Consistency of objective Bayes factors as the model dimension grows

In the class of normal regression models with a finite number of regressors, and for a wide class of prior distributions, a Bayesian model selection procedure based on the Bayes factor is consistent [Casella and Moreno J. Amer. Statist. Assoc. 104 (2009) 1261--1271]. However, in models where the number of parameters increases as the sample size increases, properties of the Bayes factor are not totally understood. Here we study consistency of the Bayes factors for nested normal linear models when the number of regressors increases with the sample size. We pay attention to two successful tools for model selection [Schwarz Ann. Statist. 6 (1978) 461--464] approximation to the Bayes factor, and the Bayes factor for intrinsic priors [Berger and Pericchi J. Amer. Statist. Assoc. 91 (1996) 109--122, Moreno, Bertolino and Racugno J. Amer. Statist. Assoc. 93 (1998) 1451--1460]. We find that the the Schwarz approximation and the Bayes factor for intrinsic priors are consistent when the rate of growth of the dimension of the bigger model is $O(n^b)$ for $b<1$. When $b=1$ the Schwarz approximation is always inconsistent under the alternative while the Bayes factor for intrinsic priors is consistent except for a small set of alternative models which is characterized.Comment: Published in at http://dx.doi.org/10.1214/09-AOS754 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Consistency of Bayesian procedures for variable selection

It has long been known that for the comparison of pairwise nested models, a decision based on the Bayes factor produces a consistent model selector (in the frequentist sense). Here we go beyond the usual consistency for nested pairwise models, and show that for a wide class of prior distributions, including intrinsic priors, the corresponding Bayesian procedure for variable selection in normal regression is consistent in the entire class of normal linear models. We find that the asymptotics of the Bayes factors for intrinsic priors are equivalent to those of the Schwarz (BIC) criterion. Also, recall that the Jeffreys--Lindley paradox refers to the well-known fact that a point null hypothesis on the normal mean parameter is always accepted when the variance of the conjugate prior goes to infinity. This implies that some limiting forms of proper prior distributions are not necessarily suitable for testing problems. Intrinsic priors are limits of proper prior distributions, and for finite sample sizes they have been proved to behave extremely well for variable selection in regression; a consequence of our results is that for intrinsic priors Lindley's paradox does not arise.Comment: Published in at http://dx.doi.org/10.1214/08-AOS606 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Minimal Equation Sets for Output Computation in Object-Oriented Models

Object-oriented models of complex physical systems can have a very large number of equations and variables. For some applications, only a few output variables of the model are of actual interest. This paper presents an application of the well-known Tarjan’s algorithm, that allows to automatically select the minimal set of equations and variables required to compute the time histories of selected outputs of a given model. The application of the algorithm to a simple test case is illustrated in the paper

An XML Representation of DAE Systems Obtained from Modelica Models

This contribution presents an XML format for representation of flat Modelica models. The purpose is to offer a standardized model exchange format which is based on the DAE formalism and wich is neutral with respect to model usage. Many usages of models goes beyond what can be obtained from an execution interface offering evaluation of the model equations. Several such usages arises in the area of control engineering, where LFT transformations, derivation of robotic controllers, optimization, and real time code generation are some examples. The choice of XML is motivated by its defacto standard status and the availability of free and efficient tools. Also, the XSLT language enables specification of transformation of the XML model representation into other formats

Rate-Control or Rhythm-Contol: Where do we stand?

Atrial fibrillation is the most common sustained rhythm disturbance and its prevalence is increasing worldwide due to the progressive aging of the population. Current guidelines clearly depict the gold standard management of acute symptomatic atrial fibrillation but the best-long term approach for first or recurrent atrial fibrillation is still debated with regard to quality of life, risk of new hospitalizations, and possible disabling complications, such as thromboembolic stroke, major bleeds and death. Some authors propose that regaining sinus rhythm in all cases, thus re-establishing a physiologic cardiac function not requiring a prolonged antithrombotic therapy, avoids the threat of intracranial or extracranial haemorrhages due to Vitamin K antagonists or aspirin. On the contrary, advocates of a rate control approach with an accurate antithrombotic prophylaxis propose that such a strategy may avoid the risk of cardiovascular and non cardiovascular side effects related to antiarrhythmic drugs. This review aims to explore the state of our knowledge in order to summarize evidences and issues that need to be furthermore clarified

Beyond Simulation: Computer Aided Control System Design Using Equation-Based Object Oriented Modelling for the Next Decade

After 20 years since their birth, equation-oriented and object-oriented modelling techniques and tools are now mature, as far as solving simulation problems is concerned. Conversely, there is still much to be done in order to provide more direct support for the design of advanced, model-based control systems, starting from object-oriented plant models. Following a brief review of the current state of the art in this field, the paper presents some proposals for future developments: open model exchange formats, automatic model-order reduction techniques, automatic derivation of simplified transfer functions, automatic derivation of LFT models, automatic generation of inverse models for robotic systems, and support for nonlinear model predictive control

Effect of sterilization treatment on the corrosion behavior of NiTi endodontic instruments

This study investigates the influence of the sterilization treatment conducted at 50 °C in 5% sodium hypochlorite solution (NaClO) on the corrosion behavior of endodontic instruments made of NiTi alloy (GT Rotary and K3) and stainless steel (K File) by measuring potentiodynamic polarization curves in the same environment at 37°C. For the sake of comparison, the electrochemical characterization was also carried out on endodontic instruments that were not sterilized. The characterization of the sample surface after the electrochemical tests were carried out by means of scanning electron microscopy (SEM) coupled with X-ray energy dispersive spectroscopy (EDX). There was no significant influence of the sterilization treatment on the corrosion behavior of K File and GT Rotary endodontic instruments. On the contrary, a negative influence of the sterilization treatment on the corrosion resistance of K3 endodontic instruments was observed, and the effect appears to be more dramatic for longer treatment periods

The complex time behaviour of the microquasar GRS 1915+105 in the \rho-class observed with BeppoSAX. III: The hard X-ray delay and limit cycle mapping

The microquasar GRS1915+105 was observed by BeppoSAX in October 2000 for about ten days while the source was in \rho-mode, which is characterized by a quasi-regular type I bursting activity. This paper presents a systematic analysis of the delay of the hard and soft X-ray emission at the burst peaks. The lag, also apparent from the comparison of the [1.7-3.4] keV light curves with those in the [6.8-10.2] keV range, is evaluated and studied as a function of time, spectral parameters, and flux. We apply the limit cycle mapping technique, using as independent variables the count rate and the mean photon rate. The results using this technique were also cross-checked using a more standard approach with the cross-correlation methods. Data are organized in runs, each relative to a continuous observation interval. The detected hard-soft delay changes in the course of the pointing from about 3 s to about 10 s and presents a clear correlation with the baseline count rate.Comment: accepted for publication in A&

An XML representation of DAE systems obtained fromcontinuous-time Modelica models

This contribution outlines an XML format for representation of differential-algebraic equations (DAE) models obtained from continuous time Modelica models and possibly also from other equation-based modeling languages. The purpose is to offer a standardized model exchange format which is based on the DAE formalism and which is neutral with respect to model usage. Many usages of models go beyond what can be obtained from an execution interface offering evaluation of the model equations for simulation purposes. Several such usages arise in the area of control engineering, where dynamic optimization, Linear Fractional Transformations (LFTs), derivation of robotic controllers, model order reduction, and real time code generation are some examples. The choice of XML is motivated by its de facto standard status and the availability of free and efficient tools. Also, the XSLT language enables a convenient specification of the transformation of the XML model representation into other formats

Overdetermined Steady-State Initialization Problems in Object-Oriented Fluid System Models

The formulation of steady-state initialization problems for fluid systems is a non-trivial task. If steady-state equations are specified at the component level, the corresponding system of initial equations at the system level might be overdetermined, if index reduction eliminates some states. On the other hand, steady-state equations are not sufficient to uniquely identify one equilibrium state in the case of closed systems, so additional equations are required. The paper shows how these problems might be solved in an elegant way by formulating overdetermined initialization problems, which have more equations than unknowns and a unique solution, then solving them using a least-squares minimization algorithm. The concept is tested on a representative test case using the OpenModelica compiler