Hazard models for line transect surveys with independent observers

The likelihood function for data from independent observer line transect surveys is derived, and a hazard model is proposed for the situation where animals are available for detection only at discrete time points. Under the assumption that the time points of availability follow a Poisson point process, we obtain an analytical expression for the detection function. We discuss different criteria for choosing the hazard function and consider in particular two different parametric families of hazard functions. Discrete and continuous hazard models are compared and the robustness of the discrete model is investigated. Finally, the methodology is applied to data from a survey for minke whales in the northeastern Atlantic.     

Empirically simulated study to compare and validate sampling methods used in aerial surveys of wildlife populations

This paper compares the distribution, sampling and estimation of abundance for two animal species in an African ecosystem by means of an intensive simulation of the sampling process under a geographical information system (GIS) environment. It focuses on systematic and random sampling designs, commonly used in wildlife surveys, comparing their performance to an adaptive design at three increasing sampling intensities, using the root mean square errors (RMSE). It further assesses the impact of sampling designs and intensities on estimates of population parameters. The simulation is based on data collected during a prior survey, in which geographical locations of all observed animals were recorded. This provides more detailed data than that usually available from transect surveys. The results show precision of estimates to increase with increasing sampling intensity, while no significant differences are observed between estimates obtained under random and systematic designs. An increase in precision is observed for the adaptive design, thereby validating the use of this design for sampling clustered populations. The study illustrates the benefits of combining statistical methods with GIS techniques to increase insight into wildlife population dynamics.     

Estimating Abundance From One-Dimensional Passive Acoustic Surveys

ABSTRACT Conventional distance sampling, the most-used method of estimating animal density and abundance, requires ranges to detected individuals, which are not easily measured for vocalizations. However, in some circumstances the sequential pattern of detection of vocalizations along a transect line gives information about the range of detection. Thus, from a one-dimensional acoustic point-transect survey (i.e., records of vocalizations detected or not detected at regularly spaced listening stations) it is possible to obtain a useful estimate of density or abundance. I developed equations for estimation of density for one-dimensional surveys. Using simulations I found that for the method to have little bias when both range of detection and rate of vocalization need to be estimated, stations needed to be spaced at 30–80% of the range of detection and the rate of vocalization should be >0.7. If either the range of detection or rate of vocalization is known, conditions are relaxed, and when both parameters are known the method works well almost universally. In favorable conditions for one-dimensional methods, estimated abundances have overall errors not much larger than those from conventional line-transect distance sampling. The methods appeared useful when applied to real acoustic data from whale surveys. The techniques may also be useful in surveys with nonacoustic detection of animals.     

Characterization of measurement errors using structure‐from‐motion and photogrammetry to measure marine habitat structural complexity

Habitat structural complexity is one of the most important factors in determining the makeup of biological communities. Recent advances in structure‐from‐motion and photogrammetry have resulted in a proliferation of 3D digital representations of habitats from which structural complexity can be measured. Little attention has been paid to quantifying the measurement errors associated with these techniques, including the variability of results under different surveying and environmental conditions. Such errors have the potential to confound studies that compare habitat complexity over space and time. This study evaluated the accuracy, precision, and bias in measurements of marine habitat structural complexity derived from structure‐from‐motion and photogrammetric measurements using repeated surveys of artificial reefs (with known structure) as well as natural coral reefs. We quantified measurement errors as a function of survey image coverage, actual surface rugosity, and the morphological community composition of the habitat‐forming organisms (reef corals). Our results indicated that measurements could be biased by up to 7.5% of the total observed ranges of structural complexity based on the environmental conditions present during any particular survey. Positive relationships were found between measurement errors and actual complexity, and the strength of these relationships was increased when coral morphology and abundance were also used as predictors. The numerous advantages of structure‐from‐motion and photogrammetry techniques for quantifying and investigating marine habitats will mean that they are likely to replace traditional measurement techniques (e.g., chain‐and‐tape). To this end, our results have important implications for data collection and the interpretation of measurements when examining changes in habitat complexity using structure‐from‐motion and photogrammetry.     

Secular trend in the occurrence of asthma among children and young adults: critical appraisal of repeated cross sectional surveys.

OBJECTIVES: To review repeated surveys of the rising prevalence of obstructive lung disease among children and young adults and determine whether systematic biases may explain the observed trends. DESIGN: Review of published reports of repeated cross sectional surveys of asthma and wheezing among children and young adults. The repeated surveys used the same sampling frame, the same definition of outcome variables, and equivalent data collection methods. SETTING: Repeated surveys conducted anywhere in the world. SUBJECTS: All repeated surveys whose last set of results were published in 1983 or later. MAIN OUTCOME MEASURES: Lifetime and current prevalences of asthma and current prevalence of wheezing. The absolute increase (yearly percentage) in the prevalences of asthma and wheezing was calculated and compared between studies. RESULTS: 16 repeated surveys fulfilled the inclusion criteria. 12 reported increases in the current prevalence of asthma (from 0.09% to 0.97% a year) and eight reported increases in the current prevalence of wheezing (from 0.14% to 1.24% a year). Changes in labelling are likely to have occurred for the reporting of asthma, and information biases may have occurred for the reporting of wheezing. Only one study reported an increase in an objective measurement. CONCLUSIONS: The evidence for increased prevalences of asthma and wheezing is weak because the measures used are susceptible to systematic errors. Until repeated surveys incorporating more objective data are available no firm conclusions about increases in obstructive lung disease among children and young adults can be drawn.     

Solving some statistical problems in analyses of experiments on choices of food and on associations with habitat

Statistical tests for non-random associations with components of habitat or different kinds of prey require information about the availability of sub-habitats or types of prey. The data are obtained from sampling (Stage 1 samples). Tests are then constructed using this information to predict what will be the occupancy of habitats or composition of diet under the null hypothesis of random association. Estimates of actual occupancy of habitats or composition of diet are then obtained from Stage 2 sampling and tests are done to compare the observed data from Stage 2 with what was predicted from Stage 1.Estimates from each stage of sampling are subject to sampling error, particularly where small samples are involved. The errors involved in Stage 1 sampling are often ignored, resulting in biases in tests and excessive rejection of null hypotheses (i.e. non-random patterns are claimed when they are not present). Here, accurate tests are developed which take into account both types of error.For animals in patchy habitats, with two or more types of patch, the data from Stages 1 and 2 are used to derive maximal likelihood estimators for the proportions of area occupied by the sub-habitats and the proportions of animals in each sub-habitat. These are then used in χ² tests.For composition of diets, data are more complex, because the consumption of food of each type (on its own) must be estimated in separate experiments or sampling. So, Stage 1 sampling is more difficult and the maximal likelihood estimators described here are more complex. The accurate tests described here give much more realistic answers in that they properly control rates of Type I error, particularly with small samples. The effects of errors in Stage 1 sampling are, however, shown to be important, even for quite large samples. The tests can and should be used in any analyses of non-random association or preference among sub-habitats or types of prey.     

多维协变量具有测量误差的结构回归模型

提出具有测量误差的结构回归模型,研究可交换条件下多维协变量的测量误差对平均处理效应估计的影响,在没有其它的附加条件下,尽管大多数模型参数不可识别,平均处理效应仍可识别,由于平均处理效应的极大似然估计求解困难,建议在实际中使用拟极大似然估计作为替代。     

Evaluating pedigree data. II. Identifying the cause of error in families with inconsistencies

Pedigree data can be evaluated, and subsequently corrected, by analysis of the distribution of genetic markers, taking account of the possibility of mistyping . Using a model of pedigree error developed previously, we obtained the maximum likelihood estimates of error parameters in pedigree data from Tokelau. Posterior probabilities for the possible true relationships in each family are conditional on the putative relationships and the marker data are calculated using the parameter estimates. These probabilities are used as a basis for discriminating between pedigree error and genetic marker errors in families where inconsistencies have been observed. When applied to the Tokelau data and compared with the results of retyping inconsistent families, these statistical procedures are able to discriminate between pedigree and marker error, with approximately 90% accuracy, for families with two or more offspring. The large proportion of inconsistencies inferred to be due to marker error (61%) indicates the importance of discriminating between error sources when judging the reliability of putative relationship data. Application of our model of pedigree error has proved to be an efficient way of determining and subsequently correcting sources of error in extensive pedigree data collected in large surveys.     

Simultaneous inference for semiparametric nonlinear mixed-effects models with covariate measurement errors and missing responses

Semiparametric nonlinear mixed-effects (NLME) models are flexible for modeling complex longitudinal data. Covariates are usually introduced in the models to partially explain interindividual variations. Some covariates, however, may be measured with substantial errors. Moreover, the responses may be missing and the missingness may be nonignorable. We propose two approximate likelihood methods for semiparametric NLME models with covariate measurement errors and nonignorable missing responses. The methods are illustrated in a real data example. Simulation results show that both methods perform well and are much better than the commonly used naive method.     

A family-based likelihood ratio test for general pedigree structures that allows for genotyping error and missing data

The purpose of this work is the development of a family-based association test that allows for random genotyping errors and missing data and makes use of information on affected and unaffected pedigree members. We derive the conditional likelihood functions of the general nuclear family for the following scenarios: complete parental genotype data and no genotyping errors; only one genotyped parent and no genotyping errors; no parental genotype data and no genotyping errors; and no parental genotype data with genotyping errors. We find maximum likelihood estimates of the marker locus parameters, including the penetrances and population genotype frequencies under the null hypothesis that all penetrance values are equal and under the alternative hypothesis. We then compute the likelihood ratio test. We perform simulations to assess the adequacy of the central chi-square distribution approximation when the null hypothesis is true. We also perform simulations to compare the power of the TDT and this likelihood-based method. Finally, we apply our method to 23 SNPs genotyped in nuclear families from a recently published study of idiopathic scoliosis (IS). Our simulations suggest that this likelihood ratio test statistic follows a central chi-square distribution with 1 degree of freedom under the null hypothesis, even in the presence of missing data and genotyping errors. The power comparison shows that this likelihood ratio test is more powerful than the original TDT for the simulations considered. For the IS data, the marker rs7843033 shows the most significant evidence for our method (p = 0.0003), which is consistent with a previous report, which found rs7843033 to be the 2nd most significant TDTae p value among a set of 23 SNPs.     

Semiparametric maximum likelihood for measurement error model regression

This paper presents an EM algorithm for semiparametric likelihood analysis of linear, generalized linear, and nonlinear regression models with measurement errors in explanatory variables. A structural model is used in which probability distributions are specified for (a) the response and (b) the measurement error. A distribution is also assumed for the true explanatory variable but is left unspecified and is estimated by nonparametric maximum likelihood. For various types of extra information about the measurement error distribution, the proposed algorithm makes use of available routines that would be appropriate for likelihood analysis of (a) and (b) if the true x were available. Simulations suggest that the semiparametric maximum likelihood estimator retains a high degree of efficiency relative to the structural maximum likelihood estimator based on correct distributional assumptions and can outperform maximum likelihood based on an incorrect distributional assumption. The approach is illustrated on three examples with a variety of structures and types of extra information about the measurement error distribution.     

Statistical characterization of protein ensembles

When accounting for structural fluctuations or measurement errors, a single rigid structure may not be sufficient to represent a protein. One approach to solve this problem is to represent the possible conformations as a discrete set of observed conformations, an ensemble. In this work, we follow a different richer approach, and introduce a framework for estimating probability density functions in very high dimensions, and then apply it to represent ensembles of folded proteins. This proposed approach combines techniques such as kernel density estimation, maximum likelihood, cross-validation, and bootstrapping. We present the underlying theoretical and computational framework and apply it to artificial data and protein ensembles obtained from molecular dynamics simulations. We compare the results with those obtained experimentally, illustrating the potential and advantages of this representation.     

On the Challenge of Fitting Tree Size Distributions in Ecology

Patterns that resemble strongly skewed size distributions are frequently observed in ecology. A typical example represents tree size distributions of stem diameters. Empirical tests of ecological theories predicting their parameters have been conducted, but the results are difficult to interpret because the statistical methods that are applied to fit such decaying size distributions vary. In addition, binning of field data as well as measurement errors might potentially bias parameter estimates. Here, we compare three different methods for parameter estimation – the common maximum likelihood estimation (MLE) and two modified types of MLE correcting for binning of observations or random measurement errors. We test whether three typical frequency distributions, namely the power-law, negative exponential and Weibull distribution can be precisely identified, and how parameter estimates are biased when observations are additionally either binned or contain measurement error. We show that uncorrected MLE already loses the ability to discern functional form and parameters at relatively small levels of uncertainties. The modified MLE methods that consider such uncertainties (either binning or measurement error) are comparatively much more robust. We conclude that it is important to reduce binning of observations, if possible, and to quantify observation accuracy in empirical studies for fitting strongly skewed size distributions. In general, modified MLE methods that correct binning or measurement errors can be applied to ensure reliable results.     

A test of homogeneity of distributions when observations are subject to measurement errors

When the observed data are contaminated with errors, the standard two-sample testing approaches that ignore measurement errors may produce misleading results, including a higher type-I error rate than the nominal level. To tackle this inconsistency, a nonparametric test is proposed for testing equality of two distributions when the observed contaminated data follow the classical additive measurement error model. The proposed test takes into account the presence of errors in the observed data, and the test statistic is defined in terms of the (deconvoluted) characteristic functions of the latent variables. Proposed method is applicable to a wide range of scenarios as no parametric restrictions are imposed either on the distribution of the underlying latent variables or on the distribution of the measurement errors. Asymptotic null distribution of the test statistic is derived, which is given by an integral of a squared Gaussian process with a complicated covariance structure. For data-based calibration of the test, a new nonparametric Bootstrap method is developed under the two-sample measurement error framework and its validity is established. Finite sample performance of the proposed test is investigated through simulation studies, and the results show superior performance of the proposed method than the standard tests that exhibit inconsistent behavior. Finally, the proposed method was applied to real data sets from the National Health and Nutrition Examination Survey. An R package MEtest is available through CRAN.     

Robust Joint Modeling of Longitudinal Measurements and Competing Risks Failure Time Data

Existing methods for joint modeling of longitudinal measurements and survival data can be highly influenced by outliers in the longitudinal outcome. We propose a joint model for analysis of longitudinal measurements and competing risks failure time data which is robust in the presence of outlying longitudinal observations during follow‐up. Our model consists of a linear mixed effects sub‐model for the longitudinal outcome and a proportional cause‐specific hazards frailty sub‐model for the competing risks data, linked together by latent random effects. Instead of the usual normality assumption for measurement errors in the linear mixed effects sub‐model, we adopt a t ‐distribution which has a longer tail and thus is more robust to outliers. We derive an EM algorithm for the maximum likelihood estimates of the parameters and estimate their standard errors using a profile likelihood method. The proposed method is evaluated by simulation studies and is applied to a scleroderma lung study (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bayesian and maximum likelihood estimation of genetic maps

There has recently been increased interest in the use of Markov Chain Monte Carlo (MCMC)-based Bayesian methods for estimating genetic maps. The advantage of these methods is that they can deal accurately with missing data and genotyping errors. Here we present an extension of the previous methods that makes the Bayesian method applicable to large data sets. We present an extensive simulation study examining the statistical properties of the method and comparing it with the likelihood method implemented in Mapmaker. We show that the Maximum A Posteriori (MAP) estimator of the genetic distances, corresponding to the maximum likelihood estimator, performs better than estimators based on the posterior expectation. We also show that while the performance is similar between Mapmaker and the MCMC-based method in the absence of genotyping errors, the MCMC-based method has a distinct advantage in the presence of genotyping errors. A similar advantage of the Bayesian method was not observed for missing data. We also re-analyse a recently published set of data from the eggplant and show that the use of the MCMC-based method leads to smaller estimates of genetic distances.     

Gene assignment by means of somatic cell hybrids: a new method for the analysis of data

Summary A statistical approach to the interpretation of data from gene assignment with somatic cell hybrids is presented. The observed data are analysed under a variety of hypotheses. The fit to the hypotheses is compared by means of the likelihood obtained under a given hypothesis. Two of these hypotheses are related to fundamental questions: is a gene responsible for the enzyme observation and if so, is that gene located on a specific chromosome or could it change its position and be sometimes on chromosome j and, in another hybrid line, on chromosome k? The other hypotheses concern the assignment of the gene to just one of the chromosomes.To improve the traditional data analysis approach we considered additional information: the uncertainties and possible errors of laboratory methods in all our calculations and the length of the donor chromosomes in connection with one specific hypothesis.This method allows us to account for the reliability of the investigation methods and the nature of the hybrid lines involved. Data can be evaluated at different error probabilities within a realistic range in order to compare and discuss results.     

Application of macroscopic balances to the identification of gross measurement errors

A systematic method is presented which is capable of both detecting the presence of grossly biased measurement errors and locating the source of these errors in a bioreactor through statistical hypothesis testing. Equality constraints derived from material and energy balances are employed for the detection of data inconsistencies and for the subsequent identification of the suspect measurements by a process of data analysis and rectification. Maximum likelihood techniques are applied to the estimation of the states and parameters of the bioreactor after the suspect measurements have been eliminated. The level of significance is specified by the experimenter while the measurments are assumed to be randomly, normally distributed with zero mean and known variances. Two different approaches of data analysis, batchwise and sequential, that lead to a consistent set of adjustments on the experimental values, are discussed. Several examples based on the fermentation data taken from literature sources are presented to demonstrate the utility of the proposed method, and one set of data is solved numerically to illustrate the computational aspect of the algorithm.     

Uncertainty analysis of forest carbon sink forecast with varying measurement errors: a data assimilation approach

Aims Accurate forecast of ecosystem states is critical for improving natural resource management and climate change mitigation. Assimilating observed data into models is an effective way to reduce uncertainties in ecological forecasting. However, influences of measurement errors on parameter estimation and forecasted state changes have not been carefully examined. This study analyzed the parameter identifiability of a process-based ecosystem carbon cycle model, the sensitivity of parameter estimates and model forecasts to the magnitudes of measurement errors and the information contributions of the assimilated data to model forecasts with a data assimilation approach.Methods We applied a Markov Chain Monte Carlo method to assimilate eight biometric data sets into the Terrestrial ECOsystem model. The data were the observations of foliage biomass, wood biomass, fine root biomass, microbial biomass, litter fall, litter, soil carbon and soil respiration, collected at the Duke Forest free-air CO₂ enrichment facilities from 1996 to 2005. Three levels of measurement errors were assigned to these data sets by halving and doubling their original standard deviations.Important findings Results showed that only less than half of the 30 parameters could be constrained, though the observations were extensive and the model was relatively simple. Higher measurement errors led to higher uncertainties in parameters estimates and forecasted carbon (C) pool sizes. The long-term predictions of the slow turnover pools were affected less by the measurement errors than those of fast turnover pools. Assimilated data contributed less information for the pools with long residence times in long-term forecasts. These results indicate the residence times of C pools played a key role in regulating propagation of errors from measurements to model forecasts in a data assimilation system. Improving the estimation of parameters of slow turnover C pools is the key to better forecast long-term ecosystem C dynamics.     

cameratrapR: An R package for estimating animal density using camera trapping data

• 1.Camera trapping plays an important role in wildlife surveys, and provides valuable information for estimation of population density. While mark-recapture techniques can estimate population density for species that can be individually recognized or marked, there are no robust methods to estimate density of species that cannot be individually identified.
• 2.We developed a new approach to estimate population density based on the simulation of individual movement within the camera grid. Simulated animals followed a correlated random walk with the movement parameters of segment length, angular deflection, movement distance and home-range size derived from empirical movement paths. Movement was simulated under a series of population densities. We used the Random Forest algorithm to determine the population density with the highest likelihood of matching the camera trap data. We developed an R package, cameratrapR, to conduct simulations and estimate population density.
• 3.Compared with line transect surveys and the random encounter model, cameratrapR provides more reliable estimates of wildlife density with narrower confidence intervals. Functions are provided to visualize movement paths, derive movement parameters, and plot camera trapping results.
• 4.The package allows researchers to estimate population sizes/densities of animals that cannot be individually identified and cameras are deployed in a grid pattern.