Saturday, January 30, 2010

GOOGLE defines "inference" -- and does an interesting & useful job

By entering "define: inference" in the Google search engine, you get:

Definitions of Inference on the Web:

* the reasoning involved in drawing a conclusion or making a logical judgment on the basis of circumstantial evidence and prior conclusions rather ...

* Inference is the act or process of deriving a logical consequence conclusion from premises.

* The act or process of inferring by deduction or induction; That which is inferred; a truth or proposition drawn from another which is admitted ...

* a conclusion derived from observations

* A judgement based on reasoning rather than on direct or explicit statement. A conclusion based on facts or circumstances. For example, advised not to travel alone in temperatures exceeding fifty degrees below zero, the man in Jack London's "To Build a Fire" sets out anyway. ...

* is a logical guess based on evidence based on evidence in the text.

* A general conclusion drawn from information that is given.

* a conclusion one can draw from the presented details

* The skill of using the results of an investigation based on a premise.

* In machine learning, inference is the process of deriving conclusions or making predictions based on existing information. See Wikipedia for more.

* making conclusions about a piece of literature when the connection is not provided in a piece of literature.

* is the forming of a conclusion from premises by logical methods. (Intro)

* inferencing - This is the means by which the learner forms hypotheses, through attending to input, or using the situational context to interpret the input.

* The conclusions that one is able to draw from the data. Sometimes the numbers do not tell the whole story. Please see the section on How to use Canadian Cancer Surveillance On-Line. ...

* the process of reasoning whereby one statement (the conclusion) is derived from one or more other statements (the premises).


The dynamic evidence page

It's here: the law of evidence on Spindle Law. See also this post and this post.

Sunday, January 24, 2010

The Shonubi Problem Reappears: Estimating Drug Quantities

At the center of the Shonubi opinions -- all five(!) of them -- was the problem of using (apparently-)reliable evidence about the amount of illegal narcotics carried by a drug mule on one drug-smuggling trip to estimate the total amount of illegal narcotics carried by the drug mule during a number of other (apparent) drug-smuggling trips (eight trips in all in the Shonubi case). See United States v. Shonubi, 802 F. Supp. 859 (E.D.N.Y., 1992) (Weinstein, J.) ("Shonubi I"); United States v. Shonubi, 998 F.2d 84 (2d Cir, 1993) (Oakes, Newman & Cardamone, JJ.) ("Shonubi II"); United States v. Shonubi, 895 F.Supp. 460 (E.D.N.Y.) (Weinstein, J.) ("Shonubi III"); United States v. Shonubi, 103 F.3d 1085 (2d Cir., 1997) (Newman, Cardamone & Calabresi, JJ.) ("Shonubi IV"); United States v. Shonubi, 962 F. Supp. 370, 375 (E.D.N.Y. 1997) (Weinstein, J.) ("Shonubi V"[!]). See also P. Tillers, United States v. Shonubi: A Statistical Oddity?; "P. Tillers, Introduction: Three Original Contributions to Three Important Problems in the Law of Evidence," 18 Cardozo L. Rev. 1875 (1997); P. Tillers, "If wishes were horses: discursive comments on attempts to prevent individuals from being unfairly burdened by their reference classes," 4 Law, Probability and Risk 33 (2005).

This problem -- and the more general problem of drawing conclusions about a "population" based on a sample of the population -- reappeared (unsurprisingly) in United States v. Krasinski, 545 F.3d 546 (7th Cir. 2008).

In Krasinski the Seventh Circuit distinguished Shonubi II (and some other cases) by saying that in Krasinski, unlike in Shonubi (and in some other cited cases), the maximum and minimum amounts carried on each trip were known (pretty firmly, in any event). Id. at 552.

Otherwise, the Seventh Circuit held that the method used by the trial judge in Krasinski -- which was exactly the method originally used by Judge Weinstein in Shonubi (see Shonubi I) and condemned by the Second Circuit in Shonubi II: using the amount believed to have been carried by the drug mule on one trip to produce an average for all (apparently-)known drug-smuggling trips by the mule -- was not an abuse of discretion. The Seventh Circuit said nothing about the question that so occupied and bothered the mind of the Second Circuit: the use of "indirect" evidence to establish or estimate the total amount of the illegal drugs carried by a drug smuggler on all of the smuggler's drug-smuggling trips (that is, on all trips reasonably believed or reasonably shown to have been drug-smuggling trips). Compare my comment all evidence is circumstantial and indirect.

The Seventh Circuit said:

Krasinski maintains that the district court erred when it found him responsible for the sale of 112,000 pills. He contends he was only responsible for 30,000 pills and that any amount above that lacks sufficient indicia of reliability. A defendant has a due process right to be sentenced on the basis of reliable information, United States v. Bautista, 532 F.3d 667, 672 (7th Cir.2008), and a district court may not base its drug quantity calculation on pure speculation or “nebulous eyeballing,” United States v. Jarrett, 133 F.3d 519, 530 (7th Cir.1998). A seizure of the drugs involved in the offense, of course, provides reliable information regarding drug quantity. See Bautista, 532 F.3d at 672. Admissions in a plea agreement also conclusively establish the admitted facts. United States v. Warneke, 310 F.3d 542, 550 (7th Cir.2002) (“An admission is even better than a jury's finding beyond a reasonable doubt; it removes all contest from the case.”).

A district court may use a reasonable estimate of the quantity of drugs attributable to a defendant for guidelines purposes. United States v. Acosta, 534 F.3d 574, 582 (7th Cir.2008); see also U.S.S.G. § 2D1.1 cmt. n. 12 (“Where there is no drug seizure or the amount seized does not reflect the scale of the offense, the court shall approximate the quantity of the controlled substance.”). Here, Krasinski admitted in his plea agreement that he delivered between 5,000 and 30,000 Ecstasy pills on approximately eight to ten separate occasions. He also admitted delivering 7,000 pills on March 5, 2003. With these statements in mind, the district court first found that Krasinski delivered Ecstasy pills on seven occasions, a conservative figure in light of Krasinski's admission that he made eight to ten deliveries. The district court then took note of Krasinski's specific admission that he delivered 7,000 pills on one occasion. For the other six deliveries, the district court estimated that he delivered 17,500 pills each time, a figure he calculated by averaging the 5,000-and 30,000-pill figures. The result was a total of 112,000 pills.

As we have recognized before, arriving at sentencing determinations through averaging can be problematic. See United States v. Johnson, 185 F.3d 765, 768-69 (7th Cir.1999). “[A]t some point a court's estimation will seem less like a restrained approximation and more like unsupported conjecture.” United States v. Henderson, 58 F.3d 1145, 1152 (7th Cir.1995). A calculation based on a wide range of endpoints, for example, is cause for concern. Compare United States v. Sepulveda, 15 F.3d 1161, 1197 (1st Cir.1993) (using midpoint between four ounces and one kilogram to determine drug quantity erroneous) with United States v. Webster, 54 F.3d 1, 5-6 (1st Cir.1995) (upholding use of two ounces for circumstances where witness testified that one to three ounces supplied and eight ounces in instances where witness stated six to twelve ounces supplied). Extrapolating from a small number of known quantities also raises a red flag, especially when the maximum and minimum amounts are unknown. See Johnson, 185 F.3d at 769 (vacating sentence where amount carried on fourth trip determined only by looking to amount carried on three others); United States v. Shonubi, 998 F.2d 84, 89-90 (2d Cir.1993) (finding error in assumption that quantity of heroin possessed on one trip represented typical quantity on eight trips).

The calculation employed by the district court in this case was not the most conservative one it could have performed. The district court could have held Krasinski responsible for a one-time delivery of 7,000 pills, one delivery of 30,000 pills, and six deliveries of 5,000 pills, a calculation also consistent with the plea agreement. See Jarrett, 133 F.3d at 530-31 (approving conservative drug quantity approximation based on five months of undercover purchases and defendant's admissions). The result would have been a total of 67,000 pills, and, notably, a lower offense level for Krasinski. See Presentence Report at 6 (deeming Krasinski responsible for 80,000 to 240,000 Ecstasy pills).

Nonetheless, we cannot say that the district court's decision to hold Krasinski responsible for 112,000 pills was clearly erroneous. The district court based the number of deliveries and the range for the quantity of pills in those deliveries on numbers supplied by Krasinski himself. Significantly, unlike in Johnson, we know the maximum and minimum quantities involved. Cf. Johnson, 185 F.3d at 765. Moreover, Krasinski states in his sentencing memorandum that according to Misiolek, Ogonowski said Krasinski was responsible for about 100,000 pills, so a second source supported the decision to hold Krasinski responsible for between 80,000 and 240,000 pills, the range of pills in Krasinski's advisory guidelines range. And although Krasinski claims that Ogonowski would testify that Krasinski supplied only 30,000 pills, Krasinski cites nothing in support of his claim, and Krasinski admitted to supplying more than that in his own plea.


The dynamic evidence page

It's here: the law of evidence on Spindle Law. See also this post and this post.