Sequential and Binomial Sampling Plans to Estimate Thrips tabaci Population Density on Onion

Thrips tabaci Lindeman is a worldwide onion pest that causes economic losses of 10–60%, depending on many factors. Population sampling is essential for applying control tactics and preventing damage by the insect. Conventional sampling methods are criticized as time consuming, while fixed-precision binomial and sequential sampling plans may allow reliable estimations with a more efficient use of time. The aim of this work was to develop binomial and sequential sampling for fast reliable estimation of T. tabaci density on an onion. Forty-one commercial 1.0-ha onion plots were sampled (sample size n = 200) to characterize the spatial distribution of T. tabaci using Taylor’s power law (a = 2.586 and b = 1.511). Binomial and sequential enumerative sampling plans were then developed with precision levels of 0.10, 0.15 and 0.25. Sampling plans were validated with bootstrap simulations (1000 samples) using 10 independent data sets. Bootstrap simulation indicated that precision was satisfactory for all repetitions of the sequential sampling plan, while binomial sampling met the fixed precision in 80% of cases. Both methods reduced sampling time by around 80% relative to conventional sampling. These precise and less time-consuming sampling methods can contribute to implementation of control tactics within the integrated pest management approach.

Comparison of Accuracy Properties for Confidence Intervals of the Cross-Product Ratio of Binomial Proportions under Direct-Direct Sampling Scheme

We consider a general problem of the confidence interval for a cross-product ratio ρ=p1(1-p2)/p2(1-p1) according to data from two independent samples. Each sample may be obtained in the framework of direct Binomial sampling scheme. Asymptotic confidence intervals are constructed in accordance with direct Binomial sampling scheme, with parameter estimators demonstrating exponentially decreasing bias. Our goal is to investigate the cases when the normal approximations (which are relatively simple) for estimators of the cross-product ratio are reliable for the construction of confidence intervals. We use the closeness of the confidence coefficient to the nominal confidence level as our main evaluation criterion, and use the Monte-Carlo method to investigate the key probability characteristics of intervals corresponding to direct Binomial sampling schemes. We present estimations of the coverage probability, expectation and standard deviation of interval widths in tables and provide some recommendations for applying each obtained interval.

Unbiased and efficient log-likelihood estimation with inverse binomial sampling

The fate of scientific hypotheses often relies on the ability of a computational model to explain the data, quantified in modern statistical approaches by the likelihood function. The log-likelihood is the key element for parameter estimation and model evaluation. However, the log-likelihood of complex models in fields such as computational biology and neuroscience is often intractable to compute analytically or numerically. In those cases, researchers can often only estimate the log-likelihood by comparing observed data with synthetic observations generated by model simulations. Standard techniques to approximate the likelihood via simulation either use summary statistics of the data or are at risk of producing substantial biases in the estimate. Here, we explore another method, inverse binomial sampling (IBS), which can estimate the log-likelihood of an entire data set efficiently and without bias. For each observation, IBS draws samples from the simulator model until one matches the observation. The log-likelihood estimate is then a function of the number of samples drawn. The variance of this estimator is uniformly bounded, achieves the minimum variance for an unbiased estimator, and we can compute calibrated estimates of the variance. We provide theoretical arguments in favor of IBS and an empirical assessment of the method for maximum-likelihood estimation with simulation-based models. As case studies, we take three model-fitting problems of increasing complexity from computational and cognitive neuroscience. In all problems, IBS generally produces lower error in the estimated parameters and maximum log-likelihood values than alternative sampling methods with the same average number of samples. Our results demonstrate the potential of IBS as a practical, robust, and easy to implement method for log-likelihood evaluation when exact techniques are not available.

Transmission Bottleneck Size Estimation from Pathogen Deep-Sequencing Data, with an Application to Human Influenza A Virus

The bottleneck governing infectious disease transmission describes the size of the pathogen population transferred from a donor to a recipient host. Accurate quantification of the bottleneck size is of particular importance for rapidly evolving pathogens such as influenza virus, as narrow bottlenecks would limit the extent of transferred viral genetic diversity and, thus, have the potential to slow the rate of viral adaptation. Previous studies have estimated the transmission bottleneck size governing viral transmission through statistical analyses of variants identified in pathogen sequencing data. The methods used by these studies, however, did not account for variant calling thresholds and stochastic dynamics of the viral population within recipient hosts. Because these factors can skew bottleneck size estimates, we here introduce a new method for inferring transmission bottleneck sizes that explicitly takes these factors into account. We compare our method, based on beta-binomial sampling, with existing methods in the literature for their ability to recover the transmission bottleneck size of a simulated dataset. This comparison demonstrates that the beta-binomial sampling method is best able to accurately infer the simulated bottleneck size. We then apply our method to a recently published dataset of influenza A H1N1p and H3N2 infections, for which viral deep sequencing data from inferred donor-recipient transmission pairs are available. Our results indicate that transmission bottleneck sizes across transmission pairs are variable, yet that there is no significant difference in the overall bottleneck sizes inferred for H1N1p and H3N2. The mean bottleneck size for influenza virus in this study, considering all transmission pairs, was Nb = 196 (95% confidence interval 66-392) virions. While this estimate is consistent with previous bottleneck size estimates for this dataset, it is considerably higher than the bottleneck sizes estimated for influenza from other datasets.Author SummaryThe transmission bottleneck size describes the size of the pathogen population transferred from the donor to recipient host at the onset of infection and is a key factor in determining the rate at which a pathogen can adapt within a host population. Recent advances in sequencing technology have enabled the bottleneck size to be estimated from pathogen sequence data, though there is not yet a consensus on the statistical method to use. In this study, we introduce a new approach for inferring the transmission bottleneck size from sequencing data that accounts for the criteria used to identify sequence variants and stochasticity in pathogen replication dynamics. We show that the failure to account for these factors may lead to underestimation of the transmission bottleneck size. We apply this method to a previous dataset of human influenza A infections, showing that transmission is governed by a loose transmission bottleneck and that the bottleneck size is highly variable across transmission events. This work advances our understanding of the bottleneck size governing influenza infection and introduces a method for estimating the bottleneck size that can be applied to other rapidly evolving RNA viruses, such as norovirus and RSV.