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  • 1
    Electronic Resource
    Electronic Resource
    Dependency as a measure to estimate the order and the values of Markov processes (1977)
    Springer
    Biological cybernetics 25 (1977), S. 209-226 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract To evaluate the order and the values of Markov properties of the time series of events, we have proposed a statistical measure “dependency”:D m = (H 0 −H m )/H 0 , whereH 0 andH m are Shannon's entropy and them-th order conditional entropy, respectively. It is indicated that $$\tilde D_m = \sum\limits_{v = 1}^m {(\hat D_v - \bar D_v^{sh} } )$$ is a better point estimator ofD m, giving a total value of them-th order Markov process. Here $$\hat D_m $$ and $$\bar D_m^{sh} $$ are the estimate ofD m and the arithmetic mean of $$\hat D_m^{sh} $$ when them-th order shuffling is made many times for a given observed series, respectively. The value $$\hat D_m - \bar D_m^{sh} = d_m $$ represents Markov value of the orderm. Under the assumption that the series has continuous variables and the normal distribution, simplified dependency is defined by , where |S m | is the determinant of serial correlation coefficients. It is shown that is practically useful for the estimation of the order and the values of Markov processes with small sample size. It is also indicated that analysis is basically equivalent to the least mean-square analysis of autoregressive models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01885639
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Dependency representing Markov properties of nonstationary spike trains recorded from the cat's optic tract fibers (1979)
    Springer
    Biological cybernetics 35 (1979), S. 43-54 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract The order and the values of Markov properties of nonstationary stochastic processes are inferred by the use of them-th order Markov value and simplified dependency , respectively: and HereK=0.5log2 e, and $$\left| {\hat R_m } \right|$$ is the correlation coefficient determinant obtained from the ensemble averages of sample records. When an observed value is greater than or equal to the critical value, , the null hypothesis of the (m-1)th order, , is rejected at the level of significance α. Hereχ 1 2 (α) is the chi-square value with one degree of freedom at α andN is sample size. With these statistics it was shown that the order and the values of Markov properties of spike trains of optic tractX- andY-fibers became higher and larger, respectively, after the light spot presentation; and that the values due to negative correlation came to increase and returned to the maintained level earlier inY-fibers than inX-fibers, while the maximum values forX-fibers continued to the light off. It is discussed that Markov properties of spike trains of optic tract fibers in the visual pathway seem to constitute a significant component of the neural information code.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01845843
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
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