Lognormal Kriging and Bias-Corrected Back-Transformation

Kriging assumes spatial stationarity and does not require a specific distribution for estimated variables. However, non-symmetric distributions, often found in earth sciences, can complicate variogram calculations and lead to over-prediction, especially when high values are present. To address these challenges, data are often transformed using the natural logarithm. A challenge occurs during back-transformation of predictions and variances from the log scale to the original scale, as simple exponentiation is insufficient due to the weighted sums in log-transformed data. This post will explore the mathematical formulations essential for effective back-transformation in lognormal kriging.

Predictive Modelling of Traffic Accidents in the U.S.

Motor vehicle accidents are an important part of traffic safety research. Analyzing the factors contributing to accidents and accident severity is critical for enhancing road safety standards. In this post, traffic accident data patterns will be explored and studied using machine-learning analysis techniques.

Generalized Least Squares Regression

In OLS regression, assumptions such as independent and identically distributed errors are important for accurate estimation and inference. Heteroskedasticity, or unequal variances of residuals, can lead to biased estimates and incorrect standard errors. Alternatives to OLS, such as GLS and WLS regression, can be considered when OLS assumptions are violated. GLS is used for dependent errors, while WLS is used for independent but non-identically distributed errors.

Weighted Least Squares Regression

Heteroscedasticity in regression analysis refers to varying levels of scatter in the residuals. Its presence affects OLS estimators and standard errors, leading to biased estimates and misleading results. When errors are independent, but not identically distributed, weighted least squares regression can be used to address heteroscedasticity by placing more weight on observations with smaller error variance. This results in smaller standard errors and more precise estimators.

Trend Detection Using Survival Analysis

Non-detects in environmental data can complicate analysis if not handled properly, leading to incorrect conclusions. The mathematical structure of survival analysis is general enough that it can be used in diverse fields examining various types of data not typically associated with survival/death events or failure analysis. In this post, survival analysis methods will be applied to fit a censored linear regression model to weekly ammonium deposition data to assess temporal trends.

Arctic Sea Ice Time Series Analysis

The modeltime R library offers a wide range of features for model evaluation, selection, and forecasting using the tidymodels ecosystem. Time-series analysis of sea ice in the Arctic polar regions performed using the modeltime library suggests that the Arctic sea will be nearly ice-free in the very near future.

Temporal Behavior of Arctic Sea Ice

Passive-microwave instrumentation on satellites has allowed for the monitoring of Arctic sea ice coverage since the late 1970s, showing a long-term downward trend due to both natural variability and climate change. The rate of decline in Arctic sea ice has varied over the past 43 years, with some periods showing faster rates of loss than others. This blog post explores the temporal changes in Arctic sea ice extent using the R language for statistical computing and visualization.

Comparison of Random and Geographically Stratified Sampling

The post compares differences between simple random sampling and geographically stratified sampling. Stratified random sampling improves the spatial distribution of sample point locations by stratifying the field geographically and sampling randomly within each stratum. Different sampling patterns are compared using Monte Carlo simulations on a simulated population.

Analyses of Pesticide Concentrations in California Surface Waters

Environmental data are frequently left-censored, indicating that some values are less than the limit of quantification for the analytical methods employed. These data are problematic because censored (non-detect) values are known only to range between zero and the censoring limit. This complicates analysis of the data, including estimating statistical parameters, characterizing data distributions, and conducting inferential statistics. This post demonstrates various procedures and methods that are available in R for analyzing data containing a mixture of detects and non-detects. These methods make few or no assumptions about the data, or substitute arbitrary values (e.g., one-half the detection or reporting limit) for the non-detects.

Clustering on Principal Component Analysis

Combining principal component analysis (PCA) and clustering methods are useful for reducing the dimension of a data set into a few continuous variables containing the most important information in the data. This post illustrates how to combine PCA and clustering methods to identify patterns in a data set using the R language for statistical computing and visualization.