Stochastic hydrology: An introduction to wet statistics for dry statisticians

The paper is intended to give non-initiates some idea of the nature of stochastic hydrology. After a brief historical review it concentrates on three recent examples of stochastic modelling procedures that have aroused interest among hydrologists, namely the Hurst Effect, Short-Term Runoff Models, and Stochastic Reservoir Theory.     

Optimality and Contrasts in Block Designs with Unequal Treatment Replication

The computer construction of optimal or near‐optimal experimental designs is common in practice. Search procedures are often based on the non‐zero eigenvalues of the information matrix of the design. Minimising the average of the pairwise treatment variances can also be used as a search criterion. For equal treatment replication these approaches are equivalent to maximising the harmonic mean of the design's canonical efficiency factors, but differ when treatments are unequally replicated. This paper investigates the extent of these differences and discusses some apparent inconsistencies previously observed when comparing the optimality of equally and unequally replicated designs.     

Estimating the variance for heterogeneity in arm‐based network meta‐analysis

Network meta‐analysis can be implemented by using arm‐based or contrast‐based models. Here we focus on arm‐based models and fit them using generalized linear mixed model procedures. Full maximum likelihood (ML) estimation leads to biased trial‐by‐treatment interaction variance estimates for heterogeneity. Thus, our objective is to investigate alternative approaches to variance estimation that reduce bias compared with full ML. Specifically, we use penalized quasi‐likelihood/pseudo‐likelihood and hierarchical (h) likelihood approaches. In addition, we consider a novel model modification that yields estimators akin to the residual maximum likelihood estimator for linear mixed models. The proposed methods are compared by simulation, and 2 real datasets are used for illustration. Simulations show that penalized quasi‐likelihood/pseudo‐likelihood and h‐likelihood reduce bias and yield satisfactory coverage rates. Sum‐to‐zero restriction and baseline contrasts for random trial‐by‐treatment interaction effects, as well as a residual ML‐like adjustment, also reduce bias compared with an unconstrained model when ML is used, but coverage rates are not quite as good. Penalized quasi‐likelihood/pseudo‐likelihood and h‐likelihood are therefore recommended.