This paper presents a new method to develop stochastic deterioration models using a combination of methods including Markov chains, logistic regression, and classification trees. It is computationally more efficient to use logistic regression with the Markov chain process than it is to use optimization-based approaches, and the former is shown to marginally improve the prediction of condition ratings for small data sets. Annually inspected bridge data are split into groups using a classification tree, and logistic regression is used to determine transition probabilities for a Markov chain process. A case study was conducted to determine the effectiveness of using the proposed logistic regression and Markov chain approach for the small data sets created by the classification tree. Wyoming bridge inspection data were split into 15 subsets based on 5 explanatory variables, and deterioration models were developed for each subset. Error analysis showed that logistic regression performed marginally better than traditional methods when estimating the transition probability matrix when limited data are accessible.

This paper presents a procedure to select explanatory variables, without the influence of human bias, for deterioration model development using publicly available data for bridges in Wyoming. Using this information, including geometric data and climate information, candidate explanatory variables can be converted into normalized numeric values and analyzed prior to the development of deterministic or stochastic deterioration models. The prevailing approach for explanatory variable selection for bridge condition modeling is to use expert opinions solicited from experienced engineers. This may introduce personal human influenced biases into the deterioration modeling process. A framework using least absolute shrinkage and selection operator (LASSO) penalized regression and covariance analysis are combined to compensate for this potential bias. The resultant of LASSO, combined with the cross validation, is used to develop a LASSO solution path that visualizes the relative significance of investigated explanatory variables. In order to analyze yearly inspected data in the framework, the cross-validation analysis is used as a standard for the selection of minimum number of explanatory variables using the solution path. The proposed method is demonstrated through the creation of deterministic deterioration models for deck, superstructure, and substructure for Wyoming bridges and compared to explanatory variables using the expert selection method. The comparison shows a significant decrease in error using the presented framework based on the least squares of relative error.

The future of the Colorado River water supply (WS) affects millions of people and the US economy. A recent study suggested a cross-basin correlation between the Colorado River and its neighboring Great Salt Lake (GSL). Following that study, the feasibility of using the previously developed multi-year prediction of the GSL water level to forecast the Colorado River WS was tested. Time-series models were developed to predict the changes in WS out to 10 years. Regressive methods and the GSL water level data were used for the depiction of decadal variability of the Colorado River WS. Various time-series models suggest a decline in the 10-year averaged WS since 2013 before starting to increase around 2020. Comparison between this WS prediction and the WS projection published in a 2012 government report (derived from climate models) reveals a widened imbalance between supply and demand by 2020, a tendency that is confirmed by updated WS observation. Such information could aid in management decision-making in the face of near-future water shortages.

We propose a sparse coefficient estimation and automated model selection procedure for autoregressive processes with heavy-tailed innovations based on penalized conditional maximum likelihood. Under mild moment conditions on the innovation processes, the penalized conditional maximum likelihood estimator satisfies a strong consistency, O_P(N^−1/2) consistency, and the oracle properties, where N is the sample size. We have the freedom in choosing penalty functions based on the weak conditions on them. Two penalty functions, least absolute shrinkage and selection operator and smoothly clipped average deviation, are compared. The proposed method provides a distribution-based penalized inference to AR models, which is especially useful when the other estimation methods fail or under perform for AR processes with heavy-tailed innovations [Feigin, Resnick. Pitfalls of fitting autoregressive models for heavy-tailed time series. Extremes. 1999;1:391–422]. A simulation study confirms our theoretical results. At the end, we apply our method to a historical price data of the US Industrial Production Index for consumer goods, and obtain very promising results.