commit 9abb8d8302f7752b7f803bacc0a0a68e3992ee00
parent a53b33ee8911d15bcfd27b48dad8944d0fd86baa
Author: Anders Damsgaard <anders.damsgaard@geo.au.dk>
Date: Fri, 27 Nov 2015 16:48:47 +0100
change nesting and indentation
Diffstat:
| M | pages/methods.html | | | 158 | ++++++++++++++++++++++++++++++++++++++++--------------------------------------- |
1 file changed, 81 insertions(+), 77 deletions(-)
diff --git a/pages/methods.html b/pages/methods.html
@@ -87,85 +87,89 @@
as it experiences the variable physical environment of the
Quaternary.</p>
- </div>
-
- <div id="twostage" class="subsection scrollspy">
- <h4 class="header blue-text light">
- Two-stage glacial-interglacial forward model</h4>
- <p>The forward model builds on the assumption of a
- "two-stage uniformitarianism", meaning that the processes
- that operated during the Holocene also operated during
- earlier interglacials with comparable intensity. Likewise,
- the erosion rate during the past glacial periods is assumed
- to be comparable.</p>
-
- <p>The model approach assumes that glacial periods were
- characterized by 100% shielding and no exposure, which would
- require more than 10 m of ice thickness for production due
- to spallation (>50 m for muons). Interglacial periods are
- assumed to have been characterized by 100% exposure and zero
- shielding. The production of TCNs takes place during the
- interglacials, while erosion removes the land surface at
- different rates during the glacials and interglacials.</p>
- </div>
-
- <div id="mcmcwalker" class="subsection scrollspy">
- <h4 class="header blue-text light">
- What is a MCMC walker?</h4>
- <p>
- A MCMC walker is in this context a numerical entity which
- sequentially explores the model parameter space in order to
- obtain the closest match between the forward model and the
- observational dataset of TCNs. During each iteration
- the walker takes its current position in model space, plugs
- the parameter value into the forward model, and
- evaluates if the output result matches the observational
- record better or worse than the output at its previous
- position in model space. If the new results better matches
- the observed dataset, it continues walking in the same
- direction in model space.
- </p>
- <p>
- Starting at a random place inside the model space, a burn-in
- phase of 1000 iterations is first used to make a crude
- search of the entire model space. The burn-in phase is
- followed by a similar but more detailed and local search of
- the model space, based on the best-fit model parameters from
- the burn-in phase. The weighted least-squared misfit to
- observed TCN concentrations is used to evaluate the
- likelyhood for the combinations of model parameter values.
- The MCMC walker continues exploring the model space until it
- is sufficiently satisfied with the best model parameter
- estimate it has found.
- </p>
-
- <p>
- For a given observational data set more than one set of
- model parameters may produce forward models which
- sufficiently satisfy the MCMC walker.
- In this case the solution is <i>non-unique</i>. Even worse,
- a single MCMC walker may find an area in model space which
- seemingly is in good correspondence with the observational
- data set, but the walker is missing a much better set of
- model parameters since they are located somewhere entirely
- different in the model space. In order to mitigate these
- issues, MCMC inversions are often performed using several
- MCMC walkers. The starting point of each MCMC walker is
- chosen at random, resulting in unique walks through the
- model space. If a single walker is caught in an area of
- non-ideal solutions, chances are that the other walkers will
- find the area of better model parameters.
- </p>
+ <div id="twostage" class="subsection scrollspy">
+ <h4 class="header blue-text light">
+ Two-stage glacial-interglacial forward model</h4>
+ <p>The forward model builds on the assumption of a
+ "two-stage uniformitarianism", meaning that the
+ processes that operated during the Holocene also
+ operated during earlier interglacials with comparable
+ intensity. Likewise, the erosion rate during the past
+ glacial periods is assumed to be comparable.</p>
+
+ <p>The model approach assumes that glacial periods were
+ characterized by 100% shielding and no exposure, which
+ would require more than 10 m of ice thickness for
+ production due to spallation (>50 m for muons).
+ Interglacial periods are assumed to have been
+ characterized by 100% exposure and zero shielding. The
+ production of TCNs takes place during the interglacials,
+ while erosion removes the land surface at different
+ rates during the glacials and interglacials.</p>
+ </div>
- <p>
- The computational time depends on the number of MCMC
- walkers. When casually trying out the calculator we
- recommend using low numbers of MCMC walkers (1 to 2) in
- order to obtain fast results and reduce load on the server.
- When attempting to produce high-quality and reliable
- results, the number of walkers should be increased (3 to 4).
- </p>
+ <div id="mcmcwalker" class="subsection scrollspy">
+ <h4 class="header blue-text light">
+ What is a MCMC walker?</h4>
+ <p>
+ A MCMC walker is in this context a numerical entity
+ which sequentially explores the model parameter space in
+ order to obtain the closest match between the forward
+ model and the observational dataset of TCNs. During each
+ iteration the walker takes its current position in model
+ space, plugs the parameter value into the forward model,
+ and evaluates if the output result matches the
+ observational record better or worse than the output at
+ its previous position in model space. If the new results
+ better matches the observed dataset, it continues
+ walking in the same direction in model space.
+ </p>
+
+ <p>
+ Starting at a random place inside the model space, a
+ burn-in phase of 1000 iterations is first used to make a
+ crude search of the entire model space. The burn-in
+ phase is followed by a similar but more detailed and
+ local search of the model space, based on the best-fit
+ model parameters from the burn-in phase. The weighted
+ least-squared misfit to observed TCN concentrations is
+ used to evaluate the likelyhood for the combinations of
+ model parameter values. The MCMC walker continues
+ exploring the model space until it is sufficiently
+ satisfied with the best model parameter estimate it has
+ found.
+ </p>
+
+ <p>
+ For a given observational data set more than one set of
+ model parameters may produce forward models which
+ sufficiently satisfy the MCMC walker. In this case the
+ solution is <i>non-unique</i>. Even worse, a single MCMC
+ walker may find an area in model space which seemingly
+ is in good correspondence with the observational data
+ set, but the walker is missing a much better set of
+ model parameters since they are located somewhere
+ entirely different in the model space. In order to
+ mitigate these issues, MCMC inversions are often
+ performed using several MCMC walkers. The starting
+ point of each MCMC walker is chosen at random, resulting
+ in unique walks through the model space. If a single
+ walker is caught in an area of non-ideal solutions,
+ chances are that the other walkers will find the area of
+ better model parameters.
+ </p>
+
+ <p>
+ The computational time depends on the number of MCMC
+ walkers. When casually trying out the calculator we
+ recommend using low numbers of MCMC walkers (1 to 2) in
+ order to obtain fast results and reduce load on the
+ server. When attempting to produce high-quality and
+ reliable results, the number of walkers should be
+ increased (3 to 4).
+ </p>
+ </div>
</div>
