A semi-Markov model for stroke with piecewise-constant hazards in the presence of left, right and interval censoring.

This paper presents a parametric method of fitting semi-Markov models with piecewise-constant hazards in the presence of left, right and interval censoring. We investigate transition intensities in a three-state illness-death model with no recovery. We relax the Markov assumption by adjusting the intensity for the transition from state 2 (illness) to state 3 (death) for the time spent in state 2 through a time-varying covariate. This involves the exact time of the transition from state 1 (healthy) to state 2. When the data are subject to left or interval censoring, this time is unknown. In the estimation of the likelihood, we take into account interval censoring by integrating out all possible times for the transition from state 1 to state 2. For left censoring, we use an Expectation-Maximisation inspired algorithm. A simulation study reflects the performance of the method. The proposed combination of statistical procedures provides great flexibility. We illustrate the method in an application by using data on stroke onset for the older population from the UK Medical Research Council Cognitive Function and Ageing Study

Detecting failure of climate predictions

The practical consequences of climate change challenge society to formulate responses that are more suited to achieving long-term objectives, even if those responses have to be made in the face of uncertainty. Such a decision-analytic focus uses the products of climate science as probabilistic predictions about the effects of management policies. Here we present methods to detect when climate predictions are failing to capture the system dynamics. For a single model, we measure goodness of fit based on the empirical distribution function, and define failure when the distribution of observed values significantly diverges from the modelled distribution. For a set of models, the same statistic can be used to provide relative weights for the individual models, and we define failure when there is no linear weighting of the ensemble models that produces a satisfactory match to the observations. Early detection of failure of a set of predictions is important for improving model predictions and the decisions based on them. We show that these methods would have detected a range shift in northern pintail 20 years before it was actually discovered, and are increasingly giving more weight to those climate models that forecast a September ice-free Arctic by 2055

Dynamic tracking error with shortfall control using stochastic programming

In this contribution we tackle the issue of portfolio management combining benchmarking and risk control. We propose a dynamic tracking error problem and we consider the problem of monitoring at discrete points the shortfalls of the portfolio below a set of given reference levels of wealth.We formulate and solve the resulting dynamic optimization problem using stochastic programming. The proposed model allows for a great flexibility in the combination of the tracking goal and the downside risk protection. We provide the results of out-of-sample simulation experiments, on real data, for different portfolio configurations and different market conditions

Optimisation of NMR dynamic models I. Minimisation algorithms and their performance within the model-free and Brownian rotational diffusion spaces

The key to obtaining the model-free description of the dynamics of a macromolecule is the optimisation of the model-free and Brownian rotational diffusion parameters using the collected R1, R2 and steady-state NOE relaxation data. The problem of optimising the chi-squared value is often assumed to be trivial, however, the long chain of dependencies required for its calculation complicates the model-free chi-squared space. Convolutions are induced by the Lorentzian form of the spectral density functions, the linear recombinations of certain spectral density values to obtain the relaxation rates, the calculation of the NOE using the ratio of two of these rates, and finally the quadratic form of the chi-squared equation itself. Two major topological features of the model-free space complicate optimisation. The first is a long, shallow valley which commences at infinite correlation times and gradually approaches the minimum. The most severe convolution occurs for motions on two timescales in which the minimum is often located at the end of a long, deep, curved tunnel or multidimensional valley through the space. A large number of optimisation algorithms will be investigated and their performance compared to determine which techniques are suitable for use in model-free analysis. Local optimisation algorithms will be shown to be sufficient for minimisation not only within the model-free space but also for the minimisation of the Brownian rotational diffusion tensor. In addition the performance of the programs Modelfree and Dasha are investigated. A number of model-free optimisation failures were identified: the inability to slide along the limits, the singular matrix failure of the Levenberg–Marquardt minimisation algorithm, the low precision of both programs, and a bug in Modelfree. Significantly, the singular matrix failure of the Levenberg–Marquardt algorithm occurs when internal correlation times are undefined and is greatly amplified in model-free analysis by both the grid search and constraint algorithms. The program relax (http://www.nmr-relax.com) is also presented as a new software package designed for the analysis of macromolecular dynamics through the use of NMR relaxation data and which alleviates all of the problems inherent within model-free analysis

Understanding the adsorption process in ZIF-8 using high pressure crystallography and computational modelling

Understanding host–guest interactions and structural changes within porous materials is crucial for enhancing gas storage properties. Here, the authors combine cryogenic loading of gases with high pressure crystallography and computational techniques to obtain atomistic detail of adsorption-induced structural and energetic changes in ZIF-8

An Open Source Simulation Model for Soil and Sediment Bioturbation

Bioturbation is one of the most widespread forms of ecological engineering and has significant implications for the structure and functioning of ecosystems, yet our understanding of the processes involved in biotic mixing remains incomplete. One reason is that, despite their value and utility, most mathematical models currently applied to bioturbation data tend to neglect aspects of the natural complexity of bioturbation in favour of mathematical simplicity. At the same time, the abstract nature of these approaches limits the application of such models to a limited range of users. Here, we contend that a movement towards process-based modelling can improve both the representation of the mechanistic basis of bioturbation and the intuitiveness of modelling approaches. In support of this initiative, we present an open source modelling framework that explicitly simulates particle displacement and a worked example to facilitate application and further development. The framework combines the advantages of rule-based lattice models with the application of parameterisable probability density functions to generate mixing on the lattice. Model parameters can be fitted by experimental data and describe particle displacement at the spatial and temporal scales at which bioturbation data is routinely collected. By using the same model structure across species, but generating species-specific parameters, a generic understanding of species-specific bioturbation behaviour can be achieved. An application to a case study and comparison with a commonly used model attest the predictive power of the approach