Bias-corrected variance estimation and hypothesis testing for spatial point and marked point processes using subsampling

Summary We introduce novel regression extrapolation based methods to correct the often large bias in subsampling variance estimation as well as hypothesis testing for spatial point and marked point processes. For variance estimation, our proposed estimators are linear combinations of the usual subsampling variance estimator based on subblock sizes in a continuous interval. We show that they can achieve better rates in mean squared error than the usual subsampling variance estimator. In particular, for n×n observation windows, the optimal rate of n^?2 can be achieved if the data have a finite dependence range. For hypothesis testing, we apply the proposed regression extrapolation directly to the test statistics based on different subblock sizes, and therefore avoid the need to conduct bias correction for each element in the covariance matrix used to set up the test statistics. We assess the numerical performance of the proposed methods through simulation, and apply them to analyze a tropical forest data set.     

Fast block variance estimation procedures for inhomogeneous spatial point processes

We introduce two new variance estimation procedures that usenon-overlapping and overlapping blocks, respectively. The non-overlappingblocks estimator can be viewed as the limit of the thinned blockbootstrap estimator recently proposed in Guan Loh (2007), byletting the number of thinned processes and bootstrap samplestherein both increase to infinity. The non-overlapping blocksestimator can be obtained quickly since it does not requireany thinning or bootstrap steps, and it is more stable. Theoverlapping blocks estimator further improves the performanceof the non-overlapping blocks with a modest increase in computationtime. A simulation study demonstrates the superiority of theproposed estimators over the thinned block bootstrap estimator.     

Estimating functions for inhomogeneous spatial point processes with incomplete covariate data

The R package spatstat provides a very flexible and useful frameworkfor analysing spatial point patterns. A fundamental featureis a procedure for fitting spatial point process models dependingon covariates. However, in practice one often faces incompleteobservation of the covariates and this leads to parameter estimationerror which is difficult to quantify. In this paper, we introducea Monte Carlo version of the estimating function used in spatstatfor fitting inhomogeneous Poisson processes and certain inhomogeneouscluster processes. For this modified estimating function, itis feasible to obtain the asymptotic distribution of the parameterestimators in the case of incomplete covariate information.This allows a study of the loss of efficiency due to the missingcovariate data.     

Bayesian semiparametric intensity estimation for inhomogeneous spatial point processes

In this work we propose a fully Bayesian semiparametric method to estimate the intensity of an inhomogeneous spatial point process. The basic idea is to first convert intensity estimation into a Poisson regression setting via binning data points on a regular grid, and then model the log intensity semiparametrically using an adaptive version of Gaussian Markov random fields to smooth the corresponding counts. The inference is carried by an efficient Markov chain Monte Carlo simulation algorithm. Compared to existing methods for intensity estimation, for example, parametric modeling and kernel smoothing, the proposed estimator not only provides inference regarding the dependence of the intensity function on possible covariates, but also uses information from the data to adaptively determine the amount of smoothing at the local level. The effectiveness of using our method is demonstrated through simulation studies and an application to a rainforest dataset.     

A semi-parametric approach for comparing the estimated spectra of two stationary point processes

In this paper, we provide a semi-parametric test for the hypothesis that the spectra of two stationary point processes (SPPs) are the same. The estimates of the second-order spectral density functions of the SPPs are obtained by using two different approaches: (a) by smoothing the modified periodogram statistics using a moving average weighting scheme, (b) by employing the Welch's method on the modified periodogram statistics. The test is based on the likelihood ratio function under two alternative hypotheses. The first alternative hypothesis suggests that the ratio of the spectra is a constant (there is a shift to the power) while the second one adopts a quadratic model for the logarithmic ratio of the spectra. A comparison with a log-linear model indicates coincidence in the results. This is explained by using an illustrative example from the field of neurophysiology. It is shown that the information transferred to the spinal cord by the sensory axons, closely related with the complex physiological system called muscle spindle, under the influence of two different stimuli can be separated in two parts. The first part corresponds to the range of frequencies 0-19 Hz while the second to the range of frequencies 19-100 Hz. However, the dependence on the frequency in both parts is of a quadratic form.     

A stochastic model for estimation of mutation rates in multiple-replication proliferation processes

In this paper we propose a stochastic model based on the branching process for estimation and comparison of the mutation rates in proliferation processes of cells or microbes. We assume in this model that cells or microbes (the elements of a population) are reproduced by generations and thus the model is more suitably applicable to situations in which the new elements in a population are produced by older elements from the previous generation rather than by newly created elements from the same current generation. Cells and bacteria proliferate by binary replication, whereas the RNA viruses proliferate by multiple replication. The model is in terms of multiple replications, which includes the special case of binary replication. We propose statistical procedures for estimation and comparison of the mutation rates from data of multiple cultures with divergent culture sizes. The mutation rate is defined as the probability of mutation per replication per genome and thus can be assumed constant in the entire proliferation process. We derive the number of cultures for planning experiments to achieve desired accuracy for estimation or desired statistical power for comparing the mutation rates of two strains of microbes. We establish the efficiency of the proposed method by demonstrating how the estimation of mutation rates would be affected when the culture sizes were assumed similar but actually diverge.      

On a probabilistic model for the numerical estimation of nocturnal migration of birds

The study of nocturnal bird migration by cone methods of observation has a century-long history but has continued to be used up to the present. To describe the flux and estimate the number of passing birds a probabilistic model is proposed. This model is based on the concept of dynamic Poisson ensemble of points in appropriate phase space and has two parameters. One is scalar and the other one is functional. We constructed consistent estimations of these parameters and discuss their use for the numerical estimation of the flux of birds observed in a narrow light cone generated by the bright lunar disk and formed by an open angle of telescope. Selection on the same type of birds was suggested as the necessary condition for the model application. Ground speed of each bird was introduced into the model as a new but obligatory value determining the quantification of the flux of bird.     

Genetic inhomogeneous Poisson processes describing the roles of an isolated mature tree in forest regeneration

The spatial distribution of genotyped adult plants and offspring can be modeled by genetic inhomogeneous Poisson processes. This paper reports the development of a previously proposed point process model to cover safe site conditions for sapling survival, unknown seed sources and wider ranges of dispersal kernels. Suppose that a species has limited seed dispersal and shade-tolerance, and that young trees are clustered around highly isolated adults. The clustering might be formed solely by dispersed seeds from adults. However, the survival of the offspring might be influenced by shading by the adults crowns. The new genetic processes are applicable to such cases, as demonstrated for a young population of Fagus crenata, a shade-tolerant canopy tree species, in a 55-year-old stand regenerated after shelterwood logging. Isozyme analysis revealed that the regenerating trees were genetically related to the nearest adults, but some were not their respective daughters. The maximum likelihood method has led us to the following regeneration: seeds were dispersed mostly within 20 m of their mothers; two residual adults in the plot had equal female reproductive success; about 10% of offspring even close to the adult were not their daughters; the adults crowns reduced the survival of offspring up to 20–25 m away. However, the degree of model fitting was unsatisfactory. Hence, our models, in principle, can quantify two roles of highly isolated adults: providing seed sources and safe sites, but the case study suggests that other, unknown factors influence F. crenata regeneration after shelterwood harvesting.     

Robust spectral estimation for speed of sound with phase shift correction applied online in yeast fermentation processes

Ultrasound techniques are well suited to provide real‐time characterization of bioprocesses in non‐invasive, non‐contact, and non‐destructive low‐power consumption measurements. In this paper, a spectral analysis method was proposed to estimate time of flight (TOF) between the propagated echoes, and its corresponding speed of sound (USV). Instantaneous power spectrum distribution was used for accurate detection of echo start times, and phase shift distribution for correcting the involved phase shifts. The method was validated by reference USV for pure water at 9–30.8°C, presenting a maximum error of 0.22%, which is less than that produced by the crosscorrelation method. Sensitivity analyses indicated a precision of 6.4 × 10^?3% over 50 repeated experiments, and 0.11% over two different configurations. The method was competently implemented online in a yeast fermentation process, and the calculated USV was combined with temperature and nine signal features in an artificial neural network. The network was designed by back propagation algorithm to estimate the instantaneous density of the fermentation mixture, producing a maximum error of 0.95%.     

Applications and extensions of Chao's moment estimator for the size of a closed population

This article revisits Chao's (1989, Biometrics45, 427-438) lower bound estimator for the size of a closed population in a mark-recapture experiment where the capture probabilities vary between animals (model M(h)). First, an extension of the lower bound to models featuring a time effect and heterogeneity in capture probabilities (M(th)) is proposed. The biases of these lower bounds are shown to be a function of the heterogeneity parameter for several loglinear models for M(th). Small-sample bias reduction techniques for Chao's lower bound estimator are also derived. The application of the loglinear model underlying Chao's estimator when heterogeneity has been detected in the primary periods of a robust design is then investigated. A test for the null hypothesis that Chao's loglinear model provides unbiased abundance estimators is provided. The strategy of systematically using Chao's loglinear model in the primary periods of a robust design where heterogeneity has been detected is investigated in a Monte Carlo experiment. Its impact on the estimation of the population sizes and of the survival rates is evaluated in a Monte Carlo experiment.