Count variables are often positively skewed and may include many zero observations, requiring specific statistical approaches. Interpreting abiotic factor changes in insect populations of crop pests, under this condition, can be difficult. The analysis becomes even more complicated because of possible temporal or spatial correlation, irregularly spaced data, heterogeneity over time, and zero inflation. Generalized additive models (GAM) are important tools to evaluate abiotic factors. Moreover, Markov chain Monte Carlo (MCMC) techniques can be used to fit a model that contains a temporal correlation structure, based on Bayesian statistics (BGAM). We compared methods of modeling the effects of temperature, precipitation, and time for the Brevicoryne brassicae (L.) population in Uberlândia, Brasil. We applied the proposed BGAM to the data, comparing this to the GAM model with and without autocorrelation for time, using the statistical programming language R. Analysis of deviance identified significant effects of the smoothers for precipitation and time on the frequentist models. With BGAM, the problem in variance estimations for precipitation and temperature from the previous models was solved. Furthermore, trace and density plots for population-level effects for all parameters converged well. The estimated smoothing curves showed a linear effect with an increase of precipitation, where lower precipitation indicated no presence of the aphid. The average temperature did not affect the aphid incidence. Autocorrelation was solved with ARMA structures, and the excess of zero was solved with zero-inflation models. The example of B. brassicae incidence showed how well abiotic (and biotic) factors can be modeled and analyzed using BGAM.

中文翻译：

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在蚜虫种群研究中，通过广义可加模型和贝叶斯统计模型对超分散，自相关和零膨胀计数数据进行建模。

计数变量通常是正偏斜的，并且可能包含许多零观测值，因此需要特定的统计方法。在这种情况下，很难解释农作物虫害昆虫种群中非生物因子的变化。由于可能的时间或空间相关性，不规则间隔的数据，随时间变化的异质性以及零膨胀，分析变得更加复杂。广义加性模型（GAM）是评估非生物因素的重要工具。此外，基于贝叶斯统计（BGAM），可将马尔可夫链蒙特卡洛（MCMC）技术用于拟合包含时间相关结构的模型。我们比较了建模Brevicoryne芸苔的温度，降水和时间影响的方法巴西乌贝兰迪亚（L.）人口。我们使用统计编程语言R将建议的BGAM应用于数据，并将其与具有时间自相关和不具有时间自相关的GAM模型进行比较。偏差分析确定了平滑剂对降水量和时间的显着影响。使用BGAM，解决了先前模型中降水和温度方差估计的问题。此外，针对所有参数的总体水平影响的迹线图和密度图收敛良好。估计的平滑曲线显示出随降水增加的线性效应，其中较低的降水表明没有蚜虫。平均温度不影响蚜虫的发病率。用ARMA结构解决自相关，用零膨胀模型解决零余。芸苔芽孢杆菌发生率的例子表明，使用BGAM可以很好地建模和分析非生物（和生物）因子。