An application of the flexible multibody approach used to estimate human skeleton loading

Skeletal loading can be estimated using several approaches. The most common approach is based on utilizing mechanical principles and ground reaction forces as predictors for skeletal loading. This method can be considered as a relatively simple approach since it cannot account for muscle forces. Flexible multibody approach allows for estimating skeletal loading and strains within the bones; once bone flexibility, muscle forces, ground reaction forces and the natural motion of a subject have been accounted for. This paper presents a summary that describes how deformable bodies can be introduced to the standard multibody formulation and explains the benefits and drawbacks. As an example of application, models used to assess tibial strains among two subjects are presented. The results of the multibody simulations are compared to in vivo studies, showing acceptable correlation and method performance.

State dependent asymmetric loss and the consensus forecast of real U.S. GDP growth

It has been well documented that the consensus forecast from surveys of professional forecasters shows a bias that varies over time. In this paper, we examine whether this bias may be due to forecasters having an asymmetric loss function. In contrast to previous research, we account for the time variation in the bias by making the loss function depend on the state of the economy. The asymmetry parameter in the loss function is specified to depend on set state variables which may cause forecaster to intentionally bias their forecasts. We consider both the Lin–Ex and asymmetric power loss functions. For the commonly used Lin–Ex and Lin–Lin loss functions, we show the model can be easily estimated by least squares. We apply our methodology to the consensus forecast of real U.S. GDP growth from the Survey of Professional Forecasters. We find that forecast uncertainty has an asymmetric effect on the asymmetry parameter in the loss function dependent upon whether the economy is in expansion or contraction. When the economy is in expansion, forecaster uncertainty is related to an overprediction in the median forecast of real GDP growth. In contrast, when the economy is in contraction, forecaster uncertainty is related to an underprediction in the median forecast of real GDP growth. Our results are robust to the particular loss function that is employed in the analysis.