Summary
Grimson and Rose (1991) suggested the use of a join—count statistic for detecting spatial clusters of neurons. We observe certain practical and theoretical difficulties in following this approach and propose instead the use of a maximum statistic. For this statistic, we derive in a similar way as for the disjoint statistic in Krauth (1991) exact upper and lower bounds for the upper tail probabilities. The procedure is illustrated by real data examples.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
CLIFF, A.D. and HAGGETT, P. (1988): Atlas of Disease Distributions. Analytic Approaches to Epidemiological Data. Blackwell, Oxford.
CLIFF, A.D., HAGGETT, P., ORD, J.K., BASSETT, K.A. and DAVIES, R.B. (1975): Elements of Spatial Structure. A Quantitative Approach. Cambridge University Press, Cambridge etc.
CLIFF, A.D., HAGGETT, P., ORD, J.K. and VERSEY, G.R. (1981): Spatial Diffusion. A Historical Geography of Epidemics in an Island Community. Cambridge University Press, Cambridge etc.
CLIFF, A.D. and ORD, J.K. (1973): Spatial Autocorrelation. Pion, London.
CLIFF, A.D. and ORD, J.K. (1981): Spatial Processes. Models & Applications. Pion, London.
GALAMBOS, J. (1977): Bonferroni inequalities. Annals of Probability, 5, 577–581.
GRIMSON, R.C. and ROSE, R.D. (1991): A versatile test for clustering and a proximity analysis of neurons. Methods of Information in Medicine, 30, 299–303.
HAINING, R. (1990): Spatial data analysis in the social and environmental sciences. Cambridge University Press, Cambridge etc.
JOGDEO, K. and PATIL, G.P. (1975): Probability inequalities for certain multivariate discrete distribution. Sankya, Series B, 37, 158–164.
KOUNIAS, E.G. (1968): Bounds for the probability of a union with applications. Annals of Mathematical Statistics, 39, 2154–2158.
KOUNIAS, E. and MARIN, D. (1974): Best linear Bonferroni bounds, in: Proceedings of the Prague Symposium on Asymptotic Statistics, Vol. II, Charles University, Prague, 179–213.
KRAUTH, J. (1991): Bounds for the upper tail probabilities of the multivariate disjoint test. Biometrie und Informatik in Medizin und Biologie, 22, 147–155.
KWEREL, S. (1975): Most stringent bounds on aggregated probabilities of partially specified dependent probability systems.Journal of the American Statistical Association, 70, 472–479.
MORAN, P.A.P. (1947): Random associations on a lattice. Proceedings of the Cambridge Philosophical Society, 43, 321–328.
MORAN, P.A.P. (1948): The interpretation of statistical maps. Journal of the Royal Statistical Society, Series B, 10, 243–251.
PILAR, G., LANDMESSER, L. and BURSTEIN, L. (1980): Competition for surviving among developing ciliary ganglion cells. Journal of Neurophysiology, 43, 233–254.
SUN, N. and CASSELL, M.D. (1993): Intrinsic GABAergic neurons in the rat central extended amygdala. Journal of Comparative Neurology, 330, 381–404.
UPTON, G.J.G. and FINGLETON, B. (1988): Spatial Data Analysis by Example. Vol. I. Point Pattern and Quantitative Data. John Wiley & Sons, Chichester etc.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin · Heidelberg
About this paper
Cite this paper
Krauth, J. (1996). Spatial Clustering of Neurons by Hypergeometric Disjoint Statistics. In: Gaul, W., Pfeifer, D. (eds) From Data to Knowledge. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79999-0_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-79999-0_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60354-2
Online ISBN: 978-3-642-79999-0
eBook Packages: Springer Book Archive