timprove MCMC description - cosmo - front and backend for Markov-Chain Monte Carlo inversion of cosmogenic nuclide concentrations
(HTM) git clone git://src.adamsgaard.dk/cosmo
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(DIR) commit 34d863dbc2986f2eff0ac8ff390333c91e8fa532
(DIR) parent 6bbc2f1eca168add56b0057cd8692abdd08448bb
(HTM) Author: Anders Damsgaard <anders.damsgaard@geo.au.dk>
Date: Fri, 27 Nov 2015 16:07:08 +0100
improve MCMC description
Diffstat:
M pages/methods.html | 53 ++++++++++++++++++++++++++-----
1 file changed, 45 insertions(+), 8 deletions(-)
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(DIR) diff --git a/pages/methods.html b/pages/methods.html
t@@ -65,7 +65,28 @@
(δ<sup>18</sup>O<sub>threshold</sub>) is specified
with uniform probability across the linear
parameter interval. The user specifies the bounds
- of the model parameters, which define the model space.
+ of the model parameters.
+ </p>
+
+ <p>Given a single value of model parameters
+ (ε<sub>int</sub>, ε<sub>gla</sub>,
+ <i>t</i><sub>degla</sub>,
+ δ<sup>18</sup>O<sub>threshold</sub>), the TCN
+ concentration after the duration of e.g. the entire
+ Quaternary period in a sample can be computed. This
+ <i>forward model</i> describes a history of exhumation and
+ TCN production in a sample volume as it experiences the
+ variable physical environment of the Pleistocene.
+ </p>
+
+ <p>When model parameters
+ (ε<sub>int</sub>, ε<sub>gla</sub>,
+ <i>t</i><sub>degla</sub>,
+ δ<sup>18</sup>O<sub>threshold</sub>) are allowed to
+ vary within specified limits, they can be thought of as
+ orthogonal axes creating a coordinate system in higher-order
+ space. Every position in this model space is associated with
+ a certain set of model parameter values.
</p>
</div>
t@@ -73,13 +94,29 @@
<h4 class="header blue-text light">
What is a MCMC walker?</h4>
<p>
- forward responses are computed based on an initial set of
- model parameters that is proposed using the
- Metropolis-Hastings technique. A burn-in phase of 1000
- iterations is first used to make a crude initial search of
- the model space. This step is followed by a more detailed
- and local search of the model space based on the best-fit
- model parameters from the burn-in phase.
+ A MCMC walker is a numerical entity which sequentially
+ explores the model parameter space in order to obtain the
+ best result between a forward-model and an observational
+ dataset. 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 along the same
+ path in model space with a small random perturbation.
+ </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.
</p>
</div>