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Permutation tests are increasingly being used as a reliable method for inference in neuroimaging analysis. However, they are computationally intensive. For small, non-imaging datasets, recomputing a model thousands of times is seldom a problem, but for large, complex models this can be prohibitively slow, even with the availability of inexpensive computing power. Here we exploit properties of statistics used with the general linear model (GLM) and their distributions to obtain accelerations irrespective of generic software or hardware improvements. We compare the following approaches: (i) performing a small number of permutations; (ii) estimating the p-value as a parameter of a negative binomial distribution; (iii) fitting a generalised Pareto distribution to the tail of the permutation distribution; (iv) computing p-values based on the expected moments of the permutation distribution, approximated from a gamma distribution; (v) direct fitting of a gamma distribution to the empirical permutation distribution; and (vi) permuting a reduced number of voxels, with completion of the remainder using low rank matrix theory. Using synthetic data we assessed the different methods in terms of their error rates, power, agreement with a reference result, and the risk of taking a different decision regarding the rejection of the null hypotheses (known as the resampling risk). We also conducted a re-analysis of a voxel-based morphometry study as a real-data example. All methods yielded exact error rates. Likewise, power was similar across methods. Resampling risk was higher for methods (i), (iii) and (v). For comparable resampling risks, the method in which no permutations are done (iv) was the absolute fastest. All methods produced visually similar maps for the real data, with stronger effects being detected in the family-wise error rate corrected maps by (iii) and (v), and generally similar to the results seen in the reference set. Overall, for uncorrected p-values, method (iv) was found the best as long as symmetric errors can be assumed. In all other settings, including for familywise error corrected p-values, we recommend the tail approximation (iii). The methods considered are freely available in the tool PALM — Permutation Analysis of Linear Models. •Permutation methods can be accelerated through additional statistical approaches.•Six approaches are described and assessed.•Methods can be 100 times faster than in the non-accelerated case.•Recommendations are provided for various common scenarios.

The ever-increasing complexity of numerical models and associated computational demands have challenged classical reliability analysis methods. Surrogate model-based reliability analysis techniques, and in particular those using kriging meta-model, have gained considerable attention recently for their ability to achieve high accuracy and computational efficiency. However, existing stopping criteria, which are used to terminate the training of surrogate models, do not directly relate to the error in estimated failure probabilities. This limitation can lead to high computational demands because of unnecessary calls to costly performance functions (e.g., involving finite element models) or potentially inaccurate estimates of failure probability due to premature termination of the training process. Here, we propose the error-based stopping criterion ( ESC ) to address these limitations. First, it is shown that the total number of wrong sign estimation of the performance function for candidate design samples by kriging, S , follows a Poisson binomial distribution. This finding is subsequently used to estimate the lower and upper bounds of S for a given confidence level for sets of candidate design samples classified by kriging as safe and unsafe. An upper bound of error of the estimated failure probability is subsequently derived according to the probabilistic properties of Poisson binomial distribution. The proposed upper bound is implemented in the kriging-based reliability analysis method as the stopping criterion. The efficiency and robustness of ESC are investigated here using five benchmark reliability analysis problems. Results indicate that the proposed method achieves the set accuracy target and substantially reduces the computational demand, in some cases by over 50%.

A Poisson process is a commonly used starting point for modeling stochastic variation of ecological count data around a theoretical expectation. However, data typically show more variation than implied by the Poisson distribution. Such overdispersion is often accounted for by using models with different assumptions about how the variance changes with the expectation. The choice of these assumptions can naturally have apparent consequences for statistical inference. We propose a parameterization of the negative binomial distribution, where two overdispersion parameters are introduced to allow for various quadratic mean-–variance relationships, including the ones assumed in the most commonly used approaches. Using bird migration as an example, we present hypothetical scenarios on how overdispersion can arise due to sampling, flocking behavior or aggregation, environmental variability, or combinations of these factors. For all considered scenarios, mean-–variance relationships can be appropriately described by the negative binomial distribution with two overdispersion parameters. To illustrate, we apply the model to empirical migration data with a high level of overdispersion, gaining clearly different model fits with different assumptions about mean-–variance relationships. The proposed framework can be a useful approximation for modeling marginal distributions of independent count data in likelihood-based analyses.

A general class of statistical models for a univariate response variable is presented which we call the generalized additive model for location, scale and shape (GAMLSS). The model assumes independent observations of the response variable y given the parameters, the explanatory variables and the values of the random effects. The distribution for the response variable in the GAMLSS can be selected from a very general family of distributions including highly skew or kurtotic continuous and discrete distributions. The systematic part of the model is expanded to allow modelling not only of the mean (or location) but also of the other parameters of the distribution of y, as parametric and/or additive nonparametric (smooth) functions of explanatory variables and/or random-effects terms. Maximum (penalized) likelihood estimation is used to fit the (non)parametric models. A Newton-Raphson or Fisher scoring algorithm is used to maximize the (penalized) likelihood. The additive terms in the model are fitted by using a backfitting algorithm. Censored data are easily incorporated into the framework. Five data sets from different fields of application are analysed to emphasize the generality of the GAMLSS class of models.

The time taken to detect a species during site occupancy surveys contains information about the observation process. Accounting for the observation process leads to better inference about site occupancy. We explore the gain in efficiency that can be obtained from time-to-detection (TTD) data and show that this model type has a significant benefit for estimating the parameters related to detection intensity. However, for estimating occupancy probability parameters, the efficiency improvement is generally very minor. To explore whether TTD data could add valuable information when detection intensities vary between sites and surveys, we developed a mixed exponential TTD occupancy model. This new model can simultaneously estimate the detection intensity and aggregation parameters when the number of detectable individuals at the site follows a negative binomial distribution. We found that this model provided a much better description of the occupancy patterns than conventional detection/nondetection methods among 63 bird species data from the Karoo region of South Africa. Ignoring the heterogeneity of detection intensity in the TTD model generally yielded a negative bias in the estimated occupancy probability. Using simulations, we briefly explore study design trade offs between numbers of sites and surveys for different occupancy modeling strategies.

A class of power series q-distributions, generated by considering a q-Taylor expansion of a parametric function into powers of the parameter, is discussed. Its q-factorial moments are obtained in terms of q-derivatives of its series (parametric) function. Also, it is shown that the convolution of power series q-distributions is also a power series q-distribution. Furthermore, the q-Poisson (Heine and Euler), q-binomial of the first kind, negative q-binomial of the second kind, and q-logarithmic distributions are shown to be members of this class of distributions and their q-factorial moments are deduced. In addition, the convolution properties of these distributions are examined.

Rift Valley Fever (RVF) is a mosquito-borne zoonotic disease often linked to climatic factors. However, identifying the onset and duration of outbreaks can be hindered by high numbers of zero counts in sparse surveillance data. We analyzed monthly RVF data from Kenya (2015–2022), compared the performance of widely used outbreak-detection methods, and developed Negative Binomial models augmented with a hidden Markov process and zero-inflation to address data sparsity. Our proposed framework estimates monthly probabilities of transitioning between endemic and epidemic phases, improving outbreak detection under various sparsity levels. Simulations and real-world applications show that this model outperforms established algorithms by reducing both false positives and negatives. When applied to Kenyan RVF data, the model suggests a weak negative association with rainfall and a weak positive association with temperature, potentially reflecting underreporting’s influence on estimated climatic effects. Overall, these findings underscore the potential of the proposed method to improve outbreak detection and public health decision-making in sparsely reported settings.

Negative binomial related distributions have been widely used in practice. The calculation of the corresponding Fisher information matrices involves the expectation of trigamma function values which can only be calculated numerically and approximately. In this paper, we propose a trigamma-free approach to approximate the expectations involving the trigamma function, along with theoretical upper bounds for approximation errors. We show by numerical studies that our approach is highly efficient and much more accurate than previous methods. We also apply our approach to compute the Fisher information matrices of zero-inflated negative binomial (ZINB) and beta negative binomial (ZIBNB) probabilistic models, as well as ZIBNB regression models.

Transport of dense core vesicles (DCVs) in neurons is crucial for distributing molecules like neuropeptides and growth factors. We studied the experimental trajectories of dynein-driven directed movement of DCVs in the ALA neuron in  C. elegans over a duration of up to 6 seconds. We analysed the DCV movement in three strains of C. elegans : (1) with normal kinesin-1 function, (2) with reduced function in kinesin light chain 2 (KLC-2), and (3) a null mutation in kinesin light chain 1 (KLC-1). We find that DCVs move superdiffusively with displacement variance in all three strains with low reversal rates and frequent immobilization of DCVs. The distribution of DCV displacements fits a beta-binomial distribution with the mean and the variance following linear and quadratic growth patterns, respectively. We propose a simple heterogeneous random walk model to explain the observed superdiffusive retrograde transport behaviour of DCV movement. This model involves a random probability with the beta density for a DCV to resume its movement or remain in the same position. To validate our model further, we measure the first passage time for a DCV to reach a certain threshold for the first time. According to the model, the first passage time distribution should follow a beta-negative binomial distribution with the same parameters as the DCV displacement distributions. Our experimental data confirm this prediction.

Abstract The intertidal rocky shores in continental Chile have high species diversity mainly in northern Chile (18-27° S), and one of the most widespread species is the gastropod Echinolittorina peruviana (Lamarck, 1822). The aim of the present study is do a first characterization of spatial distribution of E. peruviana in along rocky shore in Antofagasta town in northern Chile. Individuals were counted in nine different sites that also were determined their spectral properties using remote sensing techniques (LANDSAT ETM+). The results revealed that sites without marked human intervention have more abundant in comparison to sites located in the town, also in all studied sites was found an aggregated pattern, and in six of these sites were found a negative binomial distribution. The low density related to sites with human intervention is supported when spectral properties for sites were included. These results would agree with other similar results for rocky shore in northern and southern Chile. Resumo As costas rochosas entremarés no Chile continental apresentam alta diversidade de espécies, principalmente no norte do país (18-27 ° S), e uma das espécies mais difundidas é o gastrópode Echinolittorina peruviana (Lamarck, 1822). O objetivo do presente estudo é fazer uma primeira caracterização da distribuição espacial de E. peruviana no costão rochoso da cidade de Antofagasta no norte do Chile. Os indivíduos foram contados em nove locais diferentes onde também foram determinadas suas propriedades espectrais usando técnicas de sensoriamento remoto (LANDSAT ETM +). Os resultados revelaram que os locais sem intervenção humana marcada apresentam maior abundância em comparação aos locais localizados no município. Também em todos os locais estudados foi encontrado um padrão agregado, sendo que em seis desses locais foi encontrada uma distribuição binomial negativa. A baixa densidade relacionada a sites com intervenção humana é suportada quando as propriedades espectrais para sites foram incluídas. Esses resultados concordariam com outros resultados semelhantes para costões rochosos no norte e no sul do Chile.