An errors-in-variables model based on the Birnbaum–Saunders distribution and its diagnostics with an application to earthquake data

Stochastic Environmental Research and Risk Assessment - Regression modelling where explanatory variables are measured with error is a common problem in applied sciences. However, if inappropriate...     

Estimates of uncertainty in the prediction of past climatic variables

Fitting a regression line to a set of measurements to investigate the relationship between a proxy estimate of past climate and known climatic parameters is a routine procedure. It is generally accepted that the higher the correlation between parameters, the more reliable the reconstruction. However, there is a lack of published work upon what correlation is the minimum acceptable value. Simulated data was used to demonstrate that the relationship between proxy values and the climatic data are adversely affected by falling correlation, to the point where, in a training set consisting of 100 pairs of temperature and tree-ring proxies, the mean 95% confidence interval width for the reconstructed temperature exceeds the total range of temperatures in the training set at or below r = 0.65. This correlation is typical of that used in many climate-proxy reconstructions, and it suggests that understanding of past climate variability may be somewhat constrained.