Hierarchical log Gaussian Cox process for regeneration in uneven-aged forests

AbstractWe propose a hierarchical log Gaussian Cox process (LGCP) for point patterns, where a set of points $$\varvec{x}$$ x affects another set of points $$\varvec{y}$$ y but not vice versa. We use the model to investigate the effect of large trees on the locations of seedlings. In the model, every point in $$\varvec{x}$$ x has a parametric influence kernel or signal, which together form an influence field. Conditionally on the parameters, the influence field acts as a spatial covariate in the intensity of the model, and the intensity itself is a non-linear function of the parameters. Points outside the observation window may affect the influence field inside the window. We propose an edge correction to account for this missing data. The parameters of the model are estimated in a Bayesian framework using Markov chain Monte Carlo where a Laplace approximation is used for the Gaussian field of the LGCP model. The proposed model is used to analyze the effect of large trees on the success of regeneration in uneven-aged forest stands in Finland.

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Hidden Markov Model with Markovian emission

Monte Carlo Methods and Applications ◽

10.1515/mcma-2020-2072 ◽

2020 ◽

Vol 26 (4) ◽

pp. 303-313

Author(s):

Karima Elkimakh ◽

Abdelaziz Nasroallah

Keyword(s):

Monte Carlo ◽

Markov Chain ◽

Markov Chains ◽

Markov Model ◽

Monte Carlo Methods ◽

Hidden Markov ◽

Emission Process ◽

Numerical Examples ◽

Proposed Model ◽

Independent Markov Chain

AbstractIn our paper [A. Nasroallah and K. Elkimakh, HMM with emission process resulting from a special combination of independent Markovian emissions, Monte Carlo Methods Appl. 23 2017, 4, 287–306] we have studied, in a first scenario, the three fundamental hidden Markov problems assuming that, given the hidden process, the observed one selects emissions from a combination of independent Markov chains evolving at the same time. Here, we propose to conduct the same study with a second scenario assuming that given the hidden process, the emission process selects emissions from a combination of independent Markov chain evolving according to their own clock. Three basic numerical examples are studied to show the proper functioning of the iterative algorithm adapted to the proposed model.

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Bayesian Applications in Auditory Research

Journal of Speech Language and Hearing Research ◽

10.1044/2018_jslhr-h-astm-18-0228 ◽

2019 ◽

Vol 62 (3) ◽

pp. 577-586 ◽

Cited By ~ 9

Author(s):

Garnett P. McMillan ◽

John B. Cannon

Keyword(s):

Monte Carlo ◽

Markov Chain ◽

Bayesian Methods ◽

Prior Distribution ◽

Interim Analysis ◽

Iterative Process ◽

Bayes Theorem ◽

Sound Therapy ◽

The Many ◽

Auditory Research

Purpose This article presents a basic exploration of Bayesian inference to inform researchers unfamiliar to this type of analysis of the many advantages this readily available approach provides. Method First, we demonstrate the development of Bayes' theorem, the cornerstone of Bayesian statistics, into an iterative process of updating priors. Working with a few assumptions, including normalcy and conjugacy of prior distribution, we express how one would calculate the posterior distribution using the prior distribution and the likelihood of the parameter. Next, we move to an example in auditory research by considering the effect of sound therapy for reducing the perceived loudness of tinnitus. In this case, as well as most real-world settings, we turn to Markov chain simulations because the assumptions allowing for easy calculations no longer hold. Using Markov chain Monte Carlo methods, we can illustrate several analysis solutions given by a straightforward Bayesian approach. Conclusion Bayesian methods are widely applicable and can help scientists overcome analysis problems, including how to include existing information, run interim analysis, achieve consensus through measurement, and, most importantly, interpret results correctly. Supplemental Material https://doi.org/10.23641/asha.7822592

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