Hierarchical Bayes estimation of hunting success rates with spatial correlations

A Bayesian hierarchical generalized linear model is used to estimate hunting success rates at the subarea level for postseason harvest surveys. The model includes fixed week effects, random geographic effects, and spatial correlations between neighboring subareas. The computation is done by Gibbs sampling and adaptive rejection sampling techniques. The method is illustrated using data from the Missouri Turkey Hunting Survey in the spring of 1996. Bayesian model selection methods are used to demonstrate that there are significant week differences and spatial correlations of hunting success rates among counties. The Bayesian estimates are also shown to be quite robust in terms of changes of hyperparameters.     

Performance of sampling strategies in the presence of known spatial patterns

In crop protection and ecology accurate and precise estimates of insect populations are required for many purposes. The spatial pattern of the organism sampled, in relation to the sampling scheme adopted, affects the difference between the actual and estimated population density, the bias, and the variability of that estimate, the precision. Field monitoring schemes usually adopt time‐efficient sampling regimes involving contiguous units rather than the most efficient for estimation, the completely random sample. This paper uses spatially‐explicit ecological field data on aphids and beetles to compare common sampling regimes. The random sample was the most accurate method and often the most precise; of the contiguous schemes the line transect was superior to more compact arrangements such as a square block. Bias depended on the relationship between the size and shape of the group of units comprising the sample and the dominant cluster size underlying the spatial pattern. Existing knowledge of spatial pattern to inform the choice of sampling scheme may provide considerable improvements in accuracy. It is recommended to use line transects longer than the grain of the spatial pattern, where grain is defined as the average dimension of clusters over both patches and gaps, and with length at least twice the dominant cluster size.     

Effect of sampling strategy on estimation of fine‐scale spatial genetic structure in Androsace tapete (Primulaceae), an alpine plant endemic to Qinghai‐Tibetan Plateau

Abstract The fine‐scale spatial genetic structure (SGS) of alpine plants is receiving increasing attention, from which seed and pollen dispersal can be inferred. However, estimation of SGS may depend strongly on the sampling strategy, including the sample size and spatial sampling scheme. Here, we examined the effects of sample size and three spatial schemes, simple‐random, line‐transect, and random‐cluster sampling, on the estimation of SGS in Androsace tapete, an alpine cushion plant endemic to Qinghai‐Tibetan Plateau. Using both real data and simulated data of dominant molecular markers, we show that: (i) SGS is highly sensitive to sample strategy especially when the sample size is small (e.g., below 100); (ii) the commonly used SGS parameter (the intercept of the autocorrelogram) is more susceptible to sample error than a newly developed Sp statistic; and (iii) the random‐cluster scheme is susceptible to obvious bias in parameter estimation even when the sample size is relatively large (e.g., above 200). Overall, the line‐transect scheme is recommendable, in that it performs slightly better than the simple‐random scheme in parameter estimation and is more efficient to encompass broad spatial scales. The consistency between simulated data and real data implies that these findings might hold true in other alpine plants and more species should be examined in future work.     

二化螟种群密度的克力格估值及其模拟抽样

为设计可靠合理的二化螟幼虫种群密度抽样方案,从二化螟幼虫空间分布原始总体出发,另构建了一个随机总体和一个顺序总体,采用无放回随机抽样、间隔变程以上无放回随机抽样和基于克力格估值且初始点随机的顺序抽样对3总体进行了模拟抽样比较．结果表明,间隔变程以上随机抽样对原始总体平均数的估计优于随机抽样,且随总体聚集程度增加,间隔变程以上随机抽样愈优;正确识别种群空间格局极为重要,对聚集分布总体采用随机抽样和对随机分布总体采用间隔变程以上随机抽样均将降低抽样估计精度．针对随机抽样在应用上的局限性,提出了一种基于地统计学克力格估值、初始点随机的顺序抽样方案：它以初始点随机保证随机性,以顺序抽样保证可操作性,以二化螟种群空间分布的区域变量属性保证克力格样本较调查样本对局域样本和总体的平均数估计为优;且聚集范围一定时,总体聚集强度愈大,克力格样本局域估计和全局估计愈优于调查样本;取样间隔(以变程为标准)极为重要,样方的空间布局要平衡考虑相互独立的样方对数和变程范围内的样方对数。     

Adaptive Cluster Sampling in the Context of Restoration

Abundance is an important population state variable for monitoring restoration progress. Efficient sampling often proves difficult, however, when populations are sparse and patchily distributed, such as early after restoration planting. Adaptive cluster sampling (ACS) can help by concentrating search effort in high density areas, improving the encounter rate and the ability to detect a population change over time. To illustrate the problem, I determined conventional design sample sizes for estimating abundance of 12 natural populations and 24 recently planted populations (divided among two preserves) of Lupinus perennis L. (wild blue lupine). I then determined the variance efficiency of ACS relative to simple random sampling at fixed effort and cost for 10 additional planted populations in two habitats (field vs. shrubland). Conventional design sample sizes to estimate lupine stem density with 10% or 20% margins of error were many times greater than initial sample size and would require sampling at least 90% of the study area. Differences in effort requirements were negligible for the two preserves and natural versus planted populations. At fixed sample size, ACS equaled or outperformed simple random sampling in 40% of populations; this shifted to 50% after correcting for travel time among sample units. ACS appeared to be a better strategy for inter‐seeded shrubland habitat than for planted field habitat. Restoration monitoring programs should consider adaptive sampling designs, especially when reliable abundance estimation under conventional designs proves elusive.     

Hierarchical Bayesian modeling in dichotomous processes in the presence of nonresponse

Sampling units that do not answer a survey may dramatically affect the estimation results of interest. The response may even be conditional on the outcome of interest in the survey. If estimates are found using only those who responded, the estimate may be biased, known as nonresponse bias. We are interested in finding estimates of success rates from a survey. We begin by looking at two current Bayesian approaches to treating nonresponse in a hierarchical model. However, these approaches do not consider possible spatial correlations between domains for either success rate or response rate. We build a Bayesian hierarchical spatial model to explicitly estimate the success rate, response rate given success, and response rate given failure. The success rates in the domains of the survey are allowed to be spatially correlated. We also allow spatial dependence between domains in both response rate given success and response rate given failure. Spatial dependence is induced by a common latent spatial structure between the two conditional response rates. We use the 1998 Missouri Turkey Hunting Survey to illustrate this methodology. We find significant spatial correlation in the success rates and incorporating nonrespondents has an impact on the success rate estimates.     

Hierarchical Bayesian modeling of spatially correlated health service outcome and utilization rates

We present Bayesian hierarchical spatial models for spatially correlated small-area health service outcome and utilization rates, with a particular emphasis on the estimation of both measured and unmeasured or unknown covariate effects. This Bayesian hierarchical model framework enables simultaneous modeling of fixed covariate effects and random residual effects. The random effects are modeled via Bayesian prior specifications reflecting spatial heterogeneity globally and relative homogeneity among neighboring areas. The model inference is implemented using Markov chain Monte Carlo methods. Specifically, a hybrid Markov chain Monte Carlo algorithm (Neal, 1995, Bayesian Learning for Neural Networks; Gustafson, MacNab, and Wen, 2003, Statistics and Computing, to appear) is used for posterior sampling of the random effects. To illustrate relevant problems, methods, and techniques, we present an analysis of regional variation in intraventricular hemorrhage incidence rates among neonatal intensive care unit patients across Canada.     

Improved procedures for estimation of disease prevalence using ranked set sampling

Ranked set sampling (RSS) is a sampling procedure that can be considerably more efficient than simple random sampling (SRS). When the variable of interest is binary, ranking of the sample observations can be implemented using the estimated probabilities of success obtained from a logistic regression model developed for the binary variable. The main objective of this study is to use substantial data sets to investigate the application of RSS to estimation of a proportion for a population that is different from the one that provides the logistic regression. Our results indicate that precision in estimation of a population proportion is improved through the use of logistic regression to carry out the RSS ranking and, hence, the sample size required to achieve a desired precision is reduced. Further, the choice and the distribution of covariates in the logistic regression model are not overly crucial for the performance of a balanced RSS procedure.     

Recommendations for estimating mark rate of cetaceans in photo-ID research: A critique of field sampling protocols and variance estimation

Mark rate, or the proportion of the population with unique, identifiable marks, must be determined in order to estimate population size from photographic identification data. In this study we address field sampling protocols and estimation methods for robust estimation of mark rate and its uncertainty in cetacean populations. We present two alternatives for estimating the variance of mark rate: (1) a variance estimator for clusters of unequal sizes (SRCS) and (2) a hierarchical Bayesian model (SRCS-Bayes), and compare them to the simple random sampling (SRS) variance estimator. We tested these variance estimators using a simulation to see how they perform at varying mark rates, number of groups sampled, photos per group, and mean group sizes. The hierarchical Bayesian model outperformed the frequentist variance estimators, with the true mark rate of the population held in its 95% HDI 91.9% of the time (compared with coverage of 79% for the SRS method and 76.3% for the SRCS-Cochran method). The simulation results suggest that, ideally, mark rate and its precision should be quantified using hierarchical Bayesian modeling, and researchers should attempt to sample as many unique groups as possible to improve accuracy and precision.     

Bootstrap confidence intervals for adaptive cluster sampling

Consider a collection of spatially clustered objects where the clusters are geographically rare. Of interest is estimation of the total number of objects on the site from a sample of plots of equal size. Under these spatial conditions, adaptive cluster sampling of plots is generally useful in improving efficiency in estimation over simple random sampling without replacement (SRSWOR). In adaptive cluster sampling, when a sampled plot meets some predefined condition, neighboring plots are added to the sample. When populations are rare and clustered, the usual unbiased estimators based on small samples are often highly skewed and discrete in distribution. Thus, confidence intervals based on asymptotic normal theory may not be appropriate. We investigated several nonparametric bootstrap methods for constructing confidence intervals under adaptive cluster sampling. To perform bootstrapping, we transformed the initial sample in order to include the information from the adaptive portion of the sample yet maintain a fixed sample size. In general, coverages of bootstrap percentile methods were closer to nominal coverage than the normal approximation.     

Rarefaction and extrapolation of species richness using an area‐based Fisher's logseries

Fisher's logseries is widely used to characterize species abundance pattern, and some previous studies used it to predict species richness. However, this model, derived from the negative binomial model, degenerates at the zero‐abundance point (i.e., its probability mass fully concentrates at zero abundance, leading to an odd situation that no species can occur in the studied sample). Moreover, it is not directly related to the sampling area size. In this sense, the original Fisher's alpha (correspondingly, species richness) is incomparable among ecological communities with varying area sizes. To overcome these limitations, we developed a novel area‐based logseries model that can account for the compounding effect of the sampling area. The new model can be used to conduct area‐based rarefaction and extrapolation of species richness, with the advantage of accurately predicting species richness in a large region that has an area size being hundreds or thousands of times larger than that of a locally observed sample, provided that data follow the proposed model. The power of our proposed model has been validated by extensive numerical simulations and empirically tested through tree species richness extrapolation and interpolation in Brazilian Atlantic forests. Our parametric model is data parsimonious as it is still applicable when only the information on species number, community size, or the numbers of singleton and doubleton species in the local sample is available. Notably, in comparison with the original Fisher's method, our area‐based model can provide asymptotically unbiased variance estimation (therefore correct 95% confidence interval) for species richness. In conclusion, the proposed area‐based Fisher's logseries model can be of broad applications with clear and proper statistical background. Particularly, it is very suitable for being applied to hyperdiverse ecological assemblages in which nonparametric richness estimators were found to greatly underestimate species richness.     

Matrix heterogeneity affects population size of the harvest mice: Bayesian estimation of matrix resistance and model validation

It has been increasingly recognized that landscape matrices are an important factor determining patch connectivity and hence the population size of organisms living in highly fragmented landscapes. However, most previous studies estimated the effect of matrix heterogeneity using prior information regarding dispersal or habitat preferences of a focal organism. Here we estimated matrix resistance of harvest mice in agricultural landscapes using a novel pattern‐oriented modeling with Bayesian estimation and no prior information, and then conducted model validation using data sets independent from those used for model construction. First, we investigated the distribution patterns of harvest mice for approximately 400 habitat patches, and estimated matrix resistance for different matrix types using statistical models incorporating patch size, patch environment, and patch connectivity. We used Bayesian estimation with a Markov chain Monte Carlo algorithm, and searched for appropriate matrix resistance that best explained the distribution pattern. Patch connectivity as well as patch quality was an important determinant of local population size for the harvest mice. Moreover, matrix resistance was far from uniform, with rice and crop fields exhibiting low resistance and forests, creeks, roads and residential areas showing much higher resistance. The deviance explained by this model (heterogeneous matrix model) was much larger than that obtained by the model with no consideration of matrix heterogeneity (homogeneous matrix model). Second, we obtained distribution data from five additional landscapes that were more fragmented than that used for model construction, and used them for model validation. The heterogeneous matrix model well predicted the population size for four out of five landscapes. In contrast, the homogeneous model considerably overestimated population sizes in all cases. Our approach is widely applicable to species living in fragmented landscapes, especially those for which prior information regarding movement or dispersal is difficult to obtain.     

Interactions Between Pattern Formation and Domain Growth

In this paper we develop a theoretical framework for investigating pattern formation in biological systems for which the tissue on which the spatial pattern resides is growing at a rate which is itself regulated by the diffusible chemicals that establish the spatial pattern. We present numerical simulations for two cases of interest, namely exponential domain growth and chemically controlled growth. Our analysis reveals that for domains undergoing rapid exponential growth dilution effects associated with domain growth influence both the spatial patterns that emerge and the concentration of chemicals present in the domain. In the latter case, there is complex interplay between the effects of the chemicals on the domain size and the influence of the domain size on the formation of patterns. The nature of these interactions is revealed by a weakly nonlinear analysis of the full system. This yields a pair of nonlinear equations for the amplitude of the spatial pattern and the domain size. The domain is found to grow (or shrink) at a rate that depends quadratically on the pattern amplitude, the particular functional forms used to model the local tissue growth rate and the kinetics of the two diffusible species dictating the resulting behaviour.     

An exact sampling formula for the Wright-Fisher model and a solution to a conjecture about the finite-island model

An exact sampling formula for a Wright-Fisher population of fixed size N under the infinitely many neutral alleles model is deduced. This extends the Ewens formula for the configuration of a random sample to the case where the sample is drawn from a population of small size, that is, without the usual large-N and small-mutation-rate assumption. The formula is used to prove a conjecture ascertaining the validity of a diffusion approximation for the frequency of a mutant-type allele under weak selection in segregation with a wild-type allele in the limit finite-island model, namely, a population that is subdivided into a finite number of demes of size N and that receives an expected fraction m of migrants from a common migrant pool each generation, as the number of demes goes to infinity. This is done by applying the formula to the migrant ancestors of a single deme and sampling their types at random. The proof of the conjecture confirms an analogy between the island model and a random-mating population, but with a different timescale that has implications for estimation procedures.     

Efficient Bayesian Sample Size Calculation for Designing a Clinical Trial with Multi‐Cluster Outcome Data

Health care utilization and outcome studies call for hierarchical approaches. The objectives were to predict major complications following percutaneous coronary interventions by health providers, and to compare Bayesian and non‐Bayesian sample size calculation methods. The hierarchical data structure consisted of: (1) Strata: PGY4, PGY7, and physician assistant as providers with varied experiences; (2) Clusters: k_s providers per stratum; (3) Individuals: n_s patients reviewed by each provider. The main outcome event illustrated was mortality modeled by a Bayesian beta‐binomial model. Pilot information and assumptions were utilized to elicit beta prior distributions. Sample size calculations were based on the approximated average length, fixed at 1%, of 95% posterior intervals of the mean event rate parameter. Necessary sample sizes by both non‐Bayesian and Bayesian methods were compared. We demonstrated that the developed Bayesian methods can be efficient and may require fewer subjects to satisfy the same length criterion.     

Joint modelling of longitudinal and time-to-event data with application to predicting abdominal aortic aneurysm growth and rupture

Shared random effects joint models are becoming increasingly popular for investigating the relationship between longitudinal and time‐to‐event data. Although appealing, such complex models are computationally intensive, and quick, approximate methods may provide a reasonable alternative. In this paper, we first compare the shared random effects model with two approximate approaches: a naïve proportional hazards model with time‐dependent covariate and a two‐stage joint model, which uses plug‐in estimates of the fitted values from a longitudinal analysis as covariates in a survival model. We show that the approximate approaches should be avoided since they can severely underestimate any association between the current underlying longitudinal value and the event hazard. We present classical and Bayesian implementations of the shared random effects model and highlight the advantages of the latter for making predictions. We then apply the models described to a study of abdominal aortic aneurysms (AAA) to investigate the association between AAA diameter and the hazard of AAA rupture. Out‐of‐sample predictions of future AAA growth and hazard of rupture are derived from Bayesian posterior predictive distributions, which are easily calculated within an MCMC framework. Finally, using a multivariate survival sub‐model we show that underlying diameter rather than the rate of growth is the most important predictor of AAA rupture.     

Comparison between estimation of breeding values and fixed effects using Bayesian and empirical BLUP estimation under selection on parents and missing pedigree information

Bayesian (via Gibbs sampling) and empirical BLUP (EBLUP) estimation of fixed effects and breeding values were compared by simulation. Combinations of two simulation models (with or without effect of contemporary group (CG)), three selection schemes (random, phenotypic and BLUP selection), two levels of heritability (0.20 and 0.50) and two levels of pedigree information (0% and 15% randomly missing) were considered. Populations consisted of 450 animals spread over six discrete generations. An infinitesimal additive genetic animal model was assumed while simulating data. EBLUP and Bayesian estimates of CG effects and breeding values were, in all situations, essentially the same with respect to Spearman''s rank correlation between true and estimated values. Bias and mean square error (MSE) of EBLUP and Bayesian estimates of CG effects and breeding values showed the same pattern over the range of simulated scenarios. Methods were not biased by phenotypic and BLUP selection when pedigree information was complete, albeit MSE of estimated breeding values increased for situations where CG effects were present. Estimation of breeding values by Bayesian and EBLUP was similarly affected by joint effect of phenotypic or BLUP selection and randomly missing pedigree information. For both methods, bias and MSE of estimated breeding values and CG effects substantially increased across generations.     

Effect of sampling strategy on estimation of fine-scale spatial genetic structure in Androsace tapete (Primulaceae), an alpine plant endemic to Qinghai-Tibetan Plateau

The fine-scale spatial genetic structure (SGS) of alpine plants is receiving increasing attention, from which seed and pollen dispersal can be inferred. However, estimation of SGS may depend strongly on the sampling strategy,including the sample size and spatial sampling scheme. Here, we examined the effects of sample size and three spatial schemes, simple-random, line-transect, and random-cluster sampling, on the estimation of SGS in Androsace tapete, an alpine cushion plant endemic to Qinghai-Tibetan Plateau. Using both real data and simulated data of dominant molecular markers, we show that: (i) SGS is highly sensitive to sample strategy especially when the sample size is small (e.g., below 100); (ii) the commonly used SGS parameter (the intercept of the autocorrelogram) is more susceptible to sample error than a newly developed Sp statistic; and (iii) the random-cluster scheme is susceptible to obvious bias in parameter estimation even when the sample size is relatively large (e.g., above 200). Overall,the line-transect scheme is recommendable, in that it performs slightly better than the simple-random scheme in parameter estimation and is more efficient to encompass broad spatial scales. The consistency between simulated data and real data implies that these findings might hold true in other alpine plants and more species should be examined in future work.     

The effect of reference sample composition and size on dental age interval estimates

Objectives

Validation studies in juvenile dental age estimation primarily focus on point estimates while interval performance for reference samples of different ancestry group compositions has received minimal attention. We tested the effect of reference sample size and composition by sex and ancestry group on age interval estimates.

Materials and Methods

The dataset consisted of Moorrees et al. dental scores from panoramic radiographs of 3334 London children of Bangladeshi and European ancestry and 2–23 years of age. Model stability was assessed using standard error of mean age-at-transition for univariate cumulative probit and sample size, group mixing (sex or ancestry), and staging system as factors. Age estimation performance was tested using molar reference samples of four sizes, stratified by year of age, sex, and ancestry. Age estimates were performed using Bayesian multivariate cumulative probit with 5-fold cross-validation.

Results

Standard error increased with decreasing sample size but showed no effect from mixing by sex or ancestry. Estimating ages using a reference and target sample of different sex reduced success rate significantly. The same test by ancestry groups had a lesser effect. Small sample size (n < 20/year of age) negatively affected most performance metrics.

Discussion

We found that reference sample size, followed by sex, primarily drove age estimation performance. Combining reference samples by ancestry produced equivalent or better estimates of age by all metrics than using a single-demographic reference of smaller size. We further proposed that population specificity is an alternative hypothesis of intergroup difference that has been erroneously treated as a null.     

Prediction of protein interdomain linker regions by a hidden Markov model

MOTIVATION: Our aim was to predict protein interdomain linker regions using sequence alone, without requiring known homology. Identifying linker regions will delineate domain boundaries, and can be used to computationally dissect proteins into domains prior to clustering them into families. We developed a hidden Markov model of linker/non-linker sequence regions using a linker index derived from amino acid propensity. We employed an efficient Bayesian estimation of the model using Markov Chain Monte Carlo, Gibbs sampling in particular, to simulate parameters from the posteriors. Our model recognizes sequence data to be continuous rather than categorical, and generates a probabilistic output. RESULTS: We applied our method to a dataset of protein sequences in which domains and interdomain linkers had been delineated using the Pfam-A database. The prediction results are superior to a simpler method that also uses linker index.