The multivariate normal mean - sensitivity of its Bayesian estimates:
Selecting an a prior distribution is key to Bayesian analyses. However, there is no unique non-informative prior; for example, for estimating the mean of a multivariate Gaussian distribution when the covariance matrix is unknown. As this is a standard task (for example in metrology when applying GUM S2), we studied a range of reasonable non-informative prior distributions. The uncertainty of the mean estimate varies substantially for small and medium-sized samples depending on the choice of such prior.
publication: Bodnar, O., A. Link, K. Klauenberg, K. Jousten and C. Elster (2013). Application of Bayesian model averaging using a fixed effects model with linear drift for the analysis of key comparison CCM.PK12. Measurement Techniques 56(6):548-90. http://link.springer.com/article/10.1007/s11018-013-0249-3.
Measurement Uncertainty of ELISA Concentration Estimates in Biochemistry:
A statistical framework is developed, enabling estimation of analyte concentrations together with their associated
uncertainties for fluorescent sandwich ELISAs. Sandwich ELISAs are applied, e.g. to detect the presence
of an infection, of hormones or drugs. On the basis of data from an international
comparability study, we show that the developed Bayesian procedure is generally applicable and leads to
more reliable uncertainties than approaches applied so far. Estimates of different ELISAs and different laboratories
are more consistent than previously assumed, which points towards the validity of the estimated concentrations, the evaluated uncertainties
as well as the developed method.
Measurement Uncertainty of ELISA Concentration Estimates in Biochemistry.
International Society for Bayesian Analysis (ISBA) conference 2010 (Benidorm)
Bayesian variance separation under heteroscedasticity. Application to an unstable measurand:
Let us analyse a measurement problem, where an unstable measurand is measured at ni different times — each time by (the same set of) nj devices or laboratories. The aim is to characterise the variabilities of the devices uncoupled from the variability of the measurand.
We will formulate this measurement problem as a heteroscedastic linear mixed model (or alternatively as an nj-variate normal distribution) and develop a Bayesian approach using the non-informative Jeffreys prior to learn about the full distribution of the variance parameters.
The method developed is applied to vacuum-measurement devices calibrated at the Physikalisch-Technische Bundesanstalt (PTB), in particular to pressure that was measured simultaneously by nj=4 or nj=6 devices and repeatedly ni=16 times. The estimated variabilities for devices are robust and substantially smaller than the observed variances of their measurements. This case study demonstrates the full potential of variance separation under
heteroscedasticity, e.g. for repeated simultaneous measurement of an unstable measurand.
publication: Klauenberg, K., Jousten, K., and Elster, C. (2012). Bayesian variance separation under heteroscedasticity. Application to an unstable measurand. In Pavese, F., Br, M., Filtz, J.-R., Forbes, A. B., Pendrill, L., and Shirono, H., editors, Advanced Mathematical and Computational Tools in Metrology
and Testing, volume 9 of Series on Advances in Mathematics for Applied
Sciences vol. 84, pages 224–31, Singapore. World Scientific.
presentation: Bayesian Variance Separation Under Heteroscedasticity – Application to an Unstable Pressure Measurand. Advanced Mathematical and Computational Tools in Metrology
and Testing (AMCTM), 2011 (Göteborg) and European Network for Business and Industrial Statistics (ENBIS) conference , 2011 (Coimbra)
presentation: Bayessche Trennung von Varianzkomponenten für Druckmessungen. 5. Fachtagung ”Messunsicherheit praxisgerecht bestimmen”, 2011 (Erfurt)
Ice cores preserve valuable information about past environment and climate. To interpret the information
within them, it is pivotal to date the ice core, i.e. to relate time to depth. Existing dating methods
can be categorised as follows: (1) layer counting using the seasonality in signals, (2) glaciological
modelling describing processes such as snow accumulation and plastic deformation
of ice, (3) comparison with other dated records, or (4) any combination
of these. Currently, none of these methods benefit from statistical
We are pioneering the combined use of glaciological and statistical models
within a Bayesian framework. By formalising the uncertainty in glaciological
relations, the dating uncertainty can be derived. This approach is applied to
the dating of Antarctic ice cores and then compared to an independent dating
derived from layer counting. For the first time, the effects of uncertainty
implied by the dating method are investigated for ice core chronologies. This
provides valuable insights for the applied community.
short description: Tooth Cementum Annulation (TCA) images are microscopic images from the root of human teeth.
These digital images display annual incremental lines which can be used for age estimation. Until now, the incremental
lines (or tooth rings) have been counted manually from under the microscope or on the (digital) TCA image. Since research
using the manual observations led to contradictory results, algorithms to automatically evaluate TCA images are considered
a crucial step towards computer-assisted TCA age estimation.
TCA images can be evaluated based on measuring their features, but until now no statistical model was developed. In this
work, TCA images are modeled as hidden Markov random fields, because these models can incorporate prior knowledge about tooth
rings and are thereby able to imitate human vision. In particular, the Markov random field is specified by the FRAME model which
incorporates filter responses to the label image into the Gibbsian distribution and is thus able to take into account long-range
dependencies among the observed values and periodicity in the placement of tooth rings. The estimation of model parameters is
rendered possible via an EM algorithm. This coherent approach is developed step-by-step and tested extensively throughout this work.
Dissertation published on the Freiburger document server (FreiDoc)