<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "https://jats.nlm.nih.gov/nlm-dtd/publishing/3.0/journalpublishing3.dtd">
<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article" dtd-version="3.0" xml:lang="en">
<front>
<journal-meta>
<journal-id journal-id-type="publisher">NHESS</journal-id>
<journal-title-group>
<journal-title>Natural Hazards and Earth System Sciences</journal-title>
<abbrev-journal-title abbrev-type="publisher">NHESS</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Nat. Hazards Earth Syst. Sci.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1684-9981</issn>
<publisher><publisher-name>Copernicus Publications</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/nhess-8-335-2008</article-id>
<title-group>
<article-title>Using Bayesian methods for the parameter estimation of deformation monitoring networks</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Tanir</surname>
<given-names>E.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Felsenstein</surname>
<given-names>K.</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Yalcinkaya</surname>
<given-names>M.</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>Vienna University of Technology, Institute of Geodesy and Geophysics, 1040 Vienna, Austria</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>Karadeniz Technical University, Department of Geodesy and Photogrammetry Engineering, 61080 Trabzon, Turkey</addr-line>
</aff>
<aff id="aff3">
<label>3</label>
<addr-line>Vienna University of Technology, Institute of Statistics and Probability Theory, 1040 Vienna, Austria</addr-line>
</aff>
<pub-date pub-type="epub">
<day>11</day>
<month>04</month>
<year>2008</year>
</pub-date>
<volume>8</volume>
<issue>2</issue>
<fpage>335</fpage>
<lpage>347</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2008 E. Tanir et al.</copyright-statement>
<copyright-year>2008</copyright-year>
<license license-type="open-access">
<license-p>This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit <ext-link ext-link-type="uri"  xlink:href="https://creativecommons.org/licenses/by/3.0/">https://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions>
<self-uri xlink:href="https://nhess.copernicus.org/articles/8/335/2008/nhess-8-335-2008.html">This article is available from https://nhess.copernicus.org/articles/8/335/2008/nhess-8-335-2008.html</self-uri>
<self-uri xlink:href="https://nhess.copernicus.org/articles/8/335/2008/nhess-8-335-2008.pdf">The full text article is available as a PDF file from https://nhess.copernicus.org/articles/8/335/2008/nhess-8-335-2008.pdf</self-uri>
<abstract>
<p>In order to investigate the deformations of an area or an object, geodetic
observations are repeated at different time epochs and then these
observations of each period are adjusted independently. From the coordinate
differences between the epochs the input parameters of a deformation model
are estimated. The decision about the deformation is given by appropriate
models using the parameter estimation results from each observation period.
So, we have to be sure that we use accurately taken observations (assessing
the quality of observations) and that we also use an appropriate
mathematical model for both adjustment of period measurements and for the
deformation modelling (Caspary, 2000). All inaccuracies of the model,
especially systematic and gross errors in the observations, as well as
incorrectly evaluated a priori variances will contaminate the results and
lead to apparent deformations. Therefore, it is of prime importance to
employ all known methods which can contribute to the development of a
realistic model. In Albertella et al. (2005), a new testing procedure from
Bayesian point of view in deformation analysis was developed by taking into
consideration prior information about the displacements in case estimated
displacements are small w.r.t. (with respect to) measurement precision.
&lt;br&gt;&lt;br&gt;
Within our study, we want to introduce additional parameter estimation from
the Bayesian point of view for a deformation monitoring network which is
constructed for landslide monitoring in Macka in the province of Trabzon in
north eastern Turkey. We used LSQ parameter estimation results to set up
prior information for this additional parameter estimation procedure. The
Bayesian inference allows evaluating the probability of an event by
available prior evidences and collected observations. Bayes theorem
underlines that the observations modify through the likelihood function the
prior knowledge of the parameters, thus leading to the posterior density
function of the parameters themselves.</p>
</abstract>
<counts><page-count count="13"/></counts>
</article-meta>
</front>
<body/>
<back>
<ref-list>
<title>References</title>
<ref id="ref1">
<label>1</label><mixed-citation publication-type="other" xlink:type="simple">Albertella, A., Cazzaniga, N., Sansò, F., Sacerdote, F., Crespi, M., and Luzietti, L.: Deformations detection by a Bayesian approach: prior information representation and testing criteria definition, ISGDM2005 &amp;ndash; IAG Symposium volume n 131, 2005. </mixed-citation>
</ref>
<ref id="ref2">
<label>2</label><mixed-citation publication-type="other" xlink:type="simple">Caspary, W. F.: Concept of network and deformation analysis, Monograph 11, School of Geomatics Engineering, The University of New South Wales, Australia, 2000. </mixed-citation>
</ref>
<ref id="ref3">
<label>3</label><mixed-citation publication-type="other" xlink:type="simple">Felsenstein, K.: Mathematische methoden für die interpretation von risiken, Imago Hominis, 11, 261&amp;ndash;269, 2004. </mixed-citation>
</ref>
<ref id="ref4">
<label>4</label><mixed-citation publication-type="other" xlink:type="simple">Felsenstein, K.: Bayesian interpolation schemes for monitoring systems. In: Advances in model-oriented design and analysis, 6, Physica-Verlag, Heidelberg, 2001. </mixed-citation>
</ref>
<ref id="ref5">
<label>5</label><mixed-citation publication-type="other" xlink:type="simple">Felsenstein, K.: Bayes&apos;sche statistik für kontrollierte experimente, Vandenhoeck and Ruprecht, Göttingen, 1996. </mixed-citation>
</ref>
<ref id="ref6">
<label>6</label><mixed-citation publication-type="other" xlink:type="simple">Koch, K. R.: Bayesian Inference with Geodetic Applications, Springer, Berlin, Heidelberg, New York, 1990. </mixed-citation>
</ref>
<ref id="ref7">
<label>7</label><mixed-citation publication-type="other" xlink:type="simple">Ocakoglu, F., Gokceoglu, C., and Ercanoglu, M.: Dynamics of a Complex Mass Movements Triggered by Heavy Rainfall: A Case Study from NW Turkey, Geomorphology, 42, 329–341, 2002.</mixed-citation>
</ref>
<ref id="ref8">
<label>8</label><mixed-citation publication-type="other" xlink:type="simple">Önalp, A.: Landslides of East Black Sea Region &amp;ndash; Reasons, Analysis and Controls, 1st National Landslides Symposium of Turkey, Trabzon, Proceedings Paper, 85&amp;ndash;95, (in Turkish), 1991. </mixed-citation>
</ref>
<ref id="ref9">
<label>9</label><mixed-citation publication-type="other" xlink:type="simple">Robert, C. and Casella, G.: Monte Carlo statistical methods Springer, New York, 2004. </mixed-citation>
</ref>
<ref id="ref10">
<label>10</label><mixed-citation publication-type="other" xlink:type="simple">Robert, C.: The Bayesian Choice, Springer, New York, 2001. </mixed-citation>
</ref>
<ref id="ref11">
<label>11</label><mixed-citation publication-type="other" xlink:type="simple">Roberts, G. and Rosenthal, J.: Markov chain Monte Carlo: Some practical implications of theoretical results, Canadian J. Statist., 25, 5&amp;ndash;32, 1998. </mixed-citation>
</ref>
<ref id="ref12">
<label>12</label><mixed-citation publication-type="other" xlink:type="simple">Rowe, D.B.: Multivariate Bayesian Statistics, Chapman and Hall/CRC, London, 2002. </mixed-citation>
</ref>
<ref id="ref13">
<label>13</label><mixed-citation publication-type="other" xlink:type="simple">Tarhan, F.: A look to landslides of East Black Sea Region, 1st National Landslides Symposium of Turkey, Trabzon, Proceedings Paper, 38&amp;ndash;63 (in Turkish), 1991. </mixed-citation>
</ref>
<ref id="ref14">
<label>14</label><mixed-citation publication-type="other" xlink:type="simple">Yalcinkaya, M. and Bayrak, T.: Dynamic model for monitoring landslides with emphasis on underground water in Trabzon province, Northeastern Turkey, Journal of Surveying Engineering, August 2003, 129(3), 115&amp;ndash;124. 2003. </mixed-citation>
</ref>
<ref id="ref15">
<label>15</label><mixed-citation publication-type="other" xlink:type="simple">Yalcinkaya M., Tanir, E.: A study on using Bayesian statistics in geodetic deformation analysis, Proceedings 11th International FIG Symposium on Deformation Measurements, Santorini (Thera) Island, Greece, 25&amp;ndash;28~May~2003, 2003. </mixed-citation>
</ref>
<ref id="ref16">
<label>16</label><mixed-citation publication-type="other" xlink:type="simple">Yalcinkaya, M. and Bayrak, T.: Comparison of static, kinematic and dynamic geodetic deformation models for Kutlugün landslide in northeastern Turkey, Natural Hazards, January~2005, 34(1), 91&amp;ndash;110, 2005. </mixed-citation>
</ref>
</ref-list>
</back>
</article>