Estimation of Parameters in Random Effect Models with Incidence Matrix Uncertainty

Random effect models have been widely applied in many fields of research. However, models with uncertain design matrices for random effects have been little investigated before. In some applications with such problems, an expectation method has been used for simplicity. This method does not include the extra information of uncertainty in the design matrix is not included. The closed solution for this problem is generally difficult to attain. We therefore propose an two-step algorithm for estimating the parameters, especially the variance components in the model. The implementation is based on Monte Carlo approximation and a Newton-Raphson-based EM algorithm. As an example, a simulated genetics dataset was analyzed. The results showed that the proportion of the total variance explained by the random effects was accurately estimated, which was highly underestimated by the expectation method. By introducing heuristic search and optimization methods, the algorithm can possibly be developed to infer the 'model-based' best design matrix and the corresponding best estimates.

Generalized pseudo-likelihood estimates for markov random fields on lattice

In this paper we generalize Besag's pseudo-likelihood function for spatial statistical models on a region of a lattice. The correspondingly defined maximum generalized pseudo-likelihood estimates (MGPLEs) are natural extensions of Besag's maximum pseudo-likelihood estimate (MPLE). The MGPLEs connect the MPLE and the maximum likelihood estimate. We carry out experimental calculations of the MGPLEs for spatial processes on the lattice. These simulation results clearly show better performances of the MGPLEs than the MPLE, and the performances of differently defined MGPLEs are compared. These are also illustrated by the application to two real data sets.

Chromatic and luminance losses with multiple sclerosis and optic neuritis measured using dynamic random luminance contrast noise

We measured thresholds for detecting changes in colour and in luminance contrast in observers with multiple sclerosis (MS) and/or optic neuritis (ON) to determine whether reduced sensitivity occurs principally in red-green or blue-yellow second-stage chromatic channels or in an achromatic channel. Colour thresholds for the observers with MS/ON were higher in the red-green direction than in the blue-yellow direction, indicating greater levels of red-green loss than blue-yellow loss. Achromatic thresholds were raised less than either red-green or blue-yellow thresholds, showing less luminance-contrast loss than chromatic loss. With the MS/ON observers, blue-yellow and red-green thresholds were positively correlated but increasing impairment was associated with more rapid changes in red-green thresholds than blue-yellow thresholds. These findings indicate that demyelinating disease selectively reduces sensitivity to colour vision over luminance vision and red-green colours over blue-yellow colours.

Class library ranlip for multivariate nonuniform random variate generation

This paper describes generation of nonuniform random variates from Lipschitz-continuous densities using acceptance/rejection, and the class library _ranlip which implements this method. It is assumed that the required distribution has Lipschitz-continuous density, which is either given analytically or as a black box. The algorithm builds a piecewise constant upper approximation to the density (the hat function), using a large number of its values and subdivision of the domain into hyperrectangles. The class library _ranlip provides very competitive preprocessing and generation times, and yields small rejection constant, which is a measure of efficiency of the generation step. It exhibits good performance for up to five variables, and provides the user with a black box nonuniform random variate generator for a large class of distributions, in particular, multimodal distributions. It will be valuable for researchers who frequently face the task of sampling from unusual distributions, for which specialized random variate generators are not available.

Universal nonuniform random vector generator based on acceptance-rejection

The acceptance/rejection approach is widely used in universal nonuniform random number generators. Its key part is an accurate approximation of a given probability density from above by a hat function. This article uses a piecewise constant hat function, whose values are overestimates of the density on the elements of the partition of the domain. It uses a sawtooth overestimate of Lipschitz continuous densities, and then examines all local maximizers of such an overestimate. The method is applicable to multivariate multimodal distributions. It exhibits relatively short preprocessing time and fast generation of random variates from a very large class of distributions

Extracting Causal Graphs from an Open Provenance Data Model

The open provenance architecture (OPA) approach to the challenge was distinct in several regards. In particular, it is based on an open, well-defined data model and architecture, allowing different components of the challenge workflow to independently record documentation, and for the workflow to be executed in any environment. Another noticeable feature is that we distinguish between the data recorded about what has occurred, emphprocess documentation, and the emphprovenance of a data item, which is all that caused the data item to be as it is and is obtained as the result of a query over process documentation. This distinction allows us to tailor the system to separately best address the requirements of recording and querying documentation. Other notable features include the explicit recording of causal relationships between both events and data items, an interaction-based world model, intensional definition of data items in queries rather than relying on explicit naming mechanisms, and emphstyling of documentation to support non-functional application requirements such as reducing storage costs or ensuring privacy of data. In this paper we describe how each of these features aid us in answering the challenge provenance queries.

Groups, graphs and mutually unbiased bases

A new characteristic free approach to constructing large sets of mutually unbiased bases in Hilbert space is developed. We associate with a seed set of bases a finite subgroup of which defines a strongly regular graph. Large sets of mutually unbiased bases are obtained as the cliques of the graph.

Simulation of dynamic recrystallization using random grid cellular automata

Computer simulation is a powerful tool to predict microstructure and its evolution in dynamic and post-dynamic recrystallization. CAFE proposed as an appropriate approach by combining finite element (FE) method and cellular automata (CA) for recrystallization simulation. In the current study, a random grid cellular automaton (CA), as micro-scale model, based on finite element (FE), as macro-scale method, has been used to study initial and evolving microstructural features; including nuclei densities, dislocation densities, grain size and grain boundary movement during dynamic recrystallization in a C-Mn steel. An optimized relation has been established between mechanical variables and evolving microstructure features during recrystallization and grain growth. In this model, the microstructure is defined as cells located within grains and grain boundaries while dislocations are randomly dispersed throughout microstructure. Changes of dislocation density during deformation are described considering hardening, recovery and recrystallization. Recrystallization is assumed to initiate near grain boundaries and nucleation rate was considered constant (site-saturated condition). The model produced a mathematical formulation which captured the initial and evolving microstructural entities and linked their effects to measurable macroscopic variables (e.g. stress).