Summary
We are interested in studying the spatial dependency between the positions of on and off cholinergic amacrine cells because we hope this will tell us something about how the two cell types emerge during development.
Our goal in is to demonstrate how recently developed Monte Carlo methods for conducting likelihood-based analysis of realistic point process models can lead to sharper inferences about the bivariate structure of the data. In particular, we will formulate and fit a bivariate pairwise interaction model for the amacrines data, and will argue that likelihood-based inference within this model is both statistically more efficient and scientifically more relevant than ad hoc testing of benchmark hypotheses such as independence.
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References
A.J. Baddeley, J. Møller and R.P. Waagepetersen. Non-and semiparametric estimation of interaction in inhomogeneous point patterns. Statistica Neerlandica, 54(3):329–350, 2000.
A.J. Baddeley, R.A. Moyeed, C.V. Howard and A. Boyde. Analysis of a three-dimensional point pattern with replication. Applied Statistics, 42:641–668, 1993.
A.J. Baddeley and R. Turner. Practical maximum pseudolikelihood for spatial point processes. New Zealand Journal of Statistics, 42:283–322, 2000.
J.E. Besag, R. Milne and S. Zachary. Point process limits of lattice processes. Journal of Applied Probability, 19:210–216, 1982.
C. Brandon. Cholinergic neurons in the rabbit retina: dendritic branching and ultrastructural connectivity. Brain Research, 426:119–130, 1987.
P.J. Diggle. Displaced amacrine cells in the retina of a rabbit: analysis of a bivariate spatial point pattern. Journal of Neuroscience Methods, 18:115–125, 1986.
P.J. Diggle. Statistical Analysis of Spatial Point Patterns, 2nd ed. Oxford University Press, 2003.
P.J. Diggle and R.J. Gratton. Monte carlo methods of inference for implicit statistical models (with discussion). Journal of the Royal Statistical Society B, 46:193–227, 1984.
P.J. Diggle, N. Lange and F. Benes. Analysis of variance for replicated spatial point patterns in clinical neuroanatomy. Journal of the American Statistical Association, 86:618–625, 1991.
P.J. Diggle, J. Mateu and H.E. Clough. A comparison between parametric and non-parametric approaches to the analysis of replicated spatial point patterns. Advances in Applied Probability, 32:331–343, 2000.
T. Euler, P.B. Detwiler and W. Denk. Directionally selective calcium signals in dendrites of starburst amacrine cells. Nature, 418:845–852, 2002.
E.V. Famiglietti. “starburst” amacrine cells and cholinergic neurons: mirror-symmetric on and off amacrine cells of rabbit retina. Brain Research, 261:138–144, 1983.
E.V. Famiglietti. Starburst amacrine cells: morphological constancy and systematic variation in the anisotropic field of rabbit retinal neurons. Journal of Neuroscience, 5:562–577, 1985.
D.J. Gates and M. Westcott. Clustering estimates in spatial point distributions with unstable potentials. Annals of the Institute of Statistical Mathematics, 38 A:55–67, 1986.
C.J. Geyer. Likelihood inference for spatial point processes. In O.E. Barndorff-Nielsen, W.S. Kendall and M.N.M. van Lieshout, editors, Stochastic Geometry: likelihood and computation, pages 141–172. Chapman and Hall/CRC, 1999.
C.J. Geyer and E.A. Thompson. Constrained monte carlo maximum likelihood for dependent data (with discussion). Journal of the Royal Statistical Society B, 54:657–699, 1992.
A. Hughes. New perspectives in retinal organisation. Progress in Retinal Research, 4:243–314, 1985.
H.W. Lotwick and B.W. Silverman. Methods for analysing spatial processes of several types of points. Journal of the Royal Statistical Society, 44:1982, 406–413.
B.D Ripley. The second-order analysis of stationary point processes. Journal of Applied Probability, 13:255–266, 1976.
B.D. Ripley. Modelling spatial patterns. Journal of the Royal Statistical Society B, 39:172–212, 1977.
B.D. Ripley and F.P. Kelly. Markov point processes. Journal of the London Mathematical Society, 15:188–192, 1977.
D. Strauss. A model for clustering. Biometrika, 63:467–475, 1975.
M. Tauchi and R.H. Masland. The shape and arrangement of the cholinergic neurons in the rabbit retina. Proceedings of the Royal Society, London, B, 23:101–119, 1984.
M.N.M. van Lieshout. Markov point processes and their applications. Imperial College Press, 2000.
E. Wienawa-Narkiewicz. Light and Electron Microscopic Studies of Retinal Organisation. PhD thesis, Australian National University, Canberra, 1983.
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Diggle, P.J., Eglen, S.J., Troy, J.B. (2006). Modelling the Bivariate Spatial Distribution of Amacrine Cells. In: Baddeley, A., Gregori, P., Mateu, J., Stoica, R., Stoyan, D. (eds) Case Studies in Spatial Point Process Modeling. Lecture Notes in Statistics, vol 185. Springer, New York, NY. https://doi.org/10.1007/0-387-31144-0_12
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DOI: https://doi.org/10.1007/0-387-31144-0_12
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