Investigations of a compartmental model for leucine kinetics using nonlinear mixed effects models with ordinary and stochastic differential equations

Nonlinear mixed effects models represent a powerful tool to simultaneously analyze data from several individuals. In this study a compartmental model of leucine kinetics is examined and extended with a stochastic differential equation to model non-steady state concentrations of free leucine in the plasma. Data obtained from tracer/tracee experiments for a group of healthy control individuals and a group of individuals suffering from diabetes mellitus type 2 are analyzed. We find that the interindividual variation of the model parameters is much smaller for the nonlinear mixed effects models, compared to traditional estimates obtained from each individual separately. Using the mixed effects approach, the population parameters are estimated well also when only half of the data are used for each individual. For a typical individual the amount of free leucine is predicted to vary with a standard deviation of 8.9% around a mean value during the experiment. Moreover, leucine degradation and protein uptake of leucine is smaller, proteolysis larger, and the amount of free leucine in the body is much larger for the diabetic individuals than the control individuals. In conclusion nonlinear mixed effects models offers improved estimates for model parameters in complex models based on tracer/tracee data and may be a suitable tool to reduce data sampling in clinical studies

Combining long memory and level shifts in modeling and forecasting the volatility of asset returns

We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean- and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in high-frequency measures of volatility whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes, and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons

Intervention analysis with state-space models to estimate discontinuities due to a survey redesign

An important quality aspect of official statistics produced by national statistical institutes is comparability over time. To maintain uninterrupted time series, surveys conducted by national statistical institutes are often kept unchanged as long as possible. To improve the quality or efficiency of a survey process, however, it remains inevitable to adjust methods or redesign this process from time to time. Adjustments in the survey process generally affect survey characteristics such as response bias and therefore have a systematic effect on the parameter estimates of a sample survey. Therefore, it is important that the effects of a survey redesign on the estimated series are explained and quantified. In this paper a structural time series model is applied to estimate discontinuities in series of the Dutch survey on social participation and environmental consciousness due to a redesign of the underlying survey process.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS305 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Time Series Analysis

We provide a concise overview of time series analysis in the time and frequency domains, with lots of references for further reading.time series analysis, time domain, frequency domain, Research Methods/ Statistical Methods,

Adaptive and robust fractional gain based interpolatory cubature Kalman filter

In this study, we put forward the robust fractional gain based interpolatory cubature Kalman filter (FGBICKF) and the adaptive FGBICKF (AFGBICKF) for the development of the state estimators for stochastic nonlinear dynamics system. FGBICKF introduces a fractional gain to interpolatory cubature Kalman filter to increase the robustness of state estimation. AFGBICKF is developed to enhance the state estimation adaptive to stochastic nonlinear dynamics system with unknown process noise covariance through recursive estimation. The simulations on re-entry target tracking system have shown that the performance of FGBICKF is superior to that of cubature Kalman filter and interpolatory cubature Kalman filter, and standard deviation of FGBICKF is closer to posterior Cramér-Rao lower bound. Moreover, our simulations have also demonstrated that AFGBICKF remains stable even when the initial process noise covariance increase, proving its adaptiveness, robustness, and effectiveness on state estimation