Although some debate has focused on when a validation statistic, such as CE or RE, is significant, a more meaningful approach may be to concentrate on the implied
prediction intervals for a given reconstruction.
Assuming no autocorrelation for RSS (based on the DW test with GISS data), I regressed the annual temperature anomalies for the period 1979 - 2007 and determined
the prediction intervals for individual years shown in the graph below.
The prediction intervals for individual years show that a beginning point and ending point predicted from the regression could fall close together.
The Forecasting Problem To determine the best policies to implement now to deal with the social or physical environment of the future, a policy maker should obtain forecasts and
prediction intervals for each of the following: 1.
The second of the two most striking features is that
the prediction intervals for shares of the vote are enormous.
Not exact matches
The
prediction ranges (95 % confidence
intervals) from the polls model includes the Rallings and Thrasher
predictions for Labour and the Liberal Democrats, but narrowly misses
for the Conservatives.
Of course using different local election results produces different
predictions, but note that
for all three parties the confidence
intervals of both
predictions overlap.
By verified, I mean that
for a 50 year
prediction, you move the start and end dates back in time at 10 or 20 year
intervals until you run out of good data to compare against.
The Met Office Hadley Centre (Hadley Centre
for Climate
Prediction and Research) climate change model, Hadley Centre Coupled Model, version 3 (HadCM3)[53], a coupled atmosphere - ocean general circulation model, was used
for the time
intervals 2020, 2050 and 2080 (note these date represent a time windows of ten years either side of the time
interval date, i.e. 2020 is an average of the years 2010 — 2029, 2050
for 2040 — 2059 and 2080
for 2070 — 2089), under three emission scenarios of the IPCC Special Report on Emissions Scenarios (SRES)[54]: scenario A1B (maximum energy requirements; emissions differentiated dependent on fuel sources; balance across sources), A2A (high energy requirements; emissions less than A1 / Fl) and B2A (lower energy requirements; emissions greater than B1).
Do you overlay «confidence
intervals» or «
prediction error» bars on the analyses you provide
for clients?
We also discuss confidence
intervals for these
predictions.
I hope this exercise can be repeated annually or at 5 year
intervals, and include the
predictions from other models
for comparison (one other is presented above), such as Latif et al's model and Tsonis et al's model, along with the simple linear plus sinusoid.
I think what this point highlights is that without an a priori belief about the relationship between time from
prediction and an expected confidence
interval for prediction accuracy, it's very hard to know where the finish line is in this kind of an evaluation.
Past variations suggest a 95 % confidence
interval for this
prediction ranging from 3.2 to 5.2 million km2 (+ / - 1.0).
And the distinction between weather and climate is bogus — simply provides another uncertain averaging
interval for an escape hatch when the wrong
predictions become too embarrassing.
These new sea ice proxy records are needed (1) to fully prove the scenarios of a succession from an extended ice shelf to polynya / open - water conditions (cf., Fig. 6), (2) to reconstruct in more detail the changes in sea ice cover
for early, middle and late LIG
intervals characterized by very different external forcings and related internal feedback mechanisms, and (3) to allow a more fundamental proxy data / modeling comparison that results in model improvements and better reproduction of the LIG climatic evolution and
prediction of future climatic scenarios20, 21,22,23, 64.
apart from the ludicrous «confidence
intervals» which show
for most if not all
predictions that the standard errors are larger than the predicted effects.
The code here follows the method of Zervas 2009, «Sea Level Variations of the United States 1854 - 2006,» NOAA Technical Report NOS CO-OPS 053, p. 15 - 24, to account
for autocorrelation, when calculating confidence
intervals and
prediction intervals...
A Fourier analysis of each 4 kyr
interval can then be used to produce a local «
prediction»
for the subsequent 1 ka, based on the putative cycles in the preceding 4 kyr.
Even a low CE value may still provide
prediction intervals that are useful
for drawing particular scientific conclusions.
The figure also illustrates
predictions made at proxy values A and B and the corresponding
prediction intervals (wide blue lines)
for the temperature.
You state exactly that which you know within an acceptable confidence
interval that is the norm
for that discipline, but not by hindcasting, but by making
predictions of key variables whose values were not determined in the past, to show the validity of your theory / model.
The
predictions could be made
for any future period at one year
intervals.
This is the one I think looks like yours: http://img710.imageshack.us/i/compareb.png/ This is with increased
prediction interval to take care
for autocorrelation, might be too simplified though: