tag:blogger.com,1999:blog-9093436161326155359.post8932855353818363520..comments2017-09-22T16:49:07.340+01:00Comments on Variable Variability: Statistically significant trends - Short-term temperature trend are more uncertain than you probably thinkVictor Venemahttp://www.blogger.com/profile/02842816166712285801noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-9093436161326155359.post-20539035418323498742016-12-09T14:41:29.417+00:002016-12-09T14:41:29.417+00:00Yes, for long periods inhomogeneities and how well...Yes, for long periods inhomogeneities and how well we can correct them become more important. That is the argument I make at the end of my post. <br /><br />Also for longer periods the assumption that the trend is linear no longer works. <br /><br />Reality is complicated and there is no end to how many complications one can add. I was trained as a physicist and thus have the tendency to go to the simplest system that demonstrates the effect and study that system well. I feel that is the best route to understanding. You seem to be more of a climatologist; they like adding bells and whistles.<br /><br />You are the second person this week protesting that I did not write the post they would have wanted me to write. Auto-correlations mean that you have effectively less samples and that short term trends thus become even more uncertain. The auto-correlations for annual mean temperatures are modest. Monthly data has much stronger auto-correlations. Thus you do not get much more data when you go from annual to monthly data. You do get additional complications due to the uncertainty in the seasonal cycle and that the fluctuations also have a seasonal cycle. I did not want to got there, but show the principle.<br /><br />If you write a post about monthly data do let me know, would be interested how much difference that makes compared to the factor 32 in uncertainty for a period that 10 times as long. Would be surprised if this difference is not still a lot larger for trends than it is for averages and also a lot larger than just a factor 10.Victor Venemahttps://www.blogger.com/profile/02842816166712285801noreply@blogger.comtag:blogger.com,1999:blog-9093436161326155359.post-29041121373275710452016-12-08T20:27:39.164+00:002016-12-08T20:27:39.164+00:00I figured I should let you know I've published...I figured I should let you know I've published a <a href="http://www.hi-izuru.org/wp_blog/2016/12/some-small-things/" rel="nofollow">post</a> which is highly critical of this. You can read the details if you want, but put simply, the "analysis" used in this post is garbage. The series used in it are so radically different from what we have for temperature records the results of this "analysis" are meaningless.<br /><br />Two central differences are: 1) Temperature data is not limited to annual records. The idea we have only 10 data points for 10 years of temperatures is laughable and necessary to come up with the claim there is 32 times as much uncertainty in 10 year trends as in 100 year trends. 2) The trends in this "analysis" are estimated for data which has no uncertainty. In the real world, individual points of data have uncertainty, and that uncertainty increases the further back in time you go. The increased uncertainty of past temperatures over recent temperatures would necessarily increase the uncertainty in any 100 year trend relative to any trend during the 21st century.<br /><br />The "analysis" used in this post is highly misleading. As a consequence, the results are greatly exaggerated.Brandon Shollenbergerhttps://www.blogger.com/profile/10456232054745393048noreply@blogger.comtag:blogger.com,1999:blog-9093436161326155359.post-56027850635937581992016-12-01T21:56:21.199+00:002016-12-01T21:56:21.199+00:00With "at least 17 years" Santer does not...With "at least 17 years" Santer does not say that 17 years is enough, only that less is certainly not enough. So also with Santer you can call out people looking at short-term trends longer than 17 years.<br /><br />And if I recall correctly, this was a study based on climate model data. <a href="https://www.climate-lab-book.ac.uk/2013/variable-variability/" rel="nofollow">Models vary enormously when it comes to their internal variability</a>, Ed Hawkins shows in his blog post with the best title ever. So I would add an additional buffer for that. <br /><br />Tamino is great. Everyone should read his posts before making a fool of themselves with another paper with "hiatus" in the title or abstract.Victor Venemahttps://www.blogger.com/profile/02842816166712285801noreply@blogger.comtag:blogger.com,1999:blog-9093436161326155359.post-11070200758438342032016-12-01T19:12:44.299+00:002016-12-01T19:12:44.299+00:00I usually use 30 yeras, and call out any global &q...I usually use 30 yeras, and call out any global "trend" with less than 17 years:<br />"...Our results show that temperature records of at least 17 years in length are required for identifying human effects on global-mean tropospheric temperature."<br />"Separating signal and noise in atmospheric temperature changes: The importance of timescale" JGR Atmospheres, Santer et al 2011<br />http://onlinelibrary.wiley.com/doi/10.1029/2011JD016263/abstract<br /><br />and a lot of Blog posts from tamino on too short periods and broken trends; e.g. https://tamino.wordpress.com.../2016/10/18/breaking-bad/realfacepalmnoreply@blogger.comtag:blogger.com,1999:blog-9093436161326155359.post-81370700571057033082016-12-01T10:14:14.919+00:002016-12-01T10:14:14.919+00:00No problem, the caveat is giving in the comments a...No problem, the caveat is giving in the comments and that is all that is needed. It is a difficult issue, because quite often it is reasonable to say that statistical significance means that the effect is unlikely to have occurred by chance, but the form of the analysis doesn't (and indeed can't) actually establish that. Unfortunately it is the question we want to ask, so it is natural to interpret the p-value as an answer to that question, rather than the question the NHST actually answers. The same problem arises with confidence intervals, most interpret them as meaning that the true value of the statistic lies in the interval with 95% probability, but unfortunately that is not what it actually means as it would also be assigning a probability to the truth of a particular hypothesis. <br /><br />While I am a Bayesian by inclination, it is best to be happy with both approaches and use the method that most directly answers the question you actually want answered. Unfortunately most of the time frequentist methods are easy to apply, but don't directly answer the question posed and are conceptually difficult, whereas Bayesian methods directly answer the question posed and are conceptually straight-forward, but the implementation is so tricky that they are not that often used (although improvements in software are helping this).<br /><br />Interpreting a frequentist test in a Bayesian manner is fine in my book, provided the switch in frameworks is noted.<br /><br />"There are worse people."<br /><br />yes, those statistical pedants are the worst in my experience! ;o)Dikran Marsupialnoreply@blogger.comtag:blogger.com,1999:blog-9093436161326155359.post-4699893692375085562016-12-01T01:33:04.326+00:002016-12-01T01:33:04.326+00:00Yes, I know I should have talked about accepting o...Yes, I know I should have talked about accepting or rejecting the null hypothesis. If only because when the trend was larger, that could also have been because the signal was not made of random numbers, but correlated numbers. <br /><br />I did not want to go there to make it accessible and shorter. I thought within that limit, it was quite a nifty formulation. :) If that means I am a fake Bayesian, that is okay. There are worse people. Victor Venemahttps://www.blogger.com/profile/02842816166712285801noreply@blogger.comtag:blogger.com,1999:blog-9093436161326155359.post-91179516393577802472016-11-30T18:42:42.508+00:002016-11-30T18:42:42.508+00:00"That something is statistically significant ...<i>"That something is statistically significant means that it is unlikely to happen due to chance alone. When we call a trend statistically significant, it means that it is unlikely that there was no trend, but that the trend you see is due to chance."</i><br /><br />I don't think that is quite true. If an effect is statistically significant it means that if it happened by chance, it would be unusual to see an effect size as large as that observed, which is not quite the same thing. The p-value is p(X>xo|H0)m i.e. the probability of an effect size (X) greater than that actually observed (xo) IF the null hypothesis (the effect is due to chance), rather than p(H0|xo) i.e. the probability that the effect was due to change (the null hypothesis) given the observed effect size. Unfortunately a frequentist hypothesis test fundamentally can't tell you p(H0|xo) (i.e. the thing you really want to know) because a frequentist can't assign a non-trivial probability to the truth of a particular hypothesis as it has no long run frequency (the way they define a probability), it is either true or it isn't - it isn't a random variable. This is why we should just say "we are [un]able to reject the null hypothesis" rather than say that the result probably occurred by chance, or that it didn't (well actually we can, but if we do so we are silently switching to a subjectivist Bayesian framework without stating our priors). The message of the post though, I totally agree with!Dikran Marsupialnoreply@blogger.com