Talks and presentations

A spatio-temporal model for locations of trees in the Barro Colorado Island plot

May 15, 2019

Talk, Point processes in space, time and beyond, Skagen, Denmark

Locations of alive trees in the 50-hectare permanent study plot in the tropical rain forest of Barro Colorado Island (BCI), Gatun Lake, Panama, have been recorded in 8 consecutive censuses since 1980. In each census, new trees tend to grow near existing trees in the preceding census due to seed dispersal mechanisms and favorable topography and soil conditions. On the other hand, the elimination of trees from one census to the next seems to occur more frequently in dense areas where there are competitions for resources and light among trees. We introduce a spatio-temporal model for population dynamics in the BCI plot and discuss parameter estimation methods and model checking tools for the introduced model.

A deep learning approach to modeling spatial point patterns of locations of different tree species in a tropical rainforest

April 19, 2019

Talk, 4th International Conference on Natural Sciences: Mathematics & Computer, Sanandaj, Iran

Spatial point patterns of locations of trees in a rainforest are influenced by environmental conditions and many known and unknown ecological processes that are not directly observable. In this talk we propose a multilayer perceptrons model in order to relate the spatial patterns of trees to observed environmental variables and latent random fields, which accounts for all unobserved influential factors. We use the variational autoencoder approach to fit the proposed model and estimate (encode) the generative latent random fields.

A model for time series of spatial point patterns

January 15, 2019

Talk, International Conference on Recent Achievements in Mathematical Science, Yazd, Iran

A spatial point pattern $\mathbf{x}$ on $S\subset\mathbb{R}^{d}$, $d\geq2$, is a locally finite subset of $S$; i.e. for any bounded Borel set $B\subset S$, $\mathbf{x}\cap B$ if finite. Let $\mathcal{X}$ be the set of all point patterns on $S$ and $\mathcal{N}$ denotes the Borel $\sigma$-algebra of subsets of $\mathcal{X}$. Then a random object $X:(\Omega,\mathcal{F},\mathbb{P})\to(\mathcal{X},\mathcal{N},P_{X})$ is called a spatial point process on $S$. Assume that for each $t\in\mathbb{Z}$, $X_{t}$ is a spatial point process on $S$. Then ${X_t: t\in\mathbb{Z}}$ is a $\mathcal{X}$-valued time series that can not be explained in the classical time series framework. Such time series are encountered in various applications. In the present work, a framework for analyzing time series of spatial point patterns is developed and a simple model for the population dynamic in the BCI plot is introduced. In addition, parameter estimation for the proposed model is discussed.

Generalized K function for spatial point processes

August 26, 2018

Talk, 14th Iranian Statis-tical Conference, Shahroud, Iran

We introduce a generalized version of the well know Ripley’s K function in order to obtain higher order characteristics for spatial point processes. The generalized K function admits a simple closed form for the Poisson process and a tractable analytical expression is obtained for the third order K function in case of the planar Thomas process. An unbiased nonparametric estimator for the generalized K function is also discussed.

Estimation of the pair correlation function

May 25, 2018

Conference proceedings talk, 12th French-Danish Work-shop on Spatial Statistics and Image Analysis in Biology, Aalborg, Denmark

The pair correlation function is a key summary statistic in analyzing spatial point patterns. It has become an important tool in forestry, cosmology and other disciplines. Kernel smoothing methods are often used to estimate the pair correlation function, similar to kernel estimation of probability densities. However, the kernel estimator with symmetric bounded support kernels suffers from the well-known boundary bias problem and the bias and variance of a kernel estimate depend critically on the choice of kernel bandwidth. In the present research project, we aim to use asymmetric kernel functions in order to eliminate the boundary bias issue and develop a feasible methodology for optimal choice of the bandwidth.

Product density functions of Neyman-Scott point processes

August 24, 2016

Talk, 13th Iranian Statistical Conference, Kerman, Iran

We provide a general formula for the product density functions of a Neyman-Scott process. Upper bounds and relation with the characteristic function of the process’ kernel are also discussed. In addition, closed expressions are presented for the third and fourth order product densities of the Thomas process.

A. Jalilian