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Note: some of the following material refers to analyses at
http://noosphere.princeton.edu/impulse.html
This is a temporary page to allow access for commentary.
The plot ImpEvperRcpNew.gif (bargraph in the impulse page)
compares the cumulative event Z-score for
the impulse and non-impulse event sets using Z^2 and covar.
Background: If the Z^2 and covar are both cumulatively significant over
the events, do the individual event zscores then correlate? That would
open the door to testing for anomalous event data (as distinguished from
purely random data). Answer: there is no correlation between Z^2 and
covar zscores for the events. Question: Do the Z^2 and covar then "turn
on" at random, or are they responding to different "signals"? The plot
tries to get at this question.
It shows that the Z^2 stat is only significant for the non-impulse set.
The covar stat is only significant for the impulse set.
So the two stats are distiguished by dividing the events into impuse and
non-impulse sets. Mean tests between the 4 high/low pairs (Imp-Z^2 vs
Imp-covar, etc) give pvals of 0.01 to 0.06. It's not due to outliers:
symmetric trimming of zscores increases the significance.
So we are left with the question: Are the impulse events different,
having a "covar signal", or is this just chance?
Note on the calc of probs:
There is one chisqr df for each second of Z^2 and for each second of covar[z^2].
One second of the dispersion stat therefore has df = 2.
Note: the covar (and hence the dispersion stat) is only approximately chisqr.
It's a good approx once df > 60 and gets better with more df.
It is *not*, however, asymptotically chisqr!
For the display of cumdevs:
Often I convert a block of seconds to a zscore, which is then plotted as a cumdev.
(It's often clearest to represent cumdevs as normal random walks)
This is usually obvious from the veritcal scale.
Recent plots on the superposition of impulse events and quakes have used
one-minute blocks for the cumdevs, for example.
Through the Oraworld event, there are 169 accepted, non-epoch events.
Impulse events are defined as sudden, un-anticipated events having a precise start point.
Thus an earthquake is an impulse event. A commando raid launched during an ongoing hostage crisis is not.
Impulse events allow for the:
1. clear definition of an event class
2. alignment of events to the start time for studying pre-event effects
I have refined the list since IONS. There I used about 56, now I use 46.
The 46 event set excludes events 1,2 and 3. Events 1-3 are in Aug 1998
when the network is sparse and the data gappy.
They are excluded to avoid problems in subsequent analyses with the impulse set.
Their exclusion doesn't change the overall picture.
I didn't have the Oraworld Resonance data at the time of the plots.
That's why there are *168* -46 = 122 non-impulse, non-epoch events.
Here are some general comments about what we've learned:
Recipe 1 (Z^2) stands out from the early blocking/recipe study as being 'best':
1. It has the highest cumul over events for different reg/resolution
blockings [ Z approx 2.7 ]
Recipe 1 suggests that :
1. node pairs may be more important than individual regs
2. 1-second resolution may be most sensitive resolution
The Device variance analysis gives:
1. the dev var is marginally significant for the events, suggesting it has a role to play
2. it is [nearly] uncorrelated with recipe 1, so it can be considered in parallel
The inclusion of the covar stat is an important step in the analysis because:
1. It is a 'logical' extension of recipe 1
2. It is [nearly]uncorrelated with recipe 1 and the dev var.
3. It gives a significant cumul over events [ Z approx 2.4 ]
The covar is a 'success'.
That is, we took lessons from recipe 1 [ node pairs & 1-sec res ] and
applied them to a *different* stat, but also sensitive to node pairs at 1-sec res.
And the result over the events is significant. The covar is more than
'just another stat' because it is based on a prior that says we know
where to look.
The covar success suggests:
1. Analysis should focus first non-epoch events. This avoids confounding
predictions with the working notion that 1-sec res is important. After
we know more, we'll go back to epoch events.
2. Studies should use both the Z^2 and covar.
With this success, look at some outstanding problems:
1. Is the experiment significant because of data anomalies or lucky
event prediction (aka exprmtr effect)?
2. Can we look meaningfully at individual events?
3. Why does the experiment look at positive deviations from expectation?
4. Is there evidence for global consciousnsee beyond the event experiment?
5. Is there dependence on reg number N? Is there dependence the network distribution?
6. Is there a recipe choice dependent on event-type?
7. Is there evidence for pre-event effects?
We have two tools for looking at these questions:
1. Covar & Z^2. covar is essentially independent of the original predictions and complements Z^2
2. Alt-sec. It permits independent tests of the same data periods.
Problem 1: Anomalies vs Experimenter
Break it down into:
1A. Is there an experimenter effect?
1B. Are data deviations anomalous?
Answer 1A:
The weight is for NO exprmtr effect.
1. Covar is independent of formal recipes, but finds significance.
2. Event Slide studies are not easily interpreted as exprmtr or DAT.
But not definitive:
1. Covar significance is weaker than formal predictions
2. Event slide hasn't been modelled yet.
Answer 1B:
The weight is YES there are anomalies.
1. Alt-sec on the longtrend argues for real correlations over long times
2. The longtrend alt-sec is supported by the altsec analysis done over quarters
3. The alt-sec correlations occur for a period associated with an
unusual world situation, as evidenced by the presidential poll
4. **New Result**: Alt-sec zscores for events.
I calc'd event zscores using altsecs for the Z^2 and covar. There is
weak positive correlation for each stat.
(see AltsecEvZcumdev.gif, AtlsecEvZcorrDiprstat.gif : the plots show the
cumdev of Pearson correlation between event zscores obtained using
alternate seconds. This is done for the 3 stats: Z^2, covar,
dispersion). All show a positive correlation that is strong through 2002
(at better than 0.01) declines thereafter, but remains overall positive
(at z=1.3 for the dispersion stat)
Problem 2: Individual event significance?
The answer is NO:
1. Reasonable models give event effect sizes less than z=0.5. Individual
events are thus indistiguishable from random data.
2. This goes double for parts of events.
3. Essentially all references to GCP (news, internet, Targ, etc.)
completely misunderstand this point. (we have a problem.. :-) )
Problem 3: Why look at positive deviations?
1. No reason. Some recipes, in fact, don't.
2. Impulse event set suggests this class may react negatively to the Z^2 stat.
3. Non-GCP quake data also suggests this.
4. This is a main question for the analysis...
Problem 4: Evidence beyond predicted events?
Answer is YES:
1. Covar as applied to events
2. Altsec longtrend & altsec quarters in conjunction with the world situation
3. Altsec correlations for Z^2 event zscores & covar event zscores **see attached plots**
4. Poll results
5. Non-GCP quakes
But not definitive:
1. No hypotheses tested
2. Poll and quake results are very tentative and 'data-miney'
Problem 5: N and distance dependences?
Note:
1. Modelling can't go forward without some answers
2. These are related in a node pair approach
3. N increases roughly linearly with time
4. But pair number increases as N^2 !
5. And event effect size is constant or decreases with time! (Decrease is borderline significant)
Partial answers:
The puzzle is that the effect size doesn't change but we are
entertaining a pair node model where the number of pairs increases
hugely over time (1999-01: 36 pairs, 2005-01: 1650 pairs).
Why?
If there is a proximity factor of the node pair reactivity, then:
1. The number of effective nodes actually grows as N, not N^2 (this is very approximate)
2. The signal-to-noise may actually decrease as the network adds distant
regs. (consistent with the measured event effect sizes)
Evidence:
1. The fraction of proximate pairs in the network (proximate=on the same
continent) varies between .5 and .25 (see NodePairFrctInterp.gif)
The fraction is (#pairsEuro+#pairsNorthAm)/#total_pairs. The plot
interpolates the fraction values for Newyears 1999-2005. (I'll redo this
more precisely soon.)
2. The variation of these proximate fractions correlates with event zscore for both the Z^2 and covar.
3. The correlation of proximate fractions and the Dispersion stat has a zscore of 2.2 (pval=0.013)
Problem 5: continuation..
Conclusions:
1. First, the obvious: If there is NO N dependence and NO distance dependence,
then there is no reason to have a GCP network. A single reg would be just as good.
2. Thus we assume at least one of these factors is important.
3. We get different modelling possibilities if the dependences are included or not.
4. A quick check I can do is to calculate the events using only European and only NorthAm regs.
5. A full look is a long calc which weights pairs by distance and takes different combos of the weighted pairs.
Problem 6: Should recipes depend on event-type?
1. This is the event category problem, extended to different stats
2. The key here is that it takes a lot of events of one category to make a decision (minimun 50)
3. Two examples of preliminary looks are a. natural disasters: these are
strong for covar and null for the Z^2 stat. Interestingly, this is also
seen in the 95 non-GCP earthquakes. b. non-impulse events (a very fuzzy
'category'); these are strong for Z^2 and null for the covar. There is a
weak hint that a negative Z^2 could be used for the impulse or natural
disaster events (see QksR7vsImp46.gif)
Problem 7: Is there evidence for pre-event effects
1. This requires very strong evidence indeed before it can be discussed above a whisper
2. We have some precedents: 9/11 variance and the dip in the covar about 2 hrs before for impulse, quake and (separately) tsunami events.
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