Ranked Set Sub Sampling the Non Response Strata for Estimating the Difference of Means

The existence of missing observations when the difference of means is estimated determines the need of sub sampling among the non respondents. Ranked set sampling is used for sub sampling. The information provided on one of the variables by the non respondents at the first attempt permits to rank them. The behavior of a ranked set sampling model with respect to other alternattives is studied in this paper. An unbiased estimator is derived and its expected variance is obtained. The proposed model is compared with the use of simple random sampling and Two‐phase sampling for stratification.     

Landscape genetic inferences vary with sampling scenario for a pond‐breeding amphibian

A critical decision in landscape genetic studies is whether to use individuals or populations as the sampling unit. This decision affects the time and cost of sampling and may affect ecological inference. We analyzed 334 Columbia spotted frogs at 8 microsatellite loci across 40 sites in northern Idaho to determine how inferences from landscape genetic analyses would vary with sampling design. At all sites, we compared a proportion available sampling scheme (PASS), in which all samples were used, to resampled datasets of 2–11 individuals. Additionally, we compared a population sampling scheme (PSS) to an individual sampling scheme (ISS) at 18 sites with sufficient sample size. We applied an information theoretic approach with both restricted maximum likelihood and maximum likelihood estimation to evaluate competing landscape resistance hypotheses. We found that PSS supported low‐density forest when restricted maximum likelihood was used, but a combination model of most variables when maximum likelihood was used. We also saw variations when AIC was used compared to BIC. ISS supported this model as well as additional models when testing hypotheses of land cover types that create the greatest resistance to gene flow for Columbia spotted frogs. Increased sampling density and study extent, seen by comparing PSS to PASS, showed a change in model support. As number of individuals increased, model support converged at 7–9 individuals for ISS to PSS. ISS may be useful to increase study extent and sampling density, but may lack power to provide strong support for the correct model with microsatellite datasets. Our results highlight the importance of additional research on sampling design effects on landscape genetics inference.     

害虫防治决策的复序贯分析方法及抽样技术研究

复序贯抽样决策技术实际应用的受限 ,原因在于截止限序贯抽样模型的缺乏。本文在检验昆虫种群空间格局回归模型的基础上 ,推导出了目前国内常用检验回归模型的截止限序贯抽样模型 ,并将其运用于复序贯分析决策过程中。实例分析表明 ,对于同一种生物种群 ,在一定的精度 (D)和置信水平(tα)要求下 ,复序贯抽样决策技术可以大幅度地节约抽样成本     

杨扇舟蛾卵和幼虫的空间分布型及抽样技术

研究了杨扇舟蛾Clostera anachoreta(Fabricius)卵和幼虫的空间分布型及抽样技术,结果表明杨扇舟蛾卵和幼虫在杨树林的分布型均为聚集型中的负二项分布。几种抽样方法中,卵以棋盘式最好,幼虫以平行线法最好。同时建立了杨扇舟蛾卵的下层抽样模型为y=2.4481x 0.4243;幼虫的中、下层抽样模型为y=2.4605x 3.9126。     

Backrub-like backbone simulation recapitulates natural protein conformational variability and improves mutant side-chain prediction

Incorporation of effective backbone sampling into protein simulation and design is an important step in increasing the accuracy of computational protein modeling. Recent analysis of high-resolution crystal structures has suggested a new model, termed backrub, to describe localized, hinge-like alternative backbone and side-chain conformations observed in the crystal lattice. The model involves internal backbone rotations about axes between C-alpha atoms. Based on this observation, we have implemented a backrub-inspired sampling method in the Rosetta structure prediction and design program. We evaluate this model of backbone flexibility using three different tests. First, we show that Rosetta backrub simulations recapitulate the correlation between backbone and side-chain conformations in the high-resolution crystal structures upon which the model was based. As a second test of backrub sampling, we show that backbone flexibility improves the accuracy of predicting point-mutant side-chain conformations over fixed backbone rotameric sampling alone. Finally, we show that backrub sampling of triosephosphate isomerase loop 6 can capture the millisecond/microsecond oscillation between the open and closed states observed in solution. Our results suggest that backrub sampling captures a sizable fraction of localized conformational changes that occur in natural proteins. Application of this simple model of backbone motions may significantly improve both protein design and atomistic simulations of localized protein flexibility.     

Optimal sampling and estimation strategies under the linear model

In some cases model-based and model-assisted inferences canlead to very different estimators. These two paradigms are notso different if we search for an optimal strategy rather thanjust an optimal estimator, a strategy being a pair composedof a sampling design and an estimator. We show that, under alinear model, the optimal model-assisted strategy consists ofa balanced sampling design with inclusion probabilities thatare proportional to the standard deviations of the errors ofthe model and the Horvitz–Thompson estimator. If the heteroscedasticityof the model is 'fully explainable’ by the auxiliary variables,then this strategy is also optimal in a model-based sense. Moreover,under balanced sampling and with inclusion probabilities thatare proportional to the standard deviation of the model, thebest linear unbiased estimator and the Horvitz–Thompsonestimator are equal. Finally, it is possible to construct asingle estimator for both the design and model variance. Theinference can thus be valid under the sampling design and underthe model.     

Risk-targeted selection of agricultural holdings for post-epidemic surveillance: estimation of efficiency gains

Current post-epidemic sero-surveillance uses random selection of animal holdings. A better strategy may be to estimate the benefits gained by sampling each farm and use this to target selection. In this study we estimate the probability of undiscovered infection for sheep farms in Devon after the 2001 foot-and-mouth disease outbreak using the combination of a previously published model of daily infection risk and a simple model of probability of discovery of infection during the outbreak. This allows comparison of the system sensitivity (ability to detect infection in the area) of arbitrary, random sampling compared to risk-targeted selection across a full range of sampling budgets. We show that it is possible to achieve 95% system sensitivity by sampling, on average, 945 farms with random sampling and 184 farms with risk-targeted sampling. We also examine the effect of ordering samples by risk to expedite return to a disease-free status. Risk ordering the sampling process results in detection of positive farms, if present, 15.6 days sooner than with randomly ordered sampling, assuming 50 farms are tested per day.     

Multi-variate models are essential for understanding vertebrate diversification in deep time

Statistical models are helping palaeontologists to elucidate the history of biodiversity. Sampling standardization has been extensively applied to remedy the effects of uneven sampling in large datasets of fossil invertebrates. However, many vertebrate datasets are smaller, and the issue of uneven sampling has commonly been ignored, or approached using pairwise comparisons with a numerical proxy for sampling effort. Although most authors find a strong correlation between palaeodiversity and sampling proxies, weak correlation is recorded in some datasets. This has led several authors to conclude that uneven sampling does not influence our view of vertebrate macroevolution. We demonstrate that multi-variate regression models incorporating a model of underlying biological diversification, as well as a sampling proxy, fit observed sauropodomorph dinosaur palaeodiversity best. This bivariate model is a better fit than separate univariate models, and illustrates that observed palaeodiversity is a composite pattern, representing a biological signal overprinted by variation in sampling effort. Multi-variate models and other approaches that consider sampling as an essential component of palaeodiversity are central to gaining a more complete understanding of deep time vertebrate diversification.     

Two-phase species–time relationships in North American land birds

The species–time relationship (STR) is a macroecological pattern describing the increase in the observed species richness with the length of time censused. Understanding STRs is important for understanding the ecological processes underlying temporal turnover and species richness. However, accurate characterization of the STR has been hampered by the influence of sampling. I analysed STRs for 521 breeding bird survey communities. I used a model of sampling effects to demonstrate that the increase in richness was not due exclusively to sampling. I estimated the time scale at which ecological processes became dominant over sampling effects using a two‐phase model combining a sampling phase and either a power function or logarithmic ecological phase. These two‐phase models performed significantly better than sampling alone and better than simple power and logarithmic functions. Most community dynamics were dominated by ecological processes over scales <5 years. This technique provides an example of a rigorous, quantitative approach to separating sampling from ecological processes.     

Monte Carlo Simulation of Pathogen Behavior during the Sprout Production Process

Food-borne disease outbreaks linked to the consumption of raw sprouts have become a concern over the past decade. A Monte Carlo simulation model of the sprout production process was created to determine the most-effective points for pathogen control. Published literature was reviewed, and relevant data were compiled. Appropriate statistical distributions were determined and used to create the Monte Carlo model with Analytica software. Factors modeled included initial pathogen concentration and prevalence, seed disinfection effectiveness, and sampling of seeds prior to sprouting, sampling of irrigation water, or sampling of the finished product. Pathogen concentration and uniformity of seed contamination had a large effect on the fraction of contaminated batches predicted by the simulation. The model predicted that sprout sampling and irrigation water sampling at the end of the sprouting process would be more effective in pathogen detection than seed sampling prior to production. Day of sampling and type of sample (sprout or water) taken had a minimal effect on rate of detection. Seed disinfection reduced the proportion of contaminated batches, but in some cases it also reduced the ability to detect the pathogen when it was present, because cell numbers were reduced below the detection limit. Both the amount sampled and the pathogen detection limit were shown to be important variables in determining sampling effectiveness. This simulation can also be used to guide further research and compare the levels of effectiveness of different risk reduction strategies.     

吉林蛟河阔叶红松林物种多度分布模型研究

以吉林蛟河阔叶红松林的木本植物为研究对象,将30hm²的样地面积划分为5m×5m,10m×10m,20m×20m,25m×25m的连续取样单元,在4个不同尺度下分别统计各物种在每个取样单元中的有无,得到每个物种在不同尺度下的取样单元数。利用随机分布模型和负二项分布模型分析物种的多度分布,对比预测多度与观测多度讨论两个模型的科学性与实用性。结果表明：对于阔叶红松林而言,负二项分布模型在所有研究尺度上的预测精度都要优于随机分布模型。随机分布和负二项分布的模型预测误差随着研究尺度的增大而增大,因此选取较小的取样单元可以切实提高物种多度的预测精度。利用随机分布和负二项分布模型对多度较小的物种进行预测的效果要优于多度较大的物种。负二项分布模型适合用来模拟阔叶红松林的物种多度分布格局,并且模型的拟合效果受取样单元大小影响。     

Using Inverse Probability Bootstrap Sampling to Eliminate Sample Induced Bias in Model Based Analysis of Unequal Probability Samples

In ecology, as in other research fields, efficient sampling for population estimation often drives sample designs toward unequal probability sampling, such as in stratified sampling. Design based statistical analysis tools are appropriate for seamless integration of sample design into the statistical analysis. However, it is also common and necessary, after a sampling design has been implemented, to use datasets to address questions that, in many cases, were not considered during the sampling design phase. Questions may arise requiring the use of model based statistical tools such as multiple regression, quantile regression, or regression tree analysis. However, such model based tools may require, for ensuring unbiased estimation, data from simple random samples, which can be problematic when analyzing data from unequal probability designs. Despite numerous method specific tools available to properly account for sampling design, too often in the analysis of ecological data, sample design is ignored and consequences are not properly considered. We demonstrate here that violation of this assumption can lead to biased parameter estimates in ecological research. In addition, to the set of tools available for researchers to properly account for sampling design in model based analysis, we introduce inverse probability bootstrapping (IPB). Inverse probability bootstrapping is an easily implemented method for obtaining equal probability re-samples from a probability sample, from which unbiased model based estimates can be made. We demonstrate the potential for bias in model-based analyses that ignore sample inclusion probabilities, and the effectiveness of IPB sampling in eliminating this bias, using both simulated and actual ecological data. For illustration, we considered three model based analysis tools—linear regression, quantile regression, and boosted regression tree analysis. In all models, using both simulated and actual ecological data, we found inferences to be biased, sometimes severely, when sample inclusion probabilities were ignored, while IPB sampling effectively produced unbiased parameter estimates.     

Monte Carlo simulation of pathogen behavior during the sprout production process

Food-borne disease outbreaks linked to the consumption of raw sprouts have become a concern over the past decade. A Monte Carlo simulation model of the sprout production process was created to determine the most-effective points for pathogen control. Published literature was reviewed, and relevant data were compiled. Appropriate statistical distributions were determined and used to create the Monte Carlo model with Analytica software. Factors modeled included initial pathogen concentration and prevalence, seed disinfection effectiveness, and sampling of seeds prior to sprouting, sampling of irrigation water, or sampling of the finished product. Pathogen concentration and uniformity of seed contamination had a large effect on the fraction of contaminated batches predicted by the simulation. The model predicted that sprout sampling and irrigation water sampling at the end of the sprouting process would be more effective in pathogen detection than seed sampling prior to production. Day of sampling and type of sample (sprout or water) taken had a minimal effect on rate of detection. Seed disinfection reduced the proportion of contaminated batches, but in some cases it also reduced the ability to detect the pathogen when it was present, because cell numbers were reduced below the detection limit. Both the amount sampled and the pathogen detection limit were shown to be important variables in determining sampling effectiveness. This simulation can also be used to guide further research and compare the levels of effectiveness of different risk reduction strategies.     

Should we use proportional sampling for species–area studies?

Aim In this paper we aim to show that proportional sampling can detect species–area relationships (SARs) more effectively than uniform sampling. We tested the contribution of alpha and beta diversity in ant communities as explanations for the SAR. Location Tropical forest remnants in Viçosa, Minas Gerais, Brazil (20 °45′ S, 42 °50′ W). Methods We sampled 17 forest remnants with proportional sampling. To disentangle sampling effects from other mechanisms, species richness was fitted in a model with remnant size, number of samples (sampling effects) and an interaction term. Results A SAR was observed independent of the number of samples, discarding sampling effects. Alpha diversity was not influenced by remnant size, and beta diversity increased with remnant size; evidence to the fact that habitat diversity within remnants could be the dominant cause of the SAR. Such a relationship between beta diversity and remnant area may have also arisen due to the combined effects of territoriality and aggregation of ant species. Main conclusions The proposed model, together with proportional sampling, allowed the distinction between sampling effects and other mechanisms.     

A neutral sampling formula for multiple samples and an 'exact' test of neutrality

As the utility of the neutral theory of biodiversity is increasingly being recognized, there is also an increasing need for proper tools to evaluate the relative importance of neutral processes (dispersal limitation and stochasticity). One of the key features of neutral theory is its close link to data: sampling formulas, giving the probability of a data set conditional on a set of model parameters, have been developed for parameter estimation and model comparison. However, only single local samples can be handled with the currently available sampling formulas, whereas data are often available for many small spatially separated plots. Here, I present a sampling formula for multiple, spatially separated samples from the same metacommunity, which is a generalization of earlier sampling formulas. I also provide an algorithm to generate data sets with the model and I introduce a general test of neutrality that does not require an alternative model; this test compares the probability of the observed data (calculated using the new sampling formula) with the probability of model-generated data sets. I illustrate this with tree abundance data from three large Panamanian neotropical forest plots. When the test is performed with model parameters estimated from the three plots, the model cannot be rejected; however, when parameter estimates previously reported for BCI are used, the model is strongly rejected. This suggests that neutrality cannot explain the structure of the three Panamanian tree communities on the local (BCI) and regional (Panama Canal Zone) scale simultaneously. One should be aware, however, that aspects of the model other than neutrality may be responsible for its failure. I argue that the spatially implicit character of the model is a potential candidate.     

Estimating species – area relationships by modeling abundance and frequency subject to incomplete sampling

Models and data used to describe species–area relationships confound sampling with ecological process as they fail to acknowledge that estimates of species richness arise due to sampling. This compromises our ability to make ecological inferences from and about species–area relationships. We develop and illustrate hierarchical community models of abundance and frequency to estimate species richness. The models we propose separate sampling from ecological processes by explicitly accounting for the fact that sampled patches are seldom completely covered by sampling plots and that individuals present in the sampling plots are imperfectly detected. We propose a multispecies abundance model in which community assembly is treated as the summation of an ensemble of species‐level Poisson processes and estimate patch‐level species richness as a derived parameter. We use sampling process models appropriate for specific survey methods. We propose a multispecies frequency model that treats the number of plots in which a species occurs as a binomial process. We illustrate these models using data collected in surveys of early‐successional bird species and plants in young forest plantation patches. Results indicate that only mature forest plant species deviated from the constant density hypothesis, but the null model suggested that the deviations were too small to alter the form of species–area relationships. Nevertheless, results from simulations clearly show that the aggregate pattern of individual species density–area relationships and occurrence probability–area relationships can alter the form of species–area relationships. The plant community model estimated that only half of the species present in the regional species pool were encountered during the survey. The modeling framework we propose explicitly accounts for sampling processes so that ecological processes can be examined free of sampling artefacts. Our modeling approach is extensible and could be applied to a variety of study designs and allows the inclusion of additional environmental covariates.     

Importance sampling for the infinite sites model

Importance sampling or Markov Chain Monte Carlo sampling is required for state-of-the-art statistical analysis of population genetics data. The applicability of these sampling-based inference techniques depends crucially on the proposal distribution. In this paper, we discuss importance sampling for the infinite sites model. The infinite sites assumption is attractive because it constraints the number of possible genealogies, thereby allowing for the analysis of larger data sets. We recall the Griffiths-Tavaré and Stephens-Donnelly proposals and emphasize the relation between the latter proposal and exact sampling from the infinite alleles model. We also introduce a new proposal that takes knowledge of the ancestral state into account. The new proposal is derived from a new result on exact sampling from a single site. The methods are illustrated on simulated data sets and the data considered in Griffiths and Tavaré (1994).     

Multinomial-Sampling Models for Random Genetic Drift

Three different derivations of models with multinomial sampling of genotypes in a finite population are presented. The three derivations correspond to the operation of random drift through population regulation, conditioning on the total number of progeny, and culling, respectively. Generations are discrete and nonoverlapping; the diploid population mates at random. Each derivation applies to a single multiallelic locus in a monoecious or dioecious population; in the latter case, the locus may be autosomal or X-linked. Mutation and viability selection are arbitrary; there are no fertility differences. In a monoecious population, the model yields the Wright-Fisher model (i.e., multinomial sampling of genes) if and only if the viabilities are multiplicative. In a dioecious population, the analogous reduction does not occur even for pure random drift. Thus, multinomial sampling of genotypes generally does not lead to multinomial sampling of genes. Although the Wright-Fisher model probably lacks a sound biological basis and may be inaccurate for small populations, it is usually (perhaps always) a good approximation for genotypic multinomial sampling in large populations.     

Multivariate Bayesian analysis of Gaussian,right censored Gaussian,ordered categorical and binary traits using Gibbs sampling

A fully Bayesian analysis using Gibbs sampling and data augmentation in a multivariate model of Gaussian, right censored, and grouped Gaussian traits is described. The grouped Gaussian traits are either ordered categorical traits (with more than two categories) or binary traits, where the grouping is determined via thresholds on the underlying Gaussian scale, the liability scale. Allowances are made for unequal models, unknown covariance matrices and missing data. Having outlined the theory, strategies for implementation are reviewed. These include joint sampling of location parameters; efficient sampling from the fully conditional posterior distribution of augmented data, a multivariate truncated normal distribution; and sampling from the conditional inverse Wishart distribution, the fully conditional posterior distribution of the residual covariance matrix. Finally, a simulated dataset was analysed to illustrate the methodology. This paper concentrates on a model where residuals associated with liabilities of the binary traits are assumed to be independent. A Bayesian analysis using Gibbs sampling is outlined for the model where this assumption is relaxed.     

An optimization-based sampling scheme for phylogenetic trees

Much modern work in phylogenetics depends on statistical sampling approaches to phylogeny construction to estimate probability distributions of possible trees for any given input data set. Our theoretical understanding of sampling approaches to phylogenetics remains far less developed than that for optimization approaches, however, particularly with regard to the number of sampling steps needed to produce accurate samples of tree partition functions. Despite the many advantages in principle of being able to sample trees from sophisticated probabilistic models, we have little theoretical basis for concluding that the prevailing sampling approaches do in fact yield accurate samples from those models within realistic numbers of steps. We propose a novel approach to phylogenetic sampling intended to be both efficient in practice and more amenable to theoretical analysis than the prevailing methods. The method depends on replacing the standard tree rearrangement moves with an alternative Markov model in which one solves a theoretically hard but practically tractable optimization problem on each step of sampling. The resulting method can be applied to a broad range of standard probability models, yielding practical algorithms for efficient sampling and rigorous proofs of accurate sampling for heated versions of some important special cases. We demonstrate the efficiency and versatility of the method by an analysis of uncertainty in tree inference over varying input sizes. In addition to providing a new practical method for phylogenetic sampling, the technique is likely to prove applicable to many similar problems involving sampling over combinatorial objects weighted by a likelihood model.