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  • 1
    Electronic Resource
    Electronic Resource
    Learning and Updating of Uncertainty in Dirichlet Models (1997)
    Springer
    Machine learning 26 (1997), S. 43-63 
    Details
    ISSN: 0885-6125
    Keywords: Beta distribution ; Dirichlet distribution ; Dirichlet conjugate priors ; evidence propagation ; parameter estimation ; prior assessment of hyperparameters ; time series.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract In this paper we analyze the problem of learning and updating of uncertainty in Dirichlet models, where updating refers to determining the conditional distribution of a single variable when some evidence is known. We first obtain the most general family of prior-posterior distributions which is conjugate to a Dirichlet likelihood and we identify those hyperparameters that are influenced by data values. Next, we describe some methods to assess the prior hyperparameters and we give a numerical method to estimate the Dirichlet parameters in a Bayesian context, based on the posterior mode. We also give formulas for updating uncertainty by determining the conditional probabilities of single variables when the values of other variables are known. A time series approach is presented for dealing with the cases in which samples are not identically distributed, that is, the Dirichlet parameters change from sample to sample. This typically occurs when the population is observed at different times. Finally, two examples are given that illustrate the learning and updating processes and the time series approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007372016040
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  • 2
    Electronic Resource
    Electronic Resource
    An electron probe X-ray microanalytical study of bone mineral in osteogenesis imperfecta (1995)
    Springer
    Calcified tissue international 56 (1995), S. 118-122 
    Details
    ISSN: 1432-0827
    Keywords: Osteogenesis imperfecta ; Mineral ; Composition ; Microanalysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Abstract A semiquantitative electron probe X-ray microan-alytical (XRMA) technique, in conjunction with transmission electron microscopy, was used to compare the calcium to phosphorus (Ca/P) molar ratios in calcium phosphate standards of known composition, in normal bone and in bone from patients with osteogenesis imperfecta (OI). Using a modified routine processing and resin embedding schedule, the measured Ca/P molar ratio of calcium phosphates standards of known composition were found to correlate well with the Ca/P molar ratio based on their respective chemical formulae. This technique was then used to compare the Ca/P molar ratio in normal human bone and in OI bone. The Ca/P ratio values for normal bone (Ca/P=1.631) correlated well with those for chemically prepared hydroxyapatite (Ca/P=1.602), but in bone from OI patients, the Ca/P molar ratio was significantly lower (Ca/P=1.488). This study has shown that there is a lower Ca/P molar ratio in OI bone compared with normal, matched bone. This suggests that the mineral deviates from the carbanoapatite usually found in bone. Isomorphous substitutions in the carbanoapatite lattice could account for this although this study has neither proved nor disproved this. The altered bone mineral is an-other factor that could contribute to the increased fracture rate observed in OI.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00296342
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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