Brad Luen's homepage
84% of all statisticians truly hate their jobs--Todd Snider
Brad is available for tutoring, consulting, weddings, parties etc. Email at bradluen_AT_stat.Berkeley.EDU.
Current academics:
Assessing earthquake forecasts
Work in progress with Philip Stark. Statistical tests of earthquake
predictions require a null hypothesis to model occasional chance
successes. To define and quantify "chance success" is knotty. Some
null hypothses ascribe chance to the Earth: seismicity is modelled as
random. The null distribution of the number of successful prediction -
or any other test statistics - is taken to be its distribution when
the fixed set of predictions is applied to random seismicity. Such
tests tacitly assume that the predictions do not depend on the
observed seismicity. Conditioning on the predictions in this way sets
a low hurdle for statistical significance. Consider this scheme: when
an earthquake of magnitude 5.5 or greater occurs anywhere in the
world, predict that another earthquake at least as large will occur
within 21 days and an epicentral distance of 50 km. We apply this rule
to the Harvard centroid-moment-tensor (CMT) catalogue for 2000-2004 to
generate a set of predictions. The null hypothesis is that earthquake
times are exchangeable on their magnitudes and locations and on the
predictions. We generate random seismicity by permuting the times of
events in the CMT catalogue. We consider an event successfully
predicted only if (i) it falls in a prediction and (ii) there is no
larger event within 50 km in the previous 21 days. The p-value for the
observed success rate is less than 0.001: the method successfully
predicts about 5% of earthquakes, far better than "chance", because
the predictor exploits the clustering of earthquakes - occasional
foreshocks - which the null hypothesis lacks. Rather than condition on
the predictions and use a stochastic model for seismicity, it is
preferable to treat the observed seismicity as fixed, and to compare
the success rate of the predictions to the success rate of
simple-minded predictions like those just described. If the proffered
prediction do no better than a simple scheme, they have little value.
Past academics:
Luen, B., Ramanan, K. and Ziedins, I. (2006). Nonmonotonicity of phase
transitions in a loss network with controls. Ann. Appl. Probab.
16 1528-1562.
We consider a symmetric tress loss network that supports
single-link (unicast) and multi-link (multicast) calls to nearest
neighbours and has capacity C on each link. The network
operates a control so that the number of multicast calls at a link
cannot exceed C_V and the number of unicast calls at a link
cannot exceed C_E, where C_E, C_V are less than
C. We show that uniqueness of Gibbs measures on the infinite
tree is equivalent to the convergence of certain recursions of a
related map. For the case C_V = 1 and C_E = C, we
precisely characterise the phase transition surface and show that the
phase transition is always nonmonotone in the arrival rate of the
multicast calls. This model is an example of a system with hard
constraints that has weights attached to both the edges and nodes of
the network and can be viewed as a generalisation of the hard core
model that arises in statistical mechanics and combinatorics. Some of
the results obtained also hold for more general models that just the
loss network. The proofs rely on a combination of techniques from
probability theory and dynamical systems.
The place of investigations in a model of statistical literacy
Perennially in preparation. I am examining Iddo Gal's model of statistical
literacy as a base of knowledge and dispositions that would ideally
be held by all adults. Within this context, I've examined the place
of statistical investigations, and have tried to restructure the
model in a way that's more consistent with the an average person's
potential uses for statistical concepts. The argument is that
statistical literacy, and thus school-level statistics in general, is
best structured around the enquiry, because such an approach would
best-equip the statistically literate to use their methods of
thinking to approach less formal problems in less formal ways that a
professional statistician is used to. This work grew out of
discussions with Maxine Pfannkuch and Chris Wild at the University of
Auckland.
Current writing:
I review movies for Stylus.
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bradluen_AT_stat.berkeley.EDU
(change "_AT_" to "@")
