*4.13. Combining Environmental Information*

Another increasingly important issue in the environmental sciences is the need to combine information from diverse sources that relate to a common endpoint. Combining information is a very active area of statistical and applied subject-matter research.

A common technique for combining independent results is Meta analysis (see [150]), which brings together the results of different studies, reanalyzes the disparate results within the concept of their common endpoints, and provides a quantitative analysis of the phenomenon of interest based on the combined data. In the case of environmental science, the effect of interest may be very small and therefore hard to detect. The limited sample sizes or data on many multiple endpoints lead to highly localized effects.


#### *4.14. Space–Time Modeling with Applications to Atmospheric Pollution and Acid Rain*

The space time autoregressive moving average (STARMA) approach was utilized by [152] (see [153]). For most latitudes, Niu and Tiao chose the STAR(2,1) model. The authors of [154] studied the logarithms of sulfate content in rainfall at 19 sites in the eastern and mid-western United States for 24 monthly measurements from 1982 to 1983, and came up with a substantially different atmospheric contaminant model. They calculated their estimator's variance. An empirical Bayesian approach was used to generate the sample spatial covariance matrix from the residuals of the fit.

#### *4.15. Detection Limits*

The authors of [155] illustrated a robust parametric method for quantifying nondetects, using a simple probability plot regression. A straight line is fitted through the observations displayed on normal (or lognormal) probability paper. The line offers estimations for the non-detected values when extrapolated back into the non-detect zone.

#### **5. Conclusions**

The statistical concepts act as a valuable tool for monitoring environmental systems. Agricultural activities, such as timing of cropping and harvesting, timing of chemical applications, type of crops planted, irrigation scheduling, etc., require knowledge of environmental statistics. The forestry activities of a country, such as extraction of timber, forestation, reforestation projects, etc., need statistical information. In addition, in measuring environmental diversity, statistics also plays a vital role. Thus, the application of statistics is important in environmental sciences for effective and innovative monitoring of environmental variables over time. To avoid mistakes at the end of the statistical analysis, it is very important to detect the actual distribution of the observed data (see [156,157]). For environment-related problems, the lack of sufficient data is a major problem. Given a small set of data, it is very difficult to correctly detect heavy-tailed distributions. Hence, the proportion of the middle and tails of the same set of data is taken for analysis. As a result, calculating the relative frequency of the outside values and the theoretical *p*-outside values is critical. In the particular case when *p* = 0.25, *p*-outside values coincide with extreme outliers and, at least, these outside values should be estimated from the sample

(see [158,159]). They are useful in detecting the parameters that are used to find the tail of the distribution. They also help in finding probabilities of events. As *p*-outside values do not depend on moments, they can be easily applied to situations where moments are not essential or where they do not exist.

Many of the environmental difficulties discussed here are just a small sample of the wide range of challenging issues in quantitative environmental research, as well as the wide range of approaches to solving them. Based on [4,5], this review paper demonstrates that there are numerous viewpoints on the nature of Environmental Sciences and Statistics.

**Funding:** This research received no external funding.

**Acknowledgments:** We thank the two reviewers for the important remarks on the paper, completing the review in a thorough way.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

