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This Defense Intelligence Reference Document, dated 11 March 2010, was prepared by the Defense Intelligence Agency's Defense Warning Office under the Advanced Aerospace Weapon System Applications Program. It introduces the Statistical Drake Equation, which treats each Drake factor as a random variable with a mean value and a standard deviation. Using its example inputs, the paper estimates that the nearest extraterrestrial civilization lies between 1,361 and 3,979 light years away with 75% probability. The author's 2008 International Astronautical Congress paper is attached as an appendix.
From the source:Release of 2026-09-18 Incident: 3/11/10, Las Vegas, Nevada. Released with redactions. This document is a Defense Intelligence Reference Document (DIRD), a technical reference format used by the Defense Intelligence Agency (DIA) to capture baseline knowledge on a specific topic for later analytic use. DIRDs are best understood as reference and synthesis products rather than as original research. It is one of 38 DIRDs produced under the Advanced Aerospace Weapon System Applications Program (AAWSAP) between 2009 and 2011. Because AAWSAP’s scope permitted a broad range of supporting topics, not every DIRD in the series directly concerns aerospace systems or future threat assessment. The following summary reflects the DIRD’s scope and framing at the time of writing and should not be read as implying current validation of the concepts discussed. This DIRD introduces the Drake Equation, a well-known thought framework for estimating how many communicative extraterrestrial civilizations might exist in the galaxy. It reformulates the equation in statistical terms, arguing that the usual approach of assigning fixed values to its variables is too simplistic because major inputs are uncertain and are better modeled as probability distributions. Using that approach, it concludes that, if one accepts the underlying logic of the Drake Equation, the estimated number of communicating civilizations should be treated as a range of possible values, and that the likely distance between neighboring civilizations can likewise be expressed statistically rather than as a single figure. The document is primarily a mathematical and methodological exercise, and its worked examples rely on assumed values to illustrate the framework rather than to establish a firm astrophysical estimate. Overall, it is an attempt to formalize uncertainty within the Drake framework rather than an attempt to bound the actual likelihood, prevalence, or proximity of extraterrestrial civilizations.
UNCLASSIFIED/ /fOR OFFI&IAk Wlii QPU,¥ fact 2670 light years. Finally, the standard deviation equals 1309 light years: THIS IS GOOD NEWS FOR SETI, inasmuch as the nearest ET Civilization might lie at just 1 sigma =2670-1309 =1361 light years from us. From Figure 6, we see that the probability of finding ExtraTenestrials is practically zero up to a distance of about 500 light years from Earth. Then it starts increasing with the increasing distance from Earth, and reaches its maximum at _fl_ ,?- rrmde = rpeak = Ce 3 e 9 ~1933 light years. (152) This is the MOST LIKELY VALUE of the distance at which we can expect to fi11d the nearest ExtraTerrestrial civilization. It is not, however, the mean value of the probability distribution (113) for .feT_Distana,(r) . In fact, the probability density (] l 3) has an infinite tail on the right, as clearly shown in Figure 6, and hence its mean value must be higher than its peak value. As given by ( 119), its mean value is _!!_ 0"2 r,11ea 11 l'alue =C e 3 e 18 ~ 2670 light years. (153) This is the MEAN (value of the) DISTANCE at which we can expect to find ExtraTerrestrials. After having found the above two distances (1933 and 2670 light years, respectively) , the next natural question that arises is: "what is the range, forth and back around the mean value of the distance, within which we can expect to find ExtraTenestrials with "the highest hopes ?," The answer to this question is given by the notion of standard deviation, that we already found to be given by (123) _fl_ 0"2 ~ (TET_Dislana, = Ce 3 e 18 Ve9 - 1 ~1309 light years. ... (154) More precisely, this is the so called I-sigma (distance) level. Probability theory then shows that the nearest ExtraTenestrial civilization is expected to be located within this range, i.e. within the two distances of (2670-1309) = 1361 light years and (2670+ 1309) = 3979 light years, with probability given by the integral of fET_Distana, (r) taken in between these two lower and upper limits, that is: i39791ightyears /ET Distana,(r)dr~0.75 = 75% (155) 136 llightyears - In plain words: with 75% probability, the nearest ExtraTerrestrial civilization is located in between the distances of 1361 and 3979 light years from us, having assumed the input values to the Drake Equation given by Table 1. If we change those input values, then all the numbers change again. 9. THE "DATA ENRICHMENT PRINCIPLE" AS THE BEST CL T CONSEQUENCE UPON THE STATISTICAL DRAKE EQUATION (ANY NUMBER OF FACTORS ALLOWED) As a fitting climax to all the statistical equations developed so far, let us now state our "DATA ENRICHMENT PRINCIPLE," It simply states that "The Higher the Number of Factors in the Statistical Drake equation, The Better," Put in this simple way, it simply looks like a new way of saying that the CLT lets the random variable Y approach the nonnal distribution when the number of terms in the sum (4) approaches infinity. And this is the case, indeed. However, our "Data Enrichment Principle" has more profound methodological consequences that we cannot explain now, but hope to describe more precisely in one or more coming papers. CONCLUSIONS We have sought to extend the classical Drake equation to let it encompass Statistics and Probability. This approach appears to pave the way to future, more profound investigations intended not only to associate "enor bars" to each factor in the Drake equation, but especially to increase the number of factors themselves. In fact, thi s seems to be the only way to incorporate into the Drake UNCLASSIFIED/ ffOR OFFI&IAk Wlii QPII.¥ 53
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Official release, from the pursue collection. The PDF is mirrored here; the original link is above. 55 pages are in the text index: search them above, or from the library's search.