Inference in hybrid Bayesian networks using dynamic discretization

We consider approximate inference in hybrid Bayesian Networks (BNs) and present a new iterative algorithm that efficiently combines dynamic discretization with robust propagation algorithms on junction trees. Our approach offers a significant extension to Bayesian Network theory and practice by offering a flexible way of modeling continuous nodes in BNs conditioned on complex configurations of evidence and intermixed with discrete nodes as both parents and children of continuous nodes. Our algorithm is implemented in a commercial Bayesian Network software package, AgenaRisk, which allows model construction and testing to be carried out easily. The results from the empirical trials clearly show how our software can deal effectively with different type of hybrid models containing elements of expert judgment as well as statistical inference. In particular, we show how the rapid convergence of the algorithm towards zones of high probability density, make robust inference analysis possible even in situations where, due to the lack of information in both prior and data, robust sampling becomes unfeasible.     

A Hausman test for Brownian motion

New tests are proposed for the specification of the intraday price process of a risky asset, based on open, high, low, and close prices. Under the null of a Brownian process we derive two stochastically independent, unbiased volatility estimators. For a Hausman specification test we prove its equivalence with an F-test, consider its robustness against variation in drift and volatility, and analyze the power against an Ornstein–Uhlenbeck process, as well as a random walk with alternative distributions.     

Modelling Variability in the Branching Structure of Strawberry Inflorescences

The branching structure of inflorescences of the cultivated strawberry ( Fragaria × ananassa Duch.) is very variable. This paper demonstrates that some aspects of this variability are well described by a simple stochastic model of branching that has two adjustable parameters. The model is shown to provide a good fit to data from a set of almost 700 inflorescences of the cultivar Elsanta, collected over two successive years. For one parameter the maximum likelihood estimator is a moment estimator which is fully efficient even if the detailed branching structure of the inflorescences is not recorded. This parameter provides a convenient summary of branching vigour. The maximum likelihood estimator of the second parameter must be determined iteratively and can be quite inefficient unless the full branching structure is recorded. The model demonstrates that branching structure is affected by the order in which inflorescences emerge on the plant.     

A Note on the Large Sample Properties of Estimators Based on Generalized Linear Models for Correlated Pseudo‐observations

Pseudo‐values have proven very useful in censored data analysis in complex settings such as multi‐state models. It was originally suggested by Andersen et al., Biometrika, 90, 2003, 335 who also suggested to estimate standard errors using classical generalized estimating equation results. These results were studied more formally in Graw et al., Lifetime Data Anal., 15, 2009, 241 that derived some key results based on a second‐order von Mises expansion. However, results concerning large sample properties of estimates based on regression models for pseudo‐values still seem unclear. In this paper, we study these large sample properties in the simple setting of survival probabilities and show that the estimating function can be written as a U‐statistic of second order giving rise to an additional term that does not vanish asymptotically. We further show that previously advocated standard error estimates will typically be too large, although in many practical applications the difference will be of minor importance. We show how to estimate correctly the variability of the estimator. This is further studied in some simulation studies.     

Validation of Nonparametric Two-sample Bootstrap in ROC Analysis on Large Datasets

The nonparametric two-sample bootstrap is applied to computing uncertainties of measures in receiver operating characteristic (ROC) analysis on large datasets in areas such as biometrics, speaker recognition, etc. when the analytical method cannot be used. Its validation was studied by computing the standard errors of the area under ROC curve using the well-established analytical Mann–Whitney statistic method and also using the bootstrap. The analytical result is unique. The bootstrap results are expressed as a probability distribution due to its stochastic nature. The comparisons were carried out using relative errors and hypothesis testing. These match very well. This validation provides a sound foundation for such computations.     

The Local Power of the CADF and CIPS Panel Unit Root Tests

Very little is known about the local power of second generation panel unit root tests that are robust to cross-section dependence. This article derives the local asymptotic power functions of the cross-section argumented Dickey–Fuller Cross-section Augmented Dickey-Fuller (CADF) and CIPS tests of Pesaran (2007), which are among the most popular tests around.     

The Transitional Discharge Model: comparing implementation in Canada and Scotland

Effective discharge planning is needed to facilitate clients' transition from psychiatric hospital wards to community care. Previous studies have shown that client outcomes can be improved by using a Transitional Discharge Model (TDM) that includes peer support and an extension of inpatient-practitioner relationships that are introduced prior to discharge. However, countries vary in many ways that may affect implementation of the model. This article describes some of the similarities and differences related to introducing transitional discharge in two countries: Canada and Scotland. It is important to elucidate facilitators and challenges in implementing the TDM to identify and disseminate strategies to aid implementation. Implications for future implementation of the model are also discussed.