Global parameter identification of stochastic reaction networks from single trajectories

We consider the problem of inferring the unknown parameters of a stochastic biochemical network model from a single measured time-course of the concentration of some of the involved species. Such measurements are available, e.g., from live-cell fluorescence microscopy in image-based systems biology. In addition, fluctuation time-courses from, e.g., fluorescence correlation spectroscopy provide additional information about the system dynamics that can be used to more robustly infer parameters than when considering only mean concentrations. Estimating model parameters from a single experimental trajectory enables single-cell measurements and quantification of cell--cell variability. We propose a novel combination of an adaptive Monte Carlo sampler, called Gaussian Adaptation, and efficient exact stochastic simulation algorithms that allows parameter identification from single stochastic trajectories. We benchmark the proposed method on a linear and a non-linear reaction network at steady state and during transient phases. In addition, we demonstrate that the present method also provides an ellipsoidal volume estimate of the viable part of parameter space and is able to estimate the physical volume of the compartment in which the observed reactions take place.Comment: Article in print as a book chapter in Springer's "Advances in Systems Biology

Polyhedral Predictive Regions For Power System Applications

Despite substantial improvement in the development of forecasting approaches, conditional and dynamic uncertainty estimates ought to be accommodated in decision-making in power system operation and market, in order to yield either cost-optimal decisions in expectation, or decision with probabilistic guarantees. The representation of uncertainty serves as an interface between forecasting and decision-making problems, with different approaches handling various objects and their parameterization as input. Following substantial developments based on scenario-based stochastic methods, robust and chance-constrained optimization approaches have gained increasing attention. These often rely on polyhedra as a representation of the convex envelope of uncertainty. In the work, we aim to bridge the gap between the probabilistic forecasting literature and such optimization approaches by generating forecasts in the form of polyhedra with probabilistic guarantees. For that, we see polyhedra as parameterized objects under alternative definitions (under $L_1$ and $L_\infty$ norms), the parameters of which may be modelled and predicted. We additionally discuss assessing the predictive skill of such multivariate probabilistic forecasts. An application and related empirical investigation results allow us to verify probabilistic calibration and predictive skills of our polyhedra.Comment: 8 page

Investigation of Air Transportation Technology at Princeton University, 1989-1990

The Air Transportation Technology Program at Princeton University proceeded along six avenues during the past year: microburst hazards to aircraft; machine-intelligent, fault tolerant flight control; computer aided heuristics for piloted flight; stochastic robustness for flight control systems; neural networks for flight control; and computer aided control system design. These topics are briefly discussed, and an annotated bibliography of publications that appeared between January 1989 and June 1990 is given

Volatility forecasting

Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This chapter provides a selective survey of the most important theoretical developments and empirical insights to emerge from this burgeoning literature, with a distinct focus on forecasting applications. Volatility is inherently latent, and Section 1 begins with a brief intuitive account of various key volatility concepts. Section 2 then discusses a series of different economic situations in which volatility plays a crucial role, ranging from the use of volatility forecasts in portfolio allocation to density forecasting in risk management. Sections 3, 4 and 5 present a variety of alternative procedures for univariate volatility modeling and forecasting based on the GARCH, stochastic volatility and realized volatility paradigms, respectively. Section 6 extends the discussion to the multivariate problem of forecasting conditional covariances and correlations, and Section 7 discusses volatility forecast evaluation methods in both univariate and multivariate cases. Section 8 concludes briefly. JEL Klassifikation: C10, C53, G1

COMMON STOCHASTIC TRENDS IN INTERNATIONAL STOCK MARKETS: TESTING IN AN INTEGRATED FRAMEWORK

In this paper we analyze the implications for the identification of common stochastic trends among stock price indices of using data transformed on a ”real dollar” basis. By applying a “general” VAR model where all the relevant variables (stock indices, consumer price indices and the exchange rate) are included, we show that the expected results from the cointegration analysis differ substantially. In particular it is shown that if four common stochastic trends drive the system then cointegration between the indices transformed in nominal dollars should be the relevant test while the use of their “real dollars equivalent” is superfluous. In cases where three common stochastic trends exist then a reasonable specification of the model would imply that the Purchasing Power Parity condition accounts for one of them while the second one relates to a cointegrating relation between the stock indices in nominal domestic currency terms. We apply the testing methodology developed by Johansen (1992a, 1995a, 1997) and extended by Paruolo (1996) and Rahbek et al. (1999) to examine the presence of I(2) and I(1) components in a multivariate context using monthly data for the US, UK, Germany and Japan for the period 1980 – 2000. Four possible economic scenarios were considered in a bivariate setting and two of them were found to be statistically supported. By imposing linear restrictions on each cointegrating vector as suggested by Johansen and Juselius (1994), the order and rank conditions for statistical identification are satisfied while the test for economic identification was not significant for each bilateral case, namely US-UK, US-Germany, US-Japan. The main findings suggest that the policy to transform the data into a “real” dollar basis, which is often encountered in the literature, lacks empirical support. Furthermore, the stability results indicate that cointegration was established in the early 1990s which implies that some form of policy coordination between the G-7 countries was implemented in the aftermath of the October 1987 crisis.International stock markets, I(2) cointegration analysis, commom trends, identification, purchasing