In the most extreme case where they were all 100% correlated, then your N=1, and the distribution of "which decade did all the gauges show a record" becomes flat, as it's essentially a single roll of a six sided die. You're only talking about a single gauge at that point.
Stats problem - flood events
Re: Stats problem - flood events
Re: Stats problem - flood events
Also that case gives the lowest probability.
The more I think about it the more I think statistical analysis won't give a valid answer to your question. The correlation issue is important and ssems intractable.plodder wrote: ↑Tue Feb 25, 2020 11:13 amtake a look at the tweet - it's 400 gauges nationally, and there's quite a spread of records. So whilst I agree that a proper engineer would do it properly, they'd also look at the dataseries themselves to find out if the records were broken by 1mm or 100mm, the duration of the time series, interconnectivity etc.
Perhaps you'll agree that if the gauges have all been connected through the whole time series (assuming they're all the same age etc - again not true), then comparing the last 10 years to the previous 50 will still give an indication of baseline change?
More fundamentally, the question asked in the OP is essentially "Is the pattern noticed in the data unusual?" Of course it is, else you wouldn't have noticed it!
I think there's a name for the logical fallacy of testing a hypothesis with the data that generated the hypothesis, but I can't recall it. Would you have thought about "comparing the last 10 years to the previous 50" if they weren't different?
There are ways of testing for "structural change", but I think you'd need far more than five periods to compare with the latest.
Re: Stats problem - flood events
Not a stats problem, but an impressive demonstration of the effectiveness of temporary flood barriers.
This is at Ironbridge Usual view
This is at Ironbridge Usual view
My avatar was a scientific result that was later found to be 'mistaken' - I rarely claim to be 100% correct
ETA 5/8/20: I've been advised that the result was correct, it was the initial interpretation that needed to be withdrawn
Meta? I'd say so!
ETA 5/8/20: I've been advised that the result was correct, it was the initial interpretation that needed to be withdrawn
Meta? I'd say so!
Re: Stats problem - flood events
I thought that was the case, but I don't statistic very much. And I'm not sure what anti-correlations do to this.
I assume here you mean statistical analysis as opposed to trying to model the actual measured correlations and doing something Monte-Carlo.KAJ wrote: ↑Tue Feb 25, 2020 1:59 pmThe more I think about it the more I think statistical analysis won't give a valid answer to your question. The correlation issue is important and ssems intractable.plodder wrote: ↑Tue Feb 25, 2020 11:13 amtake a look at the tweet - it's 400 gauges nationally, and there's quite a spread of records. So whilst I agree that a proper engineer would do it properly, they'd also look at the dataseries themselves to find out if the records were broken by 1mm or 100mm, the duration of the time series, interconnectivity etc.
Perhaps you'll agree that if the gauges have all been connected through the whole time series (assuming they're all the same age etc - again not true), then comparing the last 10 years to the previous 50 will still give an indication of baseline change?
I did try a quick look through Tamino's blog for posts on extreme or record values, and did find this one on estimating the likelihood of record values being set. It talks a lot about survival functions, and a note at the end mentions that this kind of analysis is fundamentally different to estimating the likelihood of multiple x% per time period events.
Re: Stats problem - flood events
Yes, I'd neglected anti-correlations, but I guess they're unlikely in this context.
I think the actual correlation structure would be very complicated, the different gauges being correlated with each other and with themselves with time lags. I wouldn't like to try to model that, but I guess experts in the field know more about it than me! I still think the kind of modelling discussed upthread has very little validity.dyqik wrote: ↑Tue Feb 25, 2020 3:04 pmI assume here you mean statistical analysis as opposed to trying to model the actual measured correlations and doing something Monte-Carlo.KAJ wrote: ↑Tue Feb 25, 2020 1:59 pmThe more I think about it the more I think statistical analysis won't give a valid answer to your question. The correlation issue is important and ssems intractable.plodder wrote: ↑Tue Feb 25, 2020 11:13 amtake a look at the tweet - it's 400 gauges nationally, and there's quite a spread of records. So whilst I agree that a proper engineer would do it properly, they'd also look at the dataseries themselves to find out if the records were broken by 1mm or 100mm, the duration of the time series, interconnectivity etc.
Perhaps you'll agree that if the gauges have all been connected through the whole time series (assuming they're all the same age etc - again not true), then comparing the last 10 years to the previous 50 will still give an indication of baseline change?
Re: Stats problem - flood events
I can construct a toy model that would do that: fixed amount of precipitation arrives in a region, but it can fall on one side or another of a range of hills depending on wind direction or cloud height or something. River gauges for the rivers draining each side of the hills would then be anti-correlated to some degree.
But that's a Duplo model, rather than a Lego Technic one.