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This concise introduction provides an entry point to the world of
inverse problems and data assimilation for advanced undergraduates
and beginning graduate students in the mathematical sciences. It
will also appeal to researchers in science and engineering who are
interested in the systematic underpinnings of methodologies widely
used in their disciplines. The authors examine inverse problems and
data assimilation in turn, before exploring the use of data
assimilation methods to solve generic inverse problems by
introducing an artificial algorithmic time. Topics covered include
maximum a posteriori estimation, (stochastic) gradient descent,
variational Bayes, Monte Carlo, importance sampling and Markov
chain Monte Carlo for inverse problems; and 3DVAR, 4DVAR, extended
and ensemble Kalman filters, and particle filters for data
assimilation. The book contains a wealth of examples and exercises,
and can be used to accompany courses as well as for self-study.
This engaging retelling of the Southern Sierra Miwok legend
features the great Yosemite Valley monolith, El Capitan, and how it
came to be. Mother Grizzly Bear thinks that her two playful cubs
are wrestling and having fun along the Merced River while she is
checking her fish traps. When she returns to join her sons,
however, she discovers the cubs are nowhere to be found. It takes
an unlikely hero to bring her cubs safely home. Populated with
characters based on real Sierra animals, this story is about the
value of all beings, the nature of courage, and the idea that being
a hero has very little to do with one's size. Includes notes about
the life and culture of the Southern Sierra Miwok and a
bibliography.
This concise introduction provides an entry point to the world of
inverse problems and data assimilation for advanced undergraduates
and beginning graduate students in the mathematical sciences. It
will also appeal to researchers in science and engineering who are
interested in the systematic underpinnings of methodologies widely
used in their disciplines. The authors examine inverse problems and
data assimilation in turn, before exploring the use of data
assimilation methods to solve generic inverse problems by
introducing an artificial algorithmic time. Topics covered include
maximum a posteriori estimation, (stochastic) gradient descent,
variational Bayes, Monte Carlo, importance sampling and Markov
chain Monte Carlo for inverse problems; and 3DVAR, 4DVAR, extended
and ensemble Kalman filters, and particle filters for data
assimilation. The book contains a wealth of examples and exercises,
and can be used to accompany courses as well as for self-study.
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