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	<title>Comments on: Paul Linsay&#039;s Poisson Fit</title>
	<atom:link href="http://climateaudit.org/2007/01/06/paul-linsays-poisson-fit/feed/" rel="self" type="application/rss+xml" />
	<link>http://climateaudit.org/2007/01/06/paul-linsays-poisson-fit/</link>
	<description>by Steve McIntyre</description>
	<lastBuildDate>Sat, 18 May 2013 14:30:08 +0000</lastBuildDate>
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	<item>
		<title>By: Frank Upton</title>
		<link>http://climateaudit.org/2007/01/06/paul-linsays-poisson-fit/#comment-74718</link>
		<dc:creator><![CDATA[Frank Upton]]></dc:creator>
		<pubDate>Thu, 13 Dec 2007 17:37:18 +0000</pubDate>
		<guid isPermaLink="false">http://www.climateaudit.org/?p=1022#comment-74718</guid>
		<description><![CDATA[Months late, I know, but I just wanted to suggest that an time-variable observation bias is quite likely in hurricane detection.  A hurricane is defined as a storm in which sustained windspeeds of more than a certain speed are found, at some point in its career.  In the past, windspeeds could mostly only be measured accurately on land.  Now, windspeeds can be measured remotely by radar.  It is therefore more likely now that a storm which qualifies as a hurricane will be identified as such as than it was, say, 60 years ago.  Or have I, too, missed something?]]></description>
		<content:encoded><![CDATA[<p>Months late, I know, but I just wanted to suggest that an time-variable observation bias is quite likely in hurricane detection.  A hurricane is defined as a storm in which sustained windspeeds of more than a certain speed are found, at some point in its career.  In the past, windspeeds could mostly only be measured accurately on land.  Now, windspeeds can be measured remotely by radar.  It is therefore more likely now that a storm which qualifies as a hurricane will be identified as such as than it was, say, 60 years ago.  Or have I, too, missed something?</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: matt vooro</title>
		<link>http://climateaudit.org/2007/01/06/paul-linsays-poisson-fit/#comment-74717</link>
		<dc:creator><![CDATA[matt vooro]]></dc:creator>
		<pubDate>Fri, 24 Aug 2007 16:56:32 +0000</pubDate>
		<guid isPermaLink="false">http://www.climateaudit.org/?p=1022#comment-74717</guid>
		<description><![CDATA[NAMED STORMS AND SOLAR FLARING


Some meteorologists have observed that the key circumstances that factor into hurricane formation are primarily sea surface temperatures, wind shear, and global wind events.
They also believe that stationary high pressure centers over North America and
 El Nino cycles in the Pacific cause the Atlantic Hurricanes to turn north into the Mid-Atlantic. Also there appear to be fewer hurricanes during El Nino years more recently

While all this may be true in terms of outer symptoms, it does not explain the inner causes of hurricanes nor do they help to predict future number of named storms, a process which more recently has not been accurate.

Standard meteorology does not yet embrace the electrical nature of our weather, plasma physics, nor the plasma electrical discharge from near earth comets. Solar cycles and major solar storm events like X flares are mistakenly ignored. Yet solar flares disrupt the electrical fields of our ionosphere and atmosphere and cause electrical energy to flow between our ionosphere and upper cloud tops in developing storms.
Here is what Space Weather recently said and recorded when showing an electrical connection from the ionosphere to the top of storm clouds on August 23,2007.
 GIGANTIC JETS: Think of them as sprites on steroids: Gigantic Jets are lightning-like discharges that spring from the top of thunderstorms, reaching all the way from the thunderhead to the ionosphere 50+ miles overhead. They&#039;re enormous and powerful.
You&#039;ve never seen one? &quot;Gigantic Jets are very rare,&quot; explains atmospheric scientist and Jet-expert Oscar van der Velde of the Université Paul Sabatier&#039;s Laboratoire dAérologie in Toulouse, France. &quot;The first one was discovered in 2001 by Dr. Victor Pasko in Puerto Rico. Since then fewer than 30 jets have been recorded--mostly over open ocean and on only two occasions over land.&quot;
The resulting increased electrical currents affect the jet streams [which are also electrical] and which energize and drive our developing storms and hurricanes.

Here is what NASA said about the recent large X-20 solar flare on April 3, 2001[release 01-66]

&quot;This explosion was estimated as an X-20 flare, and was as
strong as the record X-20 flare on August 16, 1989, &quot; said Dr.
Paal Brekke, the European Space Agency Deputy Project
Scientist for the Solar and Heliospheric Observatory (SOHO),
one of a fleet of spacecraft monitoring solar activity and its
effects on the Earth. &quot;It was more powerful that the famous
March 6, 1989 flare which was related to the disruption of the
power grids in Canada.&quot;

 Canada had record high temperatures that summer [This writers comments. not by NASA]

Monday&#039;s flare and the August 1989 flare are the most powerful
recorded since regular X-ray data became available in 1976.

Solar flares, among the solar system&#039;s mightiest eruptions,
are tremendous explosions in the atmosphere of the Sun capable
of releasing as much energy as a billion megatons of TNT.
Caused by the sudden release of magnetic energy, in just a few
seconds flares can accelerate solar particles to very high
velocities, almost to the speed of light, and heat solar
material to tens of millions of degrees.

The flare erupted at 4:51 p.m. EDT Monday, and produced an R4
radio blackout on the sunlit side of the Earth. An R4
blackout, rated by the NOAA SEC, is second to the most severe
R5 classification. The classification measures the disruption
in radio communications. X-ray and ultraviolet light from the
flare changed the structure of the Earth&#039;s electrically
charged upper atmosphere (ionosphere). This affected radio
communication frequencies that either pass through the
ionosphere to satellites or are reflected by it to traverse
the globe.
[Note red highlighting is by this author ,not NASA]
Here is what flares affect
.
Industries on the ground can be adversely affected, including electrical
power generation facilities, ionospheric radio communications, satellite
communications, cellular phone networks, sensitive fabrication industries,
 plus the electrical system of our entire planet including equatorial jet streams, storm clouds, hurricanes, ionosphere, northern and southern jet streams, earths atmosphere, vertical electrical fields between earths surface and the ionosphere just to mention a few.


The reason for all the extra named storms recently 2000-2005 is not global warming but the increased number of significant solar flares, comet fly byes and the unique planetary alignment during the latter part of solar cycle #23. These events can occur any time during a solar cycle but are more prominent around the years of the solar maximum and especially during 6-7 years of the ramp down from maximum to minimum. Refer to the web page of CELESTIAL DELIGHTS by Francis Reddy   http://celestialdelights.info/sol/XCHART.GIF for an excellent article and illustration of solar flares and solar cycles during the last three solar cycles.
  The use of simple Regression analysis of past named storms to predict future storms will continue to be of limited value unless these randomly occurring solar events are taken into account as well .One cannot accurately predict the score of future ball games by simply looking at past ball games. You have look at each new year based on the unique circumstances of that new season


The attached table clearly illustrates why there were so few storms [only10] in 2006 and why the previous years 1998-2005 was so much more active in terms of named storms namely [16-28 storms/year] .The table for example shows that during 2003 there were 16 named storms and twenty [20] X class solar flares during the main hurricane season of June1-November 30. Three of the solar flares were the very large ones like X28, X17 and X10. On the other hand during 2006 there were only 10 named storms and only 4 X size solar flares of which none were during the hurricane season. During 2005 and 2003 there were 100 and 162 respectively of M size solar flares while in 2006 there were only 10. The 2000-2005 increase of named storms was not due to global warming or the years 2006-2007 would have continued to be high in terms of storms. During the period 2000-2005, much more electrical energy was pumped into our atmosphere by the solar flares especially the larger X size flares. There may have also been planetary electrical field increase brought on by the close passing of several major comets and special planetary alignments, like during September 6,1999 and August 26-29,2003. The year 2007 will likely be similar to 2006 with fewer storms as there has been no major solar flaring to date or major passing comets. It is possible but unlikely that major solar flaring will take place during a solar minimum year which the year 2007 is. Unless there will be significantly more solar flaring during the latter part of this year, the number of named storms will again be closer to the average of 9- 10 and not 15-17 as originally predicted nor the current predictions of some 13 -15 storms.



YEAR	# OF X SIZE 	DURINGG 	EL NINO	# OF NAMED 	SOLARR 	COMETS
	SOLAR	LARGE 	HURRIC.	YEAR	STORMS 	PHASE	Near
	FLARESS	FLARES	SEASON		adjustedd	not adjust.
1996	1		1		13	12	solar min	HALE BOOP
1997	3	X9.4	3	YES	8	7
1998	14		10	NA	15	14
1999	4		4		13	12	PL	LEE
2000	17	  X5.7	13		16	15	solar max	ENCKE
2001	18	 X20,X14.4	8		16	15	PL[six]	C-LINEAR  2001A2B
2002	11		9	YES	13	12
2003	20	X28,17,10	15		16	16	PL	NEAT V1
2004	12		11	YES	15	15
2005	18	X17	12	NA	28	28
2006	4	X9	0	YES	10	10
2007	0		0	NA	5	5	solar min
	to date 		to date 0		to date 	to date

            *	assumed season	June1 to
			Nov-30
	C&amp;M flares were not included
	Some flares last longer and  deposit more energy. This was not noted.

	NA	 EL NINO present but not during hurricane season
		Very minor EL NINO months at the beginning of year
	PL	Special planetary alignment during hurricane season


Since major solar flares are difficult to predict, one can recognize in what phase of the solar cycle one is predicting into and use that as an indicator of possible below average, average or above average solar storm level which in turn translates to below average, average or above average named storms. See paper by T.Bai called PERIODICITIES IN FLARE OCCURRENCE ,ANALYSIS OF CYCLES 19-23 on bai@quake.stanford.edu

 Above average flares occur during 6-7 solar ramp down period and to a lesser extent, the 3-4 years around the solar maximum. Average and below average flares occur at solar minimum and the 2-3 of the solar build up leading to solar maximum. Specific planetary alignments and the swing of major comets around our sun will also tend to increase the named storm activity.  There are exceptions to every rule and sometime things are different from the normal or the past.

For more information about the new science of weather and the electrical nature of our planet and our planets atmosphere refer to the writings of James McCanney and his latest book PRINCIPIA METEROROLOGIA  THE PHYSICS OF THE SUN]]></description>
		<content:encoded><![CDATA[<p>NAMED STORMS AND SOLAR FLARING</p>
<p>Some meteorologists have observed that the key circumstances that factor into hurricane formation are primarily sea surface temperatures, wind shear, and global wind events.<br />
They also believe that stationary high pressure centers over North America and<br />
 El Nino cycles in the Pacific cause the Atlantic Hurricanes to turn north into the Mid-Atlantic. Also there appear to be fewer hurricanes during El Nino years more recently</p>
<p>While all this may be true in terms of outer symptoms, it does not explain the inner causes of hurricanes nor do they help to predict future number of named storms, a process which more recently has not been accurate.</p>
<p>Standard meteorology does not yet embrace the electrical nature of our weather, plasma physics, nor the plasma electrical discharge from near earth comets. Solar cycles and major solar storm events like X flares are mistakenly ignored. Yet solar flares disrupt the electrical fields of our ionosphere and atmosphere and cause electrical energy to flow between our ionosphere and upper cloud tops in developing storms.<br />
Here is what Space Weather recently said and recorded when showing an electrical connection from the ionosphere to the top of storm clouds on August 23,2007.<br />
 GIGANTIC JETS: Think of them as sprites on steroids: Gigantic Jets are lightning-like discharges that spring from the top of thunderstorms, reaching all the way from the thunderhead to the ionosphere 50+ miles overhead. They&#8217;re enormous and powerful.<br />
You&#8217;ve never seen one? &#8220;Gigantic Jets are very rare,&#8221; explains atmospheric scientist and Jet-expert Oscar van der Velde of the Université Paul Sabatier&#8217;s Laboratoire dAérologie in Toulouse, France. &#8220;The first one was discovered in 2001 by Dr. Victor Pasko in Puerto Rico. Since then fewer than 30 jets have been recorded&#8211;mostly over open ocean and on only two occasions over land.&#8221;<br />
The resulting increased electrical currents affect the jet streams [which are also electrical] and which energize and drive our developing storms and hurricanes.</p>
<p>Here is what NASA said about the recent large X-20 solar flare on April 3, 2001[release 01-66]</p>
<p>&#8220;This explosion was estimated as an X-20 flare, and was as<br />
strong as the record X-20 flare on August 16, 1989, &#8221; said Dr.<br />
Paal Brekke, the European Space Agency Deputy Project<br />
Scientist for the Solar and Heliospheric Observatory (SOHO),<br />
one of a fleet of spacecraft monitoring solar activity and its<br />
effects on the Earth. &#8220;It was more powerful that the famous<br />
March 6, 1989 flare which was related to the disruption of the<br />
power grids in Canada.&#8221;</p>
<p> Canada had record high temperatures that summer [This writers comments. not by NASA]</p>
<p>Monday&#8217;s flare and the August 1989 flare are the most powerful<br />
recorded since regular X-ray data became available in 1976.</p>
<p>Solar flares, among the solar system&#8217;s mightiest eruptions,<br />
are tremendous explosions in the atmosphere of the Sun capable<br />
of releasing as much energy as a billion megatons of TNT.<br />
Caused by the sudden release of magnetic energy, in just a few<br />
seconds flares can accelerate solar particles to very high<br />
velocities, almost to the speed of light, and heat solar<br />
material to tens of millions of degrees.</p>
<p>The flare erupted at 4:51 p.m. EDT Monday, and produced an R4<br />
radio blackout on the sunlit side of the Earth. An R4<br />
blackout, rated by the NOAA SEC, is second to the most severe<br />
R5 classification. The classification measures the disruption<br />
in radio communications. X-ray and ultraviolet light from the<br />
flare changed the structure of the Earth&#8217;s electrically<br />
charged upper atmosphere (ionosphere). This affected radio<br />
communication frequencies that either pass through the<br />
ionosphere to satellites or are reflected by it to traverse<br />
the globe.<br />
[Note red highlighting is by this author ,not NASA]<br />
Here is what flares affect<br />
.<br />
Industries on the ground can be adversely affected, including electrical<br />
power generation facilities, ionospheric radio communications, satellite<br />
communications, cellular phone networks, sensitive fabrication industries,<br />
 plus the electrical system of our entire planet including equatorial jet streams, storm clouds, hurricanes, ionosphere, northern and southern jet streams, earths atmosphere, vertical electrical fields between earths surface and the ionosphere just to mention a few.</p>
<p>The reason for all the extra named storms recently 2000-2005 is not global warming but the increased number of significant solar flares, comet fly byes and the unique planetary alignment during the latter part of solar cycle #23. These events can occur any time during a solar cycle but are more prominent around the years of the solar maximum and especially during 6-7 years of the ramp down from maximum to minimum. Refer to the web page of CELESTIAL DELIGHTS by Francis Reddy   <a href="http://celestialdelights.info/sol/XCHART.GIF" rel="nofollow">http://celestialdelights.info/sol/XCHART.GIF</a> for an excellent article and illustration of solar flares and solar cycles during the last three solar cycles.<br />
  The use of simple Regression analysis of past named storms to predict future storms will continue to be of limited value unless these randomly occurring solar events are taken into account as well .One cannot accurately predict the score of future ball games by simply looking at past ball games. You have look at each new year based on the unique circumstances of that new season</p>
<p>The attached table clearly illustrates why there were so few storms [only10] in 2006 and why the previous years 1998-2005 was so much more active in terms of named storms namely [16-28 storms/year] .The table for example shows that during 2003 there were 16 named storms and twenty [20] X class solar flares during the main hurricane season of June1-November 30. Three of the solar flares were the very large ones like X28, X17 and X10. On the other hand during 2006 there were only 10 named storms and only 4 X size solar flares of which none were during the hurricane season. During 2005 and 2003 there were 100 and 162 respectively of M size solar flares while in 2006 there were only 10. The 2000-2005 increase of named storms was not due to global warming or the years 2006-2007 would have continued to be high in terms of storms. During the period 2000-2005, much more electrical energy was pumped into our atmosphere by the solar flares especially the larger X size flares. There may have also been planetary electrical field increase brought on by the close passing of several major comets and special planetary alignments, like during September 6,1999 and August 26-29,2003. The year 2007 will likely be similar to 2006 with fewer storms as there has been no major solar flaring to date or major passing comets. It is possible but unlikely that major solar flaring will take place during a solar minimum year which the year 2007 is. Unless there will be significantly more solar flaring during the latter part of this year, the number of named storms will again be closer to the average of 9- 10 and not 15-17 as originally predicted nor the current predictions of some 13 -15 storms.</p>
<p>YEAR	# OF X SIZE 	DURINGG 	EL NINO	# OF NAMED 	SOLARR 	COMETS<br />
	SOLAR	LARGE 	HURRIC.	YEAR	STORMS 	PHASE	Near<br />
	FLARESS	FLARES	SEASON		adjustedd	not adjust.<br />
1996	1		1		13	12	solar min	HALE BOOP<br />
1997	3	X9.4	3	YES	8	7<br />
1998	14		10	NA	15	14<br />
1999	4		4		13	12	PL	LEE<br />
2000	17	  X5.7	13		16	15	solar max	ENCKE<br />
2001	18	 X20,X14.4	8		16	15	PL[six]	C-LINEAR  2001A2B<br />
2002	11		9	YES	13	12<br />
2003	20	X28,17,10	15		16	16	PL	NEAT V1<br />
2004	12		11	YES	15	15<br />
2005	18	X17	12	NA	28	28<br />
2006	4	X9	0	YES	10	10<br />
2007	0		0	NA	5	5	solar min<br />
	to date 		to date 0		to date 	to date</p>
<p>            *	assumed season	June1 to<br />
			Nov-30<br />
	C&amp;M flares were not included<br />
	Some flares last longer and  deposit more energy. This was not noted.</p>
<p>	NA	 EL NINO present but not during hurricane season<br />
		Very minor EL NINO months at the beginning of year<br />
	PL	Special planetary alignment during hurricane season</p>
<p>Since major solar flares are difficult to predict, one can recognize in what phase of the solar cycle one is predicting into and use that as an indicator of possible below average, average or above average solar storm level which in turn translates to below average, average or above average named storms. See paper by T.Bai called PERIODICITIES IN FLARE OCCURRENCE ,ANALYSIS OF CYCLES 19-23 on <a href="mailto:bai@quake.stanford.edu">bai@quake.stanford.edu</a></p>
<p> Above average flares occur during 6-7 solar ramp down period and to a lesser extent, the 3-4 years around the solar maximum. Average and below average flares occur at solar minimum and the 2-3 of the solar build up leading to solar maximum. Specific planetary alignments and the swing of major comets around our sun will also tend to increase the named storm activity.  There are exceptions to every rule and sometime things are different from the normal or the past.</p>
<p>For more information about the new science of weather and the electrical nature of our planet and our planets atmosphere refer to the writings of James McCanney and his latest book PRINCIPIA METEROROLOGIA  THE PHYSICS OF THE SUN</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: John Creighton</title>
		<link>http://climateaudit.org/2007/01/06/paul-linsays-poisson-fit/#comment-74716</link>
		<dc:creator><![CDATA[John Creighton]]></dc:creator>
		<pubDate>Mon, 26 Feb 2007 00:56:38 +0000</pubDate>
		<guid isPermaLink="false">http://www.climateaudit.org/?p=1022#comment-74716</guid>
		<description><![CDATA[#186 Dan, I think a similar type of analysis would work but record high temperatures aren&#039;t really a poison process. If you find the average distance from the mean temperature at which recorded high temperatures occur and instead count the number of days which the temperatures deviates from the mean by this amount or more you would have a poison process. This could match closely the counts of record high temperatures but will not equal it exactly.]]></description>
		<content:encoded><![CDATA[<p>#186 Dan, I think a similar type of analysis would work but record high temperatures aren&#8217;t really a poison process. If you find the average distance from the mean temperature at which recorded high temperatures occur and instead count the number of days which the temperatures deviates from the mean by this amount or more you would have a poison process. This could match closely the counts of record high temperatures but will not equal it exactly.</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: Dan Hughes</title>
		<link>http://climateaudit.org/2007/01/06/paul-linsays-poisson-fit/#comment-74715</link>
		<dc:creator><![CDATA[Dan Hughes]]></dc:creator>
		<pubDate>Sun, 25 Feb 2007 12:01:50 +0000</pubDate>
		<guid isPermaLink="false">http://www.climateaudit.org/?p=1022#comment-74715</guid>
		<description><![CDATA[Speaking of counting things, would the same type of analysis apply to counting days of record-setting high and low temperatures as described &lt;a href=&quot;http://hallofrecord.blogspot.com/index.html&quot; rel=&quot;nofollow&quot;&gt;here&lt;/a&gt;?]]></description>
		<content:encoded><![CDATA[<p>Speaking of counting things, would the same type of analysis apply to counting days of record-setting high and low temperatures as described <a href="http://hallofrecord.blogspot.com/index.html" rel="nofollow">here</a>?</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: Numberwatch by John Brignell &#187; DDD</title>
		<link>http://climateaudit.org/2007/01/06/paul-linsays-poisson-fit/#comment-74714</link>
		<dc:creator><![CDATA[Numberwatch by John Brignell &#187; DDD]]></dc:creator>
		<pubDate>Sat, 24 Feb 2007 17:00:24 +0000</pubDate>
		<guid isPermaLink="false">http://www.climateaudit.org/?p=1022#comment-74714</guid>
		<description><![CDATA[[...] to that number 15, there seems to have been an outbreak of Data Deficiency Disorder over at Climate Audit. When you are stuck with a limited number of data, it is tempting to try all sorts of a posteriori [...]]]></description>
		<content:encoded><![CDATA[<p>[...] to that number 15, there seems to have been an outbreak of Data Deficiency Disorder over at Climate Audit. When you are stuck with a limited number of data, it is tempting to try all sorts of a posteriori [...]</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: Ken Fritsch</title>
		<link>http://climateaudit.org/2007/01/06/paul-linsays-poisson-fit/#comment-74713</link>
		<dc:creator><![CDATA[Ken Fritsch]]></dc:creator>
		<pubDate>Sun, 11 Feb 2007 18:07:26 +0000</pubDate>
		<guid isPermaLink="false">http://www.climateaudit.org/?p=1022#comment-74713</guid>
		<description><![CDATA[Re: #174

&lt;blockquote&gt;This case is extreme, using two discrete populations rather than a continuity, but still Ho is not reliably rejected unless the difference between populations is large - Paul Lindsay&#039;s test has little power. An alternative test, GLM, is much more powerful, and can be used to shows that the hurricane counts are not Poisson distributed.&lt;/blockquote&gt;

RichardT, I am not sure how to interpret your findings, but I would say that the p values that you and I derived for the 1945 to 2006 hurricane count fit to a Poisson distribution are close to same: 0.95 and 0.97.  It is that number that informs of the fit for that time period and gives the measure of Type II errors.  Those numbers indicate a small Type II error.  Your sensitivity test is something that shows considerably less robustness for detecting changes in means than my less than formal back-of-an-envelop test did, but that exercise is besides the point as it does not change the p value for the actual fit found.

I know that chi square goodness of fit tests can be less than robust and more sensitive tests where applicable should be applied.  For a goodness of fit for normal distribution, I was shown years ago that skewness and kurtosis tests could be superior to the chi square test and particularly when the data is sparse and binning of data becomes problematic.

I do not know how to interpret the difference in the goodness of fit tests between that for all hurricanes and land falling hurricanes for the 1945 to 2005(6) time period except to note that the sparse data for a small Poisson mean reduces the degrees of freedom to very small numbers for a chi square test.  The discrepancies between a predicted Poisson and the actual distribution for land fall hurricanes were in the middle of the range and not at the tails.

The telling analysis to me are the lack of trends in the land falling hurricanes and in the partitioned data that Steve M and David Smith have presented and analyzed &#039;€&quot; all of which point to some early undercounts and (lacking better explanations for these findings than I have seen) an immeasurable trend in total hurricanes.

I am hoping to see more details from you or Steve M on the Generalized Linear Models alternative test as I do not have much experience with fitting these models with a Poisson distribution (and ??).]]></description>
		<content:encoded><![CDATA[<p>Re: #174</p>
<blockquote><p>This case is extreme, using two discrete populations rather than a continuity, but still Ho is not reliably rejected unless the difference between populations is large &#8211; Paul Lindsay&#8217;s test has little power. An alternative test, GLM, is much more powerful, and can be used to shows that the hurricane counts are not Poisson distributed.</p></blockquote>
<p>RichardT, I am not sure how to interpret your findings, but I would say that the p values that you and I derived for the 1945 to 2006 hurricane count fit to a Poisson distribution are close to same: 0.95 and 0.97.  It is that number that informs of the fit for that time period and gives the measure of Type II errors.  Those numbers indicate a small Type II error.  Your sensitivity test is something that shows considerably less robustness for detecting changes in means than my less than formal back-of-an-envelop test did, but that exercise is besides the point as it does not change the p value for the actual fit found.</p>
<p>I know that chi square goodness of fit tests can be less than robust and more sensitive tests where applicable should be applied.  For a goodness of fit for normal distribution, I was shown years ago that skewness and kurtosis tests could be superior to the chi square test and particularly when the data is sparse and binning of data becomes problematic.</p>
<p>I do not know how to interpret the difference in the goodness of fit tests between that for all hurricanes and land falling hurricanes for the 1945 to 2005(6) time period except to note that the sparse data for a small Poisson mean reduces the degrees of freedom to very small numbers for a chi square test.  The discrepancies between a predicted Poisson and the actual distribution for land fall hurricanes were in the middle of the range and not at the tails.</p>
<p>The telling analysis to me are the lack of trends in the land falling hurricanes and in the partitioned data that Steve M and David Smith have presented and analyzed &#8216;€&#8221; all of which point to some early undercounts and (lacking better explanations for these findings than I have seen) an immeasurable trend in total hurricanes.</p>
<p>I am hoping to see more details from you or Steve M on the Generalized Linear Models alternative test as I do not have much experience with fitting these models with a Poisson distribution (and ??).</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: Ken Fritsch</title>
		<link>http://climateaudit.org/2007/01/06/paul-linsays-poisson-fit/#comment-74712</link>
		<dc:creator><![CDATA[Ken Fritsch]]></dc:creator>
		<pubDate>Sun, 11 Feb 2007 01:25:19 +0000</pubDate>
		<guid isPermaLink="false">http://www.climateaudit.org/?p=1022#comment-74712</guid>
		<description><![CDATA[Doing my standard chi square test for goodness of fit for a Poisson distribution for land falling hurricanes for the time periods 1851 to 2005, 1945 to 2005 and 1851 to 1944, I  found the following means, Xm, and chi square probabilities, p:

1851 to 2005:

Xm = 1.81 and p = 0.41

1945 to 2005:

Xm = 1.70 and p = 0.03

1851 to 1944:

Xm = 1.88 and p = 0.58

The trend line for land falling hurricane counts over the 1851 to 2005 time period has y = -0.0016x + 4.93  and R^2 = 0.0025.]]></description>
		<content:encoded><![CDATA[<p>Doing my standard chi square test for goodness of fit for a Poisson distribution for land falling hurricanes for the time periods 1851 to 2005, 1945 to 2005 and 1851 to 1944, I  found the following means, Xm, and chi square probabilities, p:</p>
<p>1851 to 2005:</p>
<p>Xm = 1.81 and p = 0.41</p>
<p>1945 to 2005:</p>
<p>Xm = 1.70 and p = 0.03</p>
<p>1851 to 1944:</p>
<p>Xm = 1.88 and p = 0.58</p>
<p>The trend line for land falling hurricane counts over the 1851 to 2005 time period has y = -0.0016x + 4.93  and R^2 = 0.0025.</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: richardT</title>
		<link>http://climateaudit.org/2007/01/06/paul-linsays-poisson-fit/#comment-74711</link>
		<dc:creator><![CDATA[richardT]]></dc:creator>
		<pubDate>Sat, 10 Feb 2007 22:49:20 +0000</pubDate>
		<guid isPermaLink="false">http://www.climateaudit.org/?p=1022#comment-74711</guid>
		<description><![CDATA[#181
try a second order term in the GLM model, else use a GAM]]></description>
		<content:encoded><![CDATA[<p>#181<br />
try a second order term in the GLM model, else use a GAM</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: Steve McIntyre</title>
		<link>http://climateaudit.org/2007/01/06/paul-linsays-poisson-fit/#comment-74710</link>
		<dc:creator><![CDATA[Steve McIntyre]]></dc:creator>
		<pubDate>Sat, 10 Feb 2007 22:19:47 +0000</pubDate>
		<guid isPermaLink="false">http://www.climateaudit.org/?p=1022#comment-74710</guid>
		<description><![CDATA[I tried the following test for a trend in the Poisson parameter (calculating glm0 as above). The trend coeffficient was not significant.

glm1=update(glm0,formula=x~1+index)
summary(glm1)

&lt;blockquote&gt;
##
#	Deviance Residuals:
#     Min        1Q    Median        3Q       Max
#-1.98996  -0.88819  -0.03531   0.52119   2.73641

#Coefficients:
#            Estimate Std. Error z value Pr(&gt;&#124;z&#124;)
#(Intercept) 1.416262   0.366138   3.868 0.000110 ***
#index       0.003170   0.002866   1.106 0.268673
#---
#Signif. codes:  0 &#039;***&#039; 0.001 &#039;**&#039; 0.01 &#039;*&#039; 0.05 &#039;.&#039; 0.1 &#039; &#039; 1

#(Dispersion parameter for poisson family taken to be 1)

#    Null deviance: 61.639  on 61  degrees of freedom
#Residual deviance: 60.414  on 60  degrees of freedom
#AIC: 287.76

#Number of Fisher Scoring iterations: 4&lt;/blockquote&gt;


anova(glm1,glm0)

&lt;blockquote&gt;
#Model 1: x ~ index
#Model 2: x ~ 1
#  Resid. Df Resid. Dev Df Deviance
#1        60     60.414
#2        61     61.639 -1   -1.225
&lt;/blockquote&gt;]]></description>
		<content:encoded><![CDATA[<p>I tried the following test for a trend in the Poisson parameter (calculating glm0 as above). The trend coeffficient was not significant.</p>
<p>glm1=update(glm0,formula=x~1+index)<br />
summary(glm1)</p>
<blockquote><p>
##<br />
#	Deviance Residuals:<br />
#     Min        1Q    Median        3Q       Max<br />
#-1.98996  -0.88819  -0.03531   0.52119   2.73641</p>
<p>#Coefficients:<br />
#            Estimate Std. Error z value Pr(&gt;|z|)<br />
#(Intercept) 1.416262   0.366138   3.868 0.000110 ***<br />
#index       0.003170   0.002866   1.106 0.268673<br />
#&#8212;<br />
#Signif. codes:  0 &#8216;***&#8217; 0.001 &#8216;**&#8217; 0.01 &#8216;*&#8217; 0.05 &#8216;.&#8217; 0.1 &#8216; &#8216; 1</p>
<p>#(Dispersion parameter for poisson family taken to be 1)</p>
<p>#    Null deviance: 61.639  on 61  degrees of freedom<br />
#Residual deviance: 60.414  on 60  degrees of freedom<br />
#AIC: 287.76</p>
<p>#Number of Fisher Scoring iterations: 4</p></blockquote>
<p>anova(glm1,glm0)</p>
<blockquote><p>
#Model 1: x ~ index<br />
#Model 2: x ~ 1<br />
#  Resid. Df Resid. Dev Df Deviance<br />
#1        60     60.414<br />
#2        61     61.639 -1   -1.225
</p></blockquote>
]]></content:encoded>
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	<item>
		<title>By: John Reid</title>
		<link>http://climateaudit.org/2007/01/06/paul-linsays-poisson-fit/#comment-74709</link>
		<dc:creator><![CDATA[John Reid]]></dc:creator>
		<pubDate>Sat, 10 Feb 2007 21:52:40 +0000</pubDate>
		<guid isPermaLink="false">http://www.climateaudit.org/?p=1022#comment-74709</guid>
		<description><![CDATA[Steve McIntyre says (#170)

&lt;blockquote&gt;
#141. John Reid, wouldn&#039;t it make more sense to test the hurricane distribution for 1945-2006 as Poisson rather than calculating a parameter for 1945-2004 and then testing 2005.
&lt;/blockquote&gt;

Yes it would. I only did it the way I did it to allow me to make the either/or argument more clearly. As it happens it may well be that the first 60 years is not significantly different from a Poisson distribution. I&#039;ll have a look at it.

JR]]></description>
		<content:encoded><![CDATA[<p>Steve McIntyre says (#170)</p>
<blockquote><p>
#141. John Reid, wouldn&#8217;t it make more sense to test the hurricane distribution for 1945-2006 as Poisson rather than calculating a parameter for 1945-2004 and then testing 2005.
</p></blockquote>
<p>Yes it would. I only did it the way I did it to allow me to make the either/or argument more clearly. As it happens it may well be that the first 60 years is not significantly different from a Poisson distribution. I&#8217;ll have a look at it.</p>
<p>JR</p>
]]></content:encoded>
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