【latex版】水贴

• Farrell Sr has left the England coaching team for role with Ireland
• ‘It’s no different for me. He’s part of a new set-up and that’s his challenge’

Owen Farrell has insisted he does not see his professional life changing hugely in the wake of his father Andy’s departure from the England setup.

For the first time in his union career, Farrell junior is about to start working with a coaching team not featuring his father, who has moved across the Irish Sea to assume new roles with Ireland and Munster.

Uncertainty
• Partial knowledge of state of the world
• Noisy observations
• Phenomena not covered by our model
• Inherent stochasticity

Probability Theory
• Declarative representation with clear
semantics
• Powerful reasoning patterns
• Established learning methods

Complex Systems
predisposing factors
symptoms
test results
diseases
treatment outcomes
class labels for
thousands of superpixels
Random variables X1,…, Xn
Joint distribution P(X1,…, Xn)

Let’s take a break from statistics and data science to think a bit about programming language theory, and how the theory relates to the programming language used in the R analysis platform (the language is technically called “S”, but we are going to just call the whole analysis system “R”).

The McNemar test [1] is a fundamental method for analyzing a dataset summarized in a 2 × 2 contingency table of two binary matched-pairs data. Despite its simple and solid theoretical background, the McNemar test is limited by its unexpectedly small power [2, 3]. Although the power could potentially be improved by a heuristic procedure, we instead construct a test procedure under an explicitly stated assumption. For this purpose, a Bayesian approach is promising. In fact, a prior density based on prior knowledge should improve the power of the derived test. The Bayesian method also admits extensions in a routine way.

Variation in cancer risk among
tissues can be explained by the
number of stem cell divisions

Some tissue types give rise to human cancers millions of times more often than other
tissue types. Although this has been recognized for more than a century, it has never been
explained. Here, we show that the lifetime risk of cancers of many different types is strongly
correlated (0.81) with the total number of divisions of the normal self-renewing cells
maintaining that tissue’s homeostasis. These results suggest that only a third of the variation
in cancer risk among tissues is attributable to environmental factors or inherited
predispositions. The majority is due to “bad luck,” that is, random mutations arising during
DNA replication in normal, noncancerous stem cells. This is important not only for
understanding the disease but also for designing strategies to limit the mortality it causes.

Extreme variation in cancer incidence across
different tissues is well known; for example,
the lifetime risk of being diagnosed
with cancer is 6.9% for lung, 1.08% for
thyroid, 0.6% for brain and the rest of the
nervous system, 0.003% for pelvic bone and
0.00072% for laryngeal cartilage (1–3). Some of
these differences are associated with well-known
risk factors such as smoking, alcohol use, ultraviolet
light, or human papilloma virus (HPV)
(4, 5), but this applies only to specific populations
exposed to potent mutagens or viruses. And such
exposures cannot explain why cancer risk in
tissues within the alimentary tract can differ by
as much as a factor of 24 [esophagus (0.51%),
large intestine (4.82%), small intestine (0.20%),
and stomach (0.86%)] (3). Moreover, cancers of
the small intestinal epithelium are three times
less common than brain tumors (3), even though
small intestinal epithelial cells are exposed to
much higher levels of environmental mutagens
than are cells within the brain, which are protected
by the blood-brain barrier.

Another well-studied contributor to cancer is
inherited genetic variation. However, only 5 to
10% of cancers have a heritable component
(6–8), and even when hereditary factors in predisposed
individuals can be identified, the way in
which these factors contribute to differences in
cancer incidences among different organs is
obscure. For example, the same, inheritedmutant
APC gene is responsible for both the predisposition
to colorectal and small intestinal cancers