arXiv subjects

J. Mulder

Publications and source records attributed to J. Mulder.

5 recordsLinked to original sources

arXiv2020

A Generalization of the Savage-Dickey Density Ratio for Testing Equality and Order Constrained Hypotheses

The Savage-Dickey density ratio is a specific expression of the Bayes factor when testing a precise (equality constrained) hypothesis against an unrestricted alternative. The expression greatly simplifies the computation of the Bayes factor at the cost of assuming a specific form of the prior under the precise hypothesis as a function of the unrestricted prior. A generalization was proposed by Verdinelli and Wasserman (1995) such that the priors can be freely specified under both hypotheses while keeping the computational advantage. This paper presents an extension of this generalization when the hypothesis has equality as well as order constraints on the parameters of interest. The methodology is used for a constrained multivariate t test using the JZS Bayes factor and a constrained hypothesis test under the multinomial model.

stat.ME↗

arXiv2019

Decision-making with multiple correlated binary outcomes in clinical trials

Clinical trials often evaluate multiple outcome variables to form a comprehensive picture of the effects of a new treatment. The resulting multidimensional insight contributes to clinically relevant and efficient decision-making about treatment superiority. Common statistical procedures to make these superiority decisions with multiple outcomes have two important shortcomings however: 1) Outcome variables are often modeled individually, and consequently fail to consider the relation between outcomes; and 2) superiority is often defined as a relevant difference on a single, on any, or on all outcomes(s); and lacks a compensatory mechanism that allows large positive effects on one or multiple outcome(s) to outweigh small negative effects on other outcomes. To address these shortcomings, this paper proposes 1) a Bayesian model for the analysis of correlated binary outcomes based on the multivariate Bernoulli distribution; and 2) a flexible decision criterion with a compensatory mechanism that captures the relative importance of the outcomes. A simulation study demonstrates that efficient and unbiased decisions can be made while Type I error rates are properly controlled. The performance of the framework is illustrated for 1) fixed, group sequential, and adaptive designs; and 2) non-informative and informative prior distributions.

stat.ME↗

arXiv2019

Default Bayesian Model Selection of Constrained Multivariate Normal Linear Models

The multivariate normal linear model is one of the most widely employed models for statistical inference in applied research. Special cases include (multivariate) t testing, (M)AN(C)OVA, (multivariate) multiple regression, and repeated measures analysis. Statistical procedures for model selection where the models may have equality and order constraints on the model parameters of interest are limited however. This paper presents a default Bayes factor for this model selection problem. The default Bayes factor is based on generalized fractional Bayes methodology where different fractions are used for different observations and where the default prior is centered on the boundary of the constrained space under investigation. First, the method is fully automatic and therefore can be applied when prior information is weak or completely unavailable. Second, using group specific fractions, the same amount of information is used from each group resulting in a minimally informative default prior having a matrix Cauchy distribution, resulting in a consistent default Bayes factor. Third, numerical computation can be done using parallelization which makes it computationally cheap. Fourth, the evidence can be updated in a relatively simple manner when observing new data. Fifth, the selection criterion can be applied relatively straightforwardly in the presence of missing data that are missing at random. Applications for the social and behavioral sciences are used for illustration.

stat.ME↗

arXiv2012

Optimization of a charge-state analyzer for ECRIS beams

A detailed experimental and simulation study of the extraction of a 24 keV He-ion beam from an ECR ion source and the subsequent beam transport through an analyzing magnet is presented. We find that such a slow ion beam is very sensitive to space-charge forces, but also that the neutralization of the beam's space charge by secondary electrons is virtually complete for beam currents up to at least 0.5 mA. The beam emittance directly behind the extraction system is 65 pi mm mrad and is determined by the fact that the ion beam is extracted in the strong magnetic fringe field of the ion source. The relatively large emittance of the beam and its non-paraxiality lead, in combination with a relatively small magnet gap, to significant beam losses and a five-fold increase of the effective beam emittance during its transport through the analyzing magnet. The calculated beam profile and phase-space distributions in the image plane of the analyzing magnet agree well with measurements. The kinematic and magnet aberrations have been studied using the calculated second-order transfer map of the analyzing magnet, with which we can reproduce the phase-space distributions of the ion beam behind the analyzing magnet. Using the transfer map and trajectory calculations we have worked out an aberration compensation scheme based on the addition of compensating hexapole components to the main dipole field by modifying the shape of the poles. The simulations predict that by compensating the kinematic and geometric aberrations in this way and enlarging the pole gap the overall beam transport efficiency can be increased from 16 to 45%.

physics.acc-ph↗

arXiv2010

The Herschel-SPIRE instrument and its in-flight performance

The Spectral and Photometric Imaging Receiver (SPIRE), is the Herschel Space Observatory`s submillimetre camera and spectrometer. It contains a three-band imaging photometer operating at 250, 350 and 500 microns, and an imaging Fourier Transform Spectrometer (FTS) which covers simultaneously its whole operating range of 194-671 microns (447-1550 GHz). The SPIRE detectors are arrays of feedhorn-coupled bolometers cooled to 0.3 K. The photometer has a field of view of 4' x 8', observed simultaneously in the three spectral bands. Its main operating mode is scan-mapping, whereby the field of view is scanned across the sky to achieve full spatial sampling and to cover large areas if desired. The spectrometer has an approximately circular field of view with a diameter of 2.6'. The spectral resolution can be adjusted between 1.2 and 25 GHz by changing the stroke length of the FTS scan mirror. Its main operating mode involves a fixed telescope pointing with multiple scans of the FTS mirror to acquire spectral data. For extended source measurements, multiple position offsets are implemented by means of an internal beam steering mirror to achieve the desired spatial sampling and by rastering of the telescope pointing to map areas larger than the field of view. The SPIRE instrument consists of a cold focal plane unit located inside the Herschel cryostat and warm electronics units, located on the spacecraft Service Module, for instrument control and data handling. Science data are transmitted to Earth with no on-board data compression, and processed by automatic pipelines to produce calibrated science products. The in-flight performance of the instrument matches or exceeds predictions based on pre-launch testing and modelling: the photometer sensitivity is comparable to or slightly better than estimated pre-launch, and the spectrometer sensitivity is also better by a factor of 1.5-2.

astro-ph.IM↗