Here is a plot of that (month is on the X).
T-statistic came in too low to calculate a p-value.
You did not calculate that right. What I wrote comes out to 1/2816, which is fully 8 orders more likely than your initial estimate. And this number is still probably a lot lower than the true probability.
There are A LOT of independent lines of evidence that point very strongly to the conclusion that humans are causing a massively disruptive change to the earth’s climate. This heatwave is not the nail in the coffin, it’s just (small) data point. Trying to oversell it like you are only serves to entrench deniers who will assume that you are making an intentionally misleading argument.
Not to be too pedantic but your back of the envelope probabilities are based on inaccurate assumptions and probably several orders of magnitude off. Specifically, your not just assuming uniform but also independent from one day to the next. A more accurate treatment would be to assume conditional dependence from one day to the next (the Markov property). Once you have a record hot day, you are significantly more likely to have another record hot day following it.
That said, it’s still low probability, just not as low as what you’re saying.
Any thoughts on how I could incorporate that for a better back of the napkin?
(Also, that number is only consider that the number presented was based on 7 independent events, not 34)
If we stick with your 1/44 assumption, we can then assume 50% chance that the following day will also be a record setting day (probably too low still but the math is easier). Your one week estimate would be (1/44)*(1/2)^6.
So the 36-day would just have a ^35 on the end instead 6, if I’m following?
While @[email protected] is right about me not being right, I’m not sure their implementation is correct either. I grabbed the data sheet from here, and have calculated the following probabilities. Now that I’m invested I really want to get this ‘right’.
This the work book I’m in.
I think its most fair to calculate this using the marginal probability of the next day being warmer for a given month. Some months are generally warming, some generally cooling, so it makes sense to base the marginal probability of the next day being warmer for a specific month (rather than all months). The probability of a given day in July being warmer than the previous day is 0.615. So pretty close to 50/50, but better to be precise. I think if we’re going to go this way, we can also give ourselves the liberty of not starting on July first, but rather then trend can start any time in July.
So now the math becomes: State one is defined as the probability of having a record warm day in July: 1/44 *days in July State two is defined as the probability the next day being warmer than the previous in July : 0.615
Which when I put it into this calculator, we get… .9981? This seems extremely low. So much so, I think either the markov chain is implemented wrong, or that the markov principal doesn’t apply here.
This would put the probability of a summer like the one as a one in 500-ish year occurrence. My understanding and read of the news is that this is an event that is on the scale of ‘has never happened before’.
Update:
So I am still not confident in the markov implementation but I put together another approach. I did a one sided T-test of this July versus all the previous Julys.
Here is a plot of that (month is on the X).
T-statistic came in too low to calculate a p-value.
deleted by creator
You did not calculate that right. What I wrote comes out to 1/2816, which is fully 8 orders more likely than your initial estimate. And this number is still probably a lot lower than the true probability.
There are A LOT of independent lines of evidence that point very strongly to the conclusion that humans are causing a massively disruptive change to the earth’s climate. This heatwave is not the nail in the coffin, it’s just (small) data point. Trying to oversell it like you are only serves to entrench deniers who will assume that you are making an intentionally misleading argument.