tag:blogger.com,1999:blog-16612221.post4187410225368737376..comments2024-03-19T03:14:04.172-04:00Comments on Rabett Run: A Puzzler, where did Loehle go too far?EliRabetthttp://www.blogger.com/profile/07957002964638398767noreply@blogger.comBlogger42125tag:blogger.com,1999:blog-16612221.post-87293292581068407902010-04-21T03:49:39.696-04:002010-04-21T03:49:39.696-04:00I would prefer Lindsay Lohan. Guess I'm old-fa...I would <em>prefer</em> Lindsay Lohan. Guess I'm old-fashioned, just don't want to think what some folks want ponies for :-(Martin Vermeerhttps://www.blogger.com/profile/04537045395760606324noreply@blogger.comtag:blogger.com,1999:blog-16612221.post-57062681022107921722010-04-20T15:43:35.804-04:002010-04-20T15:43:35.804-04:00Patrick Cottontail says...
I would like a pony, a...Patrick Cottontail says...<br /><br />I would like a pony, and my very own Lindsay Lohan.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-16612221.post-78649316322600555162010-04-17T16:02:56.034-04:002010-04-17T16:02:56.034-04:00can i have a pony?can i have a pony?carrot eaternoreply@blogger.comtag:blogger.com,1999:blog-16612221.post-52302820939747045092010-04-17T15:01:36.556-04:002010-04-17T15:01:36.556-04:00Full service:)Full service:)EliRabetthttps://www.blogger.com/profile/07957002964638398767noreply@blogger.comtag:blogger.com,1999:blog-16612221.post-37583751927218004412010-04-17T14:30:57.556-04:002010-04-17T14:30:57.556-04:00Thanks, even if it's that weird US date format...Thanks, even if it's that weird US date format. ;)TrueScepticnoreply@blogger.comtag:blogger.com,1999:blog-16612221.post-66608223907938512102010-04-17T13:12:17.022-04:002010-04-17T13:12:17.022-04:00Craig
WRT the date, True, done. Rabett Run is a f...Craig<br /><br />WRT the date, True, done. Rabett Run is a full service blog. YMMV on what it serves.EliRabetthttps://www.blogger.com/profile/07957002964638398767noreply@blogger.comtag:blogger.com,1999:blog-16612221.post-83745360333199284882010-04-17T12:54:48.925-04:002010-04-17T12:54:48.925-04:00So, Eli, are you saying that I'm unclear or th...So, Eli, are you saying that I'm unclear or that Craig is? I just played with the numbers to see what happened. <br /><br />BTW is there any easy way to answer a specific comment here, and why does the blog not show time *and date* for each comment?TrueScepticnoreply@blogger.comtag:blogger.com,1999:blog-16612221.post-66176823162080173602010-04-17T12:39:01.533-04:002010-04-17T12:39:01.533-04:00Anyrabett who teaches an introductory science clas...Anyrabett who teaches an introductory science class sees this frequently. It is a sure sign of someone who is unclear on the concept.<br /><br />OTOH, as Tamino pointed out above, many fitting procedures (OLS) require subtracting numbers from each other where there is a small difference between them, and the procedure requires many significant figures. Experience is knowing when to cut and when to paste.EliRabetthttps://www.blogger.com/profile/07957002964638398767noreply@blogger.comtag:blogger.com,1999:blog-16612221.post-83570772944405559292010-04-17T12:20:03.355-04:002010-04-17T12:20:03.355-04:00Being extremely suspicious of Craig's huge num...Being extremely suspicious of Craig's huge numbers of sig fig, I thought I'd try a simple test using the exponential formula. <br /><br />I couldn't use the the full number of sig fig in my spreadsheet. I lost 1 from a, 2 from b, and 2 from c. But anyway, the fit 1958-2008 was not particularly good. I got <br />Total squares error 59.93<br />1958 value 313.56 (actual 315.34)<br />2008 value 384.67 (actual 385.59)<br />2100 value 845.36<br /><br />I then removed a further 3 sig fig from each parameter. The results were <br />Total squares error 59.93<br />1958 value 313.56 (actual 315.34)<br />2008 value 384.67 (actual 385.59)<br />2100 value 845.36<br /><br />OK, let's round by a further 3. <br />Total squares error 59.93<br />1958 value 313.56 (actual 315.34)<br />2008 value 384.67 (actual 385.59)<br />2100 value 845.36<br /><br />And 3 more again. <br />Total squares error 64.37<br />1958 value 313.53 (actual 315.34)<br />2008 value 384.59 (actual 385.59)<br />2100 value 844.98. <br /><br />So, only now do we see any difference. In fact, if I add 2 sig back in, the result is <br />Total squares error 59.87<br />1958 value 313.56 (actual 315.34)<br />2008 value 384.67 (actual 385.59)<br />2100 value 845.36<br />At this point, <br />a=259.39458<br />b=2.9782774E-13<br />c=1.676930E-02 <br /><br />IOW, you only see any difference when using 8 instead of 9 digits. This suggests that Craig's use of such "precision" makes no sense and that it's a smokescreen for a poor analysis.TrueScepticnoreply@blogger.comtag:blogger.com,1999:blog-16612221.post-34898327283215814022010-04-16T15:12:32.962-04:002010-04-16T15:12:32.962-04:00Horatio prefers WiiHoratio prefers WiiHoratio Algeranonhttps://www.blogger.com/profile/12988805467080448954noreply@blogger.comtag:blogger.com,1999:blog-16612221.post-82238686932572828532010-04-16T07:36:56.363-04:002010-04-16T07:36:56.363-04:00Dikran also has the MATLAB symbolic maths toolbox ...Dikran also has the MATLAB symbolic maths toolbox (maple) ;o)Dikran Marsupialnoreply@blogger.comtag:blogger.com,1999:blog-16612221.post-48801027426575941842010-04-15T16:50:05.313-04:002010-04-15T16:50:05.313-04:00Very clever Eli :)
MLVery clever Eli :)<br /><br />MLAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-16612221.post-68726290102051381422010-04-15T16:27:17.113-04:002010-04-15T16:27:17.113-04:00Eli, of course, prefers MapleEli, of course, prefers MapleEliRabetthttps://www.blogger.com/profile/07957002964638398767noreply@blogger.comtag:blogger.com,1999:blog-16612221.post-2241134486922391712010-04-15T15:44:14.890-04:002010-04-15T15:44:14.890-04:00Joe said "I like Craig's backhanded dismi...Joe said <i>"I like Craig's backhanded dismissal of Matlab and R"</i><br /><br />Hang on, McIntyre likes and uses R. <br /><br />Now if I were Jonathan Leake, then tomorrow's headline might read something like this:<br /><br /><b>"Craig Loehle throws McIntyre under the bus"</b><br /><br /><i>In a startling revelation yesterday, Craig Loehle said that Stephen McIntyre uses inferior statistical software which is not suitable for conducting precise statistical analyses. This now calls into question the validity of all of Mr. McIntyre's audits. When approached for comment, Mr. McIntyre muttered something about whitewash and the Hockey Stick being a fraud before breaking down in tears. After composing himself, Mr. McIntyre said that Loehle has now been banned form his blog."</i><br /><br />It really is a nice day today :)<br /><br />MapleLeafAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-16612221.post-38220834831845999772010-04-15T14:25:26.421-04:002010-04-15T14:25:26.421-04:00The Atmospheric Environment link at the top of the...The Atmospheric Environment link at the top of the post is missing something...<br /><br />On another note, I like Craig's backhanded dismissal of Matlab and R, as apparently only Mathematica is the "high precision platform" capable of curve-fitting.joehttps://www.blogger.com/profile/06802141921007062377noreply@blogger.comtag:blogger.com,1999:blog-16612221.post-55644118973571178292010-04-15T12:16:29.784-04:002010-04-15T12:16:29.784-04:00All this curve fitting reminds Horatio more than a...All this curve fitting reminds Horatio more than a little of running on a hamster wheel. <br /><br />Consider what has happened to the growth in (yearly) emissions from the 1990's to 2000's <a href="http://news.mongabay.com/2007/0521-co2.html" rel="nofollow">decribed here</a> <br /><br /><i>"Worldwide growth in carbon dioxide emissions has doubled since the close of the 1990s, reports a study published in the early on-line edition of the Proceedings of the National Academy of Sciences."<br /><br />"A team of researchers led by Michael R. Raupach of CSIRO-Australia found that global growth rate of CO2 increased from 1.1 % per year during the 1990s to 3.1% per year in the early 2000s. The growth is being fueled primarily by developing countries, especially China and India, where economies are fast-expanding and population continues to increase at a significantly higher rate than in industrialized nations."</i><br /><br /><br />There are many many <i>many</i> things that can affect the actual emissions path that is taken, so many, in fact, that it is virtually impossible to say with any confidence what the total emissions -- and resulting increase in atmospheric CO2 concentration -- will be by 2100.<br /><br />That is precisely why the IPCC gives many different scenarios. As Eli indicates with his "watch the pea" comment, they are simply not in the business of "predicting" future emissions, nor should they be.<br /><br />For a particular scenario, they make an assumption about what will happen over the next century to yearly emissions (eg "They will grow by 2% per year" or whatever) and then calculate, based on the details of the climate system (eg how much CO2 is absorbed by oceans and other natural sinks, etc) how much that will increase the atmospheric CO2 concentration.<br /><br />Attempting to actually "forecast" future emissions (especially based on simple "curve fitting") is basically a hamster's game. It tires you out but really gets you nowhere (Horatio knows about the latter)<br /><br />Having said that, Horatio has run the numbers and thinks it should be <br />"a=259.3945817870856" <br /><br />(with an uncertainty of 1 in the last digit)Horatio Algeranonhttps://www.blogger.com/profile/12988805467080448954noreply@blogger.comtag:blogger.com,1999:blog-16612221.post-29807623616603345362010-04-15T09:23:18.611-04:002010-04-15T09:23:18.611-04:00Dikran,
I agree. I find it utterly bizarre that C...Dikran,<br /><br />I agree. I find it utterly bizarre that Craig's formulae apparently require <b>astronomical</b> numbers of sig fig to produce results that need only have only 4/5 sig fig resolution. Accuracy is another matter, and seems to be poor in any case. <br /><br />Craig,<br /><br />How did you arrive at such precise numbers?TrueScepticnoreply@blogger.comtag:blogger.com,1999:blog-16612221.post-50113029383690796632010-04-15T07:47:17.617-04:002010-04-15T07:47:17.617-04:00Here is my code, which reproduces something like C...Here is my code, which reproduces something like Craigs results, but with annual mean data, and using a reference time of 1985 to reduce numerical problems. It is all self contained, so just copy all into a single file and run. I get the following 0.5 times sum of squared errors:<br /><br /><br />exponential SSE = 13.000800<br /> quadratic SSE = 10.377087<br />saturating SSE = 8.544788<br /><br /><br />function analysis<br /><br />clear all<br /><br />maunaloa = [1958 315.23 ; 1959 315.98 ; 1960 316.91 ; 1961 317.64<br /> 1962 318.45 ; 1963 318.99 ; 1964 319.16 ; 1965 320.04<br /> 1966 321.38 ; 1967 322.16 ; 1968 323.05 ; 1969 324.63<br /> 1970 325.68 ; 1971 326.32 ; 1972 327.45 ; 1973 329.68<br /> 1974 330.25 ; 1975 331.15 ; 1976 332.15 ; 1977 333.90<br /> 1978 335.51 ; 1979 336.85 ; 1980 338.69 ; 1981 339.93<br /> 1982 341.13 ; 1983 342.78 ; 1984 344.42 ; 1985 345.90<br /> 1986 347.15 ; 1987 348.93 ; 1988 351.48 ; 1989 352.91<br /> 1990 354.19 ; 1991 355.59 ; 1992 356.37 ; 1993 357.04<br /> 1994 358.89 ; 1995 360.88 ; 1996 362.64 ; 1997 363.76<br /> 1998 366.63 ; 1999 368.31 ; 2000 369.48 ; 2001 371.02<br /> 2002 373.10 ; 2003 375.64 ; 2004 377.38 ; 2005 379.67<br /> 2006 381.84 ; 2007 383.55 ; 2008 385.34]; <br /><br />opts = optimset('Display', 'Iter', ...<br /> 'GradObj', 'off', ...<br /> 'TolX', 1e-9, ...<br /> 'TolFun', 1e-15, ...<br /> 'MaxFunEvals', 1e+6);<br /><br />[xq,Lq] = fminunc(@quadratic,[285 5 0.1],opts,maunaloa(:,1)-1985,maunaloa(:,2));<br />[xs,Ls] = fminunc(@saturating,[10 0.1 285 10],opts,maunaloa(:,1)-1985,maunaloa(:,2));<br />[xe,Le] = fminunc(@exponential,[270 70 0.01],opts,maunaloa(:,1)-1985,maunaloa(:,2));<br /><br />period = 1850:2100;<br /><br />saturatingfn = inline('x(3) + x(1)*(1-exp(x(2)*(t-x(4)))).^2', 'x', 't');<br /><br />plot(maunaloa(:,1), maunaloa(:,2), 'r-', ...<br /> period, xe(1)+xe(2)*exp(xe(3).*(period-1985)), 'b-', ...<br /> period, xq(1)+xq(2)*(period-1985)+xq(3)*(period-1985).^2, 'g-', ...<br /> period, saturatingfn(xs, period-1985), 'm-');<br />xlabel('Year');<br />ylabel('CO_2 (ppmv)');<br />legend('Mauna Loa','exponential','quadratic','saturating','Location','North');<br /><br />fprintf(1, 'exponential SSE = %f\n', Le);<br />fprintf(1, ' quadratic SSE = %f\n', Lq);<br />fprintf(1, 'saturating SSE = %f\n', Ls);<br /><br />function L = exponential(x, t, y)<br /><br />a = x(1);<br />b = x(2);<br />c = x(3);<br />expct = exp(c*t);<br />f = a + b*expct;<br />L = 0.5*sum((y-f).^2);<br /><br />function L = quadratic(x, t, y)<br /><br />a = x(1);<br />b = x(2);<br />c = x(3);<br />f = a + b*t + c*(t.^2);<br />L = 0.5*sum((y-f).^2);<br /><br />function L = saturating(x, t, y)<br /><br />a = x(1);<br />b = x(2);<br />c = x(3);<br />d = x(4);<br />f = c + a*(1-exp(b*(t-d))).^2;<br />L = 0.5*sum((y-f).^2);Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-16612221.post-5256269512968983292010-04-15T03:12:53.482-04:002010-04-15T03:12:53.482-04:00here's my code (why no pre tag?):
load co2.t...here's my code (why no pre tag?):<br /><br /><b><br />load co2.txt<br />xdata = co2(:,1) - 1985;<br />ydata = co2(:,5);<br /><br />figure(1); hold on;<br /><br />options = optimset('TolFun', 1.0e-12, 'MaxFunEvals',2000);<br />x1 = lsqcurvefit(@f, [0 100 0.01], xdata, ydata, [], [], options)<br />x2 = lsqcurvefit(@g, [1 1 1], xdata, ydata, [], [], options)<br />x3 = lsqcurvefit(@h, [616.9635436975683 0.006760893860992654 310.9394987790752 1945.6473702994858-1985], xdata, ydata, [], [], options)<br />x4 = lsqcurvefit(@k, [1 1 1 1], xdata, ydata, [], [], options)<br /><br />plotspan = [1850:2100];<br />plotspan2 = plotspan - 1985;<br /><br />axis([1850 2100 0 600])<br />plot(xdata + 1985, ydata, 'k', plotspan, f(x1, plotspan2), 'b', plotspan, g(x2, plotspan2), 'g', plotspan, h(x3, plotspan2), '--r', plotspan, k(x4, plotspan2), '--c');<br />legend('data', 'exp', 'sqr', 'sat', 'cub', 0);<br /></b><br /><br />You then need functions like h.m:<br /><br /><b><br />function y = h(x,xdata)<br /><br />e = exp(x(2)*(xdata - x(4)));<br />y = x(3) + x(1)*(1-e).*(1-e);<br /></b><br /><br />...and of course the input data in co2.txt.Martin Vermeerhttps://www.blogger.com/profile/04537045395760606324noreply@blogger.comtag:blogger.com,1999:blog-16612221.post-58491028614800118692010-04-14T16:58:20.553-04:002010-04-14T16:58:20.553-04:00"259.3945817870858" taken from Loehle..."259.3945817870858" taken from Loehle's paper. When a person quote many (many) more digits than are significant, it's usually a good indication that he does not know what he's doing re math, curve-fitting, or statistics.rabhttps://www.blogger.com/profile/10075982588165305088noreply@blogger.comtag:blogger.com,1999:blog-16612221.post-60776181841136558182010-04-14T16:41:55.455-04:002010-04-14T16:41:55.455-04:00Recent growth in CO2 concentrations is hyperexpone...Recent growth in CO2 concentrations is hyperexponential. Tamino has a post on this and by looking at the "diffs: column in<br /><a href="http://www.realclimate.org/index.php/archives/2010/03/unforced-variations-3/comment-page-12/#comment-168530" rel="nofollow">Global Warming, decade by decade</a><br />you can see it for lnCO2, decadally.David B. Bensonhttps://www.blogger.com/profile/02917182411282836875noreply@blogger.comtag:blogger.com,1999:blog-16612221.post-14123892232989325702010-04-14T14:44:17.842-04:002010-04-14T14:44:17.842-04:00Eli agrees with Dikran at least in the important p...Eli agrees with Dikran at least in the important part The basic point is that forecasts are based either on historical data or models. In this case the forecast was based on historical data. The strong deviation from from the data of two of the fitting forms is equivalent to the 1998 cherry pick we are all familiar with. <br /><br />On the centering of the fit, not so much. The farther the extrapolation, the more sensitive the fit is to noise in the data, lack of infinite precision, etc. So, saying this awkwardly, a small movement in one parameter can lead to a large on in another if you don't choose to wisely.EliRabetthttps://www.blogger.com/profile/07957002964638398767noreply@blogger.comtag:blogger.com,1999:blog-16612221.post-47116403190528981722010-04-14T14:30:18.357-04:002010-04-14T14:30:18.357-04:00Having now written some MATLAB code, I am not so s...Having now written some MATLAB code, I am not so sure the reference time is the issue. I used the yearly mean Mauna Loa data (as I don't think the annual cycle should be allowed to influence the outcome), and using a reference time of 1985 I get a plot that looks a lot like Craigs.<br /><br />I suspect the problem is flat minimum, so maybe tomorrow I'll find time to try the MCMC approach and look at the uncertainty in the forecast (which I would imagine are important in econometrics as well).<br /><br />Having said which, I have realised that the back-casting is a red-herring; the reason the data before 1958 are important because if you built a model using the available relevant knowledge (which includes the Law Dome data for instance) the quadratic and saturating models would no longer give the same forecasts, whereas the exponential one would be largely unchanged. I have more trust in a forecast from a model the more observational data it explains, especially if it explains it without re-calibration.<br /><br />The key point is "would the comment get past the reviewers had the back-casts been plotted?". I suspect the answer is probably "no".Dikran Marsupialnoreply@blogger.comtag:blogger.com,1999:blog-16612221.post-49509671489027146002010-04-14T11:13:43.001-04:002010-04-14T11:13:43.001-04:00Craig, the necessity for so many significant digit...Craig, the necessity for so many significant digits (in some case more than are supported by double precision format) seems to me an indication that the problem as posed was ill-conditioned. The fact that making a better conditioned problem by changing the reference time gives a different result suggests that it is your model fit that is unreliable, rather than Eli's?<br /><br />I disagree about the back casting comment, as a statistician what matters is decided by the needs of the application, not the statistician. Just because it doesn't matter for cell phone, doesn't mean it doesn't matter for carbon dioxide forecasts. If one model can give back-casts, but the others can't that immediately means that there is a reason to chose one model over the others, and the paper ought to have pointed out that deficiency of the saturating and polynomial models.Dikran Marsupialnoreply@blogger.comtag:blogger.com,1999:blog-16612221.post-7286655550198037432010-04-14T11:03:13.823-04:002010-04-14T11:03:13.823-04:00Loehle:
You call the hopeful extrapolation of a c...Loehle:<br /><br />You call the hopeful extrapolation of a curve fit to be a forecast?<br /><br />How about considering some emissions scenarios, and the physics of how the carbon cycle will respond? <br /><br />Maybe unphysical curve fits are allowed in econometrics. I don't know. This isn't econometrics.carrot eaternoreply@blogger.com