2,033 research outputs found
Gap bootstrap methods for massive data sets with an application to transportation engineering
In this paper we describe two bootstrap methods for massive data sets. Naive
applications of common resampling methodology are often impractical for massive
data sets due to computational burden and due to complex patterns of
inhomogeneity. In contrast, the proposed methods exploit certain structural
properties of a large class of massive data sets to break up the original
problem into a set of simpler subproblems, solve each subproblem separately
where the data exhibit approximate uniformity and where computational
complexity can be reduced to a manageable level, and then combine the results
through certain analytical considerations. The validity of the proposed methods
is proved and their finite sample properties are studied through a moderately
large simulation study. The methodology is illustrated with a real data example
from Transportation Engineering, which motivated the development of the
proposed methods.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS587 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Response to the Letter to the Editor
This paper has attracted interest around the world from the media (both TV
and newspapers). In addition, we have received letters, emails and telephone
calls. One of our favorites was a voicemail message asking us to return a call
to Australia at which point we would learn who really killed JFK. We welcome
the opportunity to respond to the letter to the editor from Mr. Fiorentino. Mr.
Fiorentino claims that our ``statement relating to the likelihood of a second
assassin based on the premise of three or more separate bullets is demonstrably
false.'' In response we would like to simply quote from page 327 of Gerald
Posner's book Case Closed, one of the most well known works supporting the
single assassin theory: ``If Connally was hit by another bullet, it had to be
fired from a second shooter, since the Warren Commission's own reconstructions
showed that Oswald could not have operated the bolt and refired in 1.4
seconds.'' Mr. Fiorentino also claims that the ``second fatal flaw is the use
of a rather uncomplicated formula based on Bayes Theorem.'' Let denote the
evidence and denote the theory that there were just two bullets (and hence
a single shooter). We used Bayes Theorem to hypothetically calculate
from and the prior probability . In order to make ten
times more likely than , the ratio of the prior probabilities
[i.e., ] would have to be greater than 15. Thus, we again
conclude that this casts serious doubt on Dr. Guinn's conclusion that the
evidence supported just two bullets. Sadly, this is far from the first time
that probability has been misunderstood and/or misapplied in a case of public
interest. A notable British example is the Clark case. See Nobles and Schiff
(2005) for details. Finally, we welcome and, in fact, encourage members of the
scientific community to provide alternative analyses of the data.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS154 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
THE IDENTIFICATION OF THE RIBOSOMAL RNA CISTRON BY SEQUENCE COMPLEMENTARITY, II. SATURATION OF AND COMPETITIVE INTERACTION AT THE RNA CISTRON
Channelized melt flow in downwelling mantle: Implications for 226Ra-210Pb disequilibria in arc magmas
We present the results of an analytical model of porous flow of viscous melt into a steadily dilating ‘‘channel’’ (defined as a cluster of smaller veins) in downwelling subarc mantle. The model predicts the pressure drop in the mantle wedge matrix surrounding the channel needed to drive melt flow as a function of position and time. Melt is sucked toward the dilatant region at a near-constant velocity (105 s1) until veins comprising the channel stop opening (t = t). Fluid elements that complete their journey within the time span t < t arrive at a channel. Our results make it possible to calculate the region of influence sampled by melt that surrounds the channel. This region is large compared to the model size of the channelized region driving flow. For a baseline dilation time of 1 year and channel half width of 2 m, melt can be sampled over an 80-m radius and has the opportunity to sample matrix material with potentially contrasting chemistry on geologically short timescales. Our mechanical results are consistent with a downgoing arc mantle wedge source region where melting and melt extraction by porous flow to a channel network are sufficiently rapid to preserve source-derived 238U-230Th-226Ra, and potentially also 226 Ra-210Pb, disequilibria, prior to magma ascent to the surface. Since this is the rate-determining step in the overall process, it allows the possibility that such short-lived disequilibria measured in arc rocks at the surface are derived from deep in the mantle wedge. Stresses due to partial melting do not appear capable of producing the desired sucking effect, while the order of magnitude rate of shear required to drive dilation of 107 s1 is much larger than values resulting from steady state subduction. We conclude that local deformation rates in excess of background plate tectonic rates are needed to ‘‘switch on’’ the dilatant channel network and to initiate the sucking effect
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