Asymptotically Optimum Estimation of a Probability in Inverse Binomial Sampling under General Loss Functions

The optimum quality that can be asymptotically achieved in the estimation of a probability p using inverse binomial sampling is addressed. A general definition of quality is used in terms of the risk associated with a loss function that satisfies certain assumptions. It is shown that the limit superior of the risk for p asymptotically small has a minimum over all (possibly randomized) estimators. This minimum is achieved by certain non-randomized estimators. The model includes commonly used quality criteria as particular cases. Applications to the non-asymptotic regime are discussed considering specific loss functions, for which minimax estimators are derived.

Optimized edge appearance probability for cooperative localization based on tree-reweighted nonparametric belief propagation

Nonparametric belief propagation (NBP) is a well-known particle-based method for distributed inference in wireless networks. NBP has a large number of applications, including cooperative localization. However, in loopy networks NBP suffers from similar problems as standard BP, such as over-confident beliefs and possible nonconvergence. Tree-reweighted NBP (TRW-NBP) can mitigate these problems, but does not easily lead to a distributed implementation due to the non-local nature of the required so-called edge appearance probabilities. In this paper, we propose a variation of TRWNBP, suitable for cooperative localization in wireless networks. Our algorithm uses a fixed edge appearance probability for every edge, and can outperform standard NBP in dense wireless networks.

Percolation in soils at Different Bulk Densities: Porosity, Connectivity and Grey Threshold.

To improve percolation modelling on soils the geometrical properties of the pore space must be understood; this includes porosity, particle and pore size distribution and connectivity of the pores. A study was conducted with a soil at different bulk densities based on 3D grey images acquired by X-ray computed tomography. The objective was to analyze the effect in percolation of aspects of pore network geometry and discuss the influence of the grey threshold applied to the images. A model based on random walk algorithms was applied to the images, combining five bulk densities with up to six threshold values per density. This allowed for a dynamical perspective of soil structure in relation to water transport through the inclusion of percolation speed in the analyses. To evaluate separately connectivity and isolate the effect of the grey threshold, a critical value of 35% of porosity was selected for every density. This value was the smallest at which total-percolation walks appeared for the all images of the same porosity and may represent a situation of percolation comparable among bulks densities. This criterion avoided an arbitrary decision in grey thresholds. Besides, a random matrix simulation at 35% of porosity with real images was used to test the existence of pore connectivity as a consequence of a non-random soil structure.

Modelling seed germination in forest tree species through survival analysis. The Pinus pinea L. case study

The direct application of existing models for seed germination may often be inadequate in the context of ecology and forestry germination experiments. This is because basic model assumptions are violated and variables available to forest managers are rarely used. In this paper, we present a method which addresses the aforementioned shortcomings. The approach is illustrated through a case study of Pinus pinea L. Our findings will also shed light on the role of germination in the general failure of natural regeneration in managed forests of this species. The presented technique consists of a mixed regression model based on survival analysis. Climate and stand covariates were tested. Data for fitting the model were gathered from a 5-year germination experiment in a mature, managed P. pinea stand in the Northern Plateau of Spain in which two different stand densities can be found. The model predictions proved to be unbiased and highly accurate when compared with the training data. Germination in P. pinea was controlled through thermal variables at stand level. At microsite level, low densities negatively affected the probability of germination. A time-lag in the response was also detected. Overall, the proposed technique provides a reliable alternative to germination modelling in ecology/forestry studies by using accessible/ suitable variables. The P. pinea case study highlights the importance of producing unbiased predictions. In this species, the occurrence and timing of germination suggest a very different regeneration strategy from that understood by forest managers until now, which may explain the high failure rate of natural regeneration in managed stands. In addition, these findings provide valuable information for the management of P. pinea under climate-change conditions.

An integral model for natural regeneration of Pinus pinea L. in the Northern Plateau (Spain) = Modelo integral de regeneración natural para Pinus pinea L. en la Meseta Norte (España)

Natural regeneration is an ecological key-process that makes plant persistence possible and, consequently, it constitutes an essential element of sustainable forest management. In this respect, natural regeneration in even-aged stands of Pinus pinea L. located in the Spanish Northern Plateau has not always been successfully achieved despite over a century of pine nut-based management. As a result, natural regeneration has recently become a major concern for forest managers when we are living a moment of rationalization of investment in silviculture. The present dissertation is addressed to provide answers to forest managers on this topic through the development of an integral regeneration multistage model for P. pinea stands in the region. From this model, recommendations for natural regeneration-based silviculture can be derived under present and future climate scenarios. Also, the model structure makes it possible to detect the likely bottlenecks affecting the process. The integral model consists of five submodels corresponding to each of the subprocesses linking the stages involved in natural regeneration (seed production, seed dispersal, seed germination, seed predation and seedling survival). The outputs of the submodels represent the transitional probabilities between these stages as a function of climatic and stand variables, which in turn are representative of the ecological factors driving regeneration. At subprocess level, the findings of this dissertation should be interpreted as follows. The scheduling of the shelterwood system currently conducted over low density stands leads to situations of dispersal limitation since the initial stages of the regeneration period. Concerning predation, predator activity appears to be only limited by the occurrence of severe summer droughts and masting events, the summer resulting in a favourable period for seed survival. Out of this time interval, predators were found to almost totally deplete seed crops. Given that P. pinea dissemination occurs in summer (i.e. the safe period against predation), the likelihood of a seed to not be destroyed is conditional to germination occurrence prior to the intensification of predator activity. However, the optimal conditions for germination seldom take place, restraining emergence to few days during the fall. Thus, the window to reach the seedling stage is narrow. In addition, the seedling survival submodel predicts extremely high seedling mortality rates and therefore only some individuals from large cohorts will be able to persist. These facts, along with the strong climate-mediated masting habit exhibited by P. pinea, reveal that viii the overall probability of establishment is low. Given this background, current management –low final stand densities resulting from intense thinning and strict felling schedules– conditions the occurrence of enough favourable events to achieve natural regeneration during the current rotation time. Stochastic simulation and optimisation computed through the integral model confirm this circumstance, suggesting that more flexible and progressive regeneration fellings should be conducted. From an ecological standpoint, these results inform a reproductive strategy leading to uneven-aged stand structures, in full accordance with the medium shade-tolerant behaviour of the species. As a final remark, stochastic simulations performed under a climate-change scenario show that regeneration in the species will not be strongly hampered in the future. This resilient behaviour highlights the fundamental ecological role played by P. pinea in demanding areas where other tree species fail to persist.

Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss

Sequential estimation of the success probability p in inverse binomial sampling is considered in this paper. For any estimator pˆ , its quality is measured by the risk associated with normalized loss functions of linear-linear or inverse-linear form. These functions are possibly asymmetric, with arbitrary slope parameters a and b for pˆ

p , respectively. Interest in these functions is motivated by their significance and potential uses, which are briefly discussed. Estimators are given for which the risk has an asymptotic value as p→0, and which guarantee that, for any p∈(0,1), the risk is lower than its asymptotic value. This allows selecting the required number of successes, r, to meet a prescribed quality irrespective of the unknown p. In addition, the proposed estimators are shown to be approximately minimax when a/b does not deviate too much from 1, and asymptotically minimax as r→∞ when a=b.

Intermittency reinjection probability density function with and without noise effects.

Intermittency phenomenon is a continuous route from regular to chaotic behaviour. Intermittency is an occurrence of a signal that alternates chaotic bursts between quasi-regular periods called laminar phases, driven by the so called reinjection probability density function (RPD). In this paper is introduced a new technique to obtain the RPD for type-II and III intermittency. The new RPD is more general than the classical one and includes the classical RPD as a particular case. The probabilities of the laminar length, the average laminar lengths and the characteristic relations are determined with and without lower bound of the reinjection in agreement with numerical simulations. Finally, it is analyzed the noise effect in intermittency. A method to obtain the noisy RPD is developed extending the procedure used in the noiseless case. The analytical results show a good agreement with numerical simulations.

Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss

Sequential estimation of the success probability $p$ in inverse binomial sampling is considered in this paper. For any estimator $\hatvap$, its quality is measured by the risk associated with normalized loss functions of linear-linear or inverse-linear form. These functions are possibly asymmetric, with arbitrary slope parameters $a$ and $b$ for $\hatvap < p$ and $\hatvap > p$ respectively. Interest in these functions is motivated by their significance and potential uses, which are briefly discussed. Estimators are given for which the risk has an asymptotic value as $p \rightarrow 0$, and which guarantee that, for any $p \in (0,1)$, the risk is lower than its asymptotic value. This allows selecting the required number of successes, $\nnum$, to meet a prescribed quality irrespective of the unknown $p$. In addition, the proposed estimators are shown to be approximately minimax when $a/b$ does not deviate too much from $1$, and asymptotically minimax as $\nnum \rightarrow \infty$ when $a=b$.