arXiv subjects

Antti Penttinen

Publications and source records attributed to Antti Penttinen.

4 recordsLinked to original sources

arXiv2019

Sequential Spatial Point Process Models for Spatio-Temporal Point Processes: A Self-Interactive Model with Application to Forest Tree Data

We model the spatial dynamics of a forest stand by using a special class of spatio-temporal point processes, the sequential spatial point process, where the spatial dimension is parameterized and the time component is atomic. The sequential spatial point processes differ from spatial point processes in the sense that the realizations are ordered sequences of spatial locations and the order of points allows us to approximate the spatial evolutionary dynamics of the process. This feature shall be useful to interpret the long-term dependence and the memory formed by the spatial history of the process. As an illustration, the sequence can represent the tree locations ordered with respect to time, or to some given quantitative marks such as tree diameters. We derive a parametric sequential spatial point process model that is expressed in terms of self-interaction of the spatial points, and then the maximum-likelihood-based inference is tractable. As an application, we apply the model obtained to forest dataset collected from the Kiihtelysvaara site in Eastern Finland. Potential applications in remote sensing of forests are discussed.

stat.AP↗

arXiv2018

Empirical Bayes to assess ecological diversity and similarity with overdispersion in multivariate counts

The assessment of diversity and similarity is relevant in monitoring the status of ecosystems. The respective indicators are based on the taxonomic composition of biological communities of interest, currently estimated through the proportions computed from sampling multivariate counts. In this work we present a novel method able to work with only one sample to estimate the taxonomic composition when the data are affected by overdispersion. The presence of overdispersion in taxonomic counts may be the result of significant environmental factors which are often unobservable but influence communities. Following the empirical Bayes approach, we combine a Bayesian model with the marginal likelihood method to jointly estimate the taxonomic proportions and the level of overdispersion from one sample of multivariate counts. Our proposal is compared to the classical maximum likelihood method in an extensive simulation study with different realistic scenarios. An application to real data from aquatic biomonitoring is also presented. In both the simulation study and the real data application, we consider communities characterized by a large number of taxonomic categories, such as aquatic macroinvertebrates or bacteria which are often overdispersed. The applicative results demonstrate an overall superiority of the empirical Bayes method in almost all examined cases, for both assessments of diversity and similarity. We would recommend practitioners in biomonitoring to use the proposed approach in addition to the traditional procedures. The empirical Bayes estimation allows to better control the error propagation due to the presence of overdispersion in biological data, with a more efficient managerial decision making.

stat.AP↗

arXiv2016

Deducing self-interaction in eye movement data using sequential spatial point processes

Eye movement data are outputs of an analyser tracking the gaze when a person is inspecting a scene. These kind of data are of increasing importance in scientific research as well as in applications, e.g. in marketing and man-machine interface planning. Thus the new areas of application call for advanced analysis tools. Our research objective is to suggest statistical modelling of eye movement sequences using sequential spatial point processes, which decomposes the variation in data into structural components having interpretation. We consider three elements of an eye movement sequence: heterogeneity of the target space, contextuality between subsequent movements, and time-dependent behaviour describing self-interaction. We propose two model constructions. One is based on the history-dependent rejection of transitions in a random walk and the other makes use of a history-adapted kernel function penalized by user-defined geometric model characteristics. Both models are inhomogeneous self-interacting random walks. Statistical inference based on the likelihood is suggested, some experiments are carried out, and the models are used for determining the uncertainty of important data summaries for eye movement data.

stat.ME↗

arXiv2013

Bayesian Modeling and MCMC Computation in Linear Logistic Regression for Presence-only Data

Presence-only data are referred to situations in which, given a censoring mechanism, a binary response can be observed only with respect to on outcome, usually called \textit{presence}. In this work we present a Bayesian approach to the problem of presence-only data based on a two levels scheme. A probability law and a case-control design are combined to handle the double source of uncertainty: one due to the censoring and one due to the sampling. We propose a new formalization for the logistic model with presence-only data that allows further insight into inferential issues related to the model. We concentrate on the case of the linear logistic regression and, in order to make inference on the parameters of interest, we present a Markov Chain Monte Carlo algorithm with data augmentation that does not require the a priori knowledge of the population prevalence. A simulation study concerning 24,000 simulated datasets related to different scenarios is presented comparing our proposal to optimal benchmarks.

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