Number Of Possible Models Research Articles

Bootstrapping multiple systems estimates to account for model selection

Multiple systems estimation using a Poisson loglinear model is a standard approach to quantifying hidden populations where data sources are based on lists of known cases. Information criteria are often used for selecting between the large number of possible models. Confidence intervals are often reported conditional on the model selected, providing an over-optimistic impression of estimation accuracy. A bootstrap approach is a natural way to account for the model selection. However, because the model selection step has to be carried out for every bootstrap replication, there may be a high or even prohibitive computational burden. We explore the merit of modifying the model selection procedure in the bootstrap to look only among a subset of models, chosen on the basis of their information criterion score on the original data. This provides large computational gains with little apparent effect on inference. We also incorporate rigorous and economical ways of approaching issues of the existence of estimators when applying the method to sparse data tables.

Gravitational reheating

Our present understanding of the reheating phase is incomplete due to a lack of observations. Apart from its cosmological implications, the reheating should play a vital role in particle physics and inflation model building. Conventionally, reheating dynamics are modeled by invoking arbitrary coupling among the inflaton and daughter fields. Such an approach lacks robust cosmological predictions, due to its arbitrary couplings, and is difficult to verify through observation. In this paper, we propose a minimal reheating scenario, where the inflaton is coupled with all the daughter fields only gravitationally. Besides being successful in reheating the Universe, the scenario offers a strong cosmological prediction of the primordial gravitational wave spectrum and discards a large number of possible models of dark matter and inflation that are otherwise consistent with Planck.

A point mutation in the nuclease domain of MLH3 eliminates repeat expansions in a mouse stem cell model of the Fragile X-related disorders.

The Fragile X-related disorders (FXDs) are Repeat Expansion Diseases, genetic disorders that result from the expansion of a disease-specific microsatellite. In those Repeat Expansion Disease models where it has been examined, expansion is dependent on functional mismatch repair (MMR) factors, including MutLγ, a heterodimer of MLH1/MLH3, one of the three MutL complexes found in mammals and a minor player in MMR. In contrast, MutLα, a much more abundant MutL complex that is the major contributor to MMR, is either not required for expansion or plays a limited role in expansion in many model systems. How MutLγ acts to generate expansions is unclear given its normal role in protecting against microsatellite instability and while MLH3 does have an associated endonuclease activity, whether that contributes to repeat expansion is uncertain. We show here, using a gene-editing approach, that a point mutation that eliminates the endonuclease activity of MLH3 eliminates expansions in an FXD mouse embryonic stem cell model. This restricts the number of possible models for repeat expansion and supports the idea that MutLγ may be a useful druggable target to reduce somatic expansion in those disorders where it contributes to disease pathology.

Floating Search Methodology for Combining Classification Models for Site Recognition in DNA Sequences.

Recognition of the functional sites of genes, such as translation initiation sites, donor and acceptor splice sites and stop codons, is a relevant part of many current problems in bioinformatics. The best approaches use sophisticated classifiers, such as support vector machines. However, with the rapid accumulation of sequence data, methods for combining many sources of evidence are necessary as it is unlikely that a single classifier can solve this problem with the best possible performance. A major issue is that the number of possible models to combine is large and the use of all of these models is impractical. In this paper we present a methodology for combining many sources of information to recognize any functional site using "floating search", a powerful heuristics applicable when the cost of evaluating each solution is high. We present experiments on four functional sites in the human genome, which is used as the target genome, and use another 20 species as sources of evidence. The proposed methodology shows significant improvement over state-of-the-art methods. The results show an advantage of the proposed method and also challenge the standard assumption of using only genomes not very close and not very far from the human to improve the recognition of functional sites.

Distinguishability study of 3-mass models for electromechanical motion systems

Physically motivated models of electromechanical motion systems are required in several applications related to control design and auto-tracking, model-based fault detection, feed-forward, and simply interpretation. However, attempts to create such models automatically via structure and parameter identification struggle with ambiguities regarding the correct internal structure of the model. Designing a reasonable set of candidate models is difficult, because it is not known which models are distinguishable and which are not. This paper gives a simple to use necessary condition for indistinguishability of multiple mass models as they are used to model the control-relevant features of motion systems. In an automated way models are generated that can be created by considering elasticities at different positions in the mechanical structures. The condition is applied to these models for the case of three masses. In three examples it is shown that the criterion simplifies the subsequent structure and parameter identification considerably by reducing the number of possible models. For higher numbers of masses, however, it would become intractable.

Distinguishability study of 3-mass models for electromechanical motion systems

Physically motivated models of electromechanical motion systems are required in several applications related to control design and auto-tracking, model-based fault detection, feed-forward, and simply interpretation. However, attempts to create such models automatically via structure and parameter identification struggle with ambiguities regarding the correct internal structure of the model. Designing a reasonable set of candidate models is difficult, because it is not known which models are distinguishable and which are not. This paper gives a simple to use necessary condition for indistinguishability of multiple mass models as they are used to model the control-relevant features of motion systems. In an automated way models are generated that can be created by considering elasticities at different positions in the mechanical structures. The condition is applied to these models for the case of three masses. In three examples it is shown that the criterion simplifies the subsequent structure and parameter identification considerably by reducing the number of possible models. For higher numbers of masses, however, it would become intractable.

Reservoir characterisation method with multi-component seismic data by unsupervised learning and colour feature blending

ABSTRACTMulti-attribute analysis of multi-component seismic data can provide abundant information on seismic hydrocarbon reservoirs. It can exploit the different responses of compressional and shear waves to the reservoir, in conjunction with colour blending and fusion technology applied to seismic images, to enable the human eye to better discriminate features in seismic data, thereby improving the accuracy of reservoir characterisation. The integration of multi-component data and sophisticated visualisation techniques helps to reduce the number of possible models of the reservoir. Thus, we designed a reservoir prediction method based on unsupervised learning and colour feature blending. First, a large number of compressional and shear wave seismic attributes were extracted using cluster analysis to conduct unsupervised learning to optimise the attributes. Then, using the different responses of compressional and shear waves to oil and gas, and an understanding of rock physics, three types of composite attribute were constructed to highlight oil and gas anomalies by multi-component seismic attributes. Finally, the three composite attributes were transformed to the colour space by a first-order linear transformation and RGB colour blending. Applying this scheme to reservoir prediction shows that unsupervised learning and colour blending techniques could help the human eye perceive geological anomalies, highlight common hydrocarbon characteristics, reduce differences and decrease interpretation ambiguity. The prediction results are essentially consistent with actual data and can be used to predict favourable exploration areas.

The non-Universal U(1) gauge extended \u03bc\u03bdSSM: anomalies cancellation and singular phenomenology

So far the most sophisticated experiments have shown no trace of new physics at the TeV scale. Consequently, new models with unexplored parameter regions are necessary to explain current results, re-examine the existing data, and propose new experiments. In this Letter, we present a modified version of the μνSSM supersymmetric model where a non-Universal extra U(1) gauge symmetry is added in order to restore an effective R-parity that ensures proton stability. We show that anomalies equations cancel without having to add any exotic matter, restricting the charges of the fields under the extra symmetry to a discrete set of values. We find that it is the viability of the model through anomalies cancellation what defines the conditions in which fermions interact with dark matter candidates via the exchange of Z′ bosons. The strict condition of universality violation means that LHC constraints for a Z′ mass do not apply directly to our model, allowing for a yet undiscovered relatively light Z′, as we discuss both in the phenomenological context and in its implications for possible flavour changing neutral currents. Moreover, we explore the possibility of isospin violating dark matter interactions; we observe that this interaction depends, surprisingly, on the Higgs charges under the new symmetry, both limiting the number of possible models and allowing to analyse indirect dark matter searches in the light of well defined, particular scenarios.

Mode jumping MCMC for Bayesian variable selection in GLMM

Generalized linear mixed models (GLMM) are used for inference and prediction in a wide range of different applications providing a powerful scientific tool. An increasing number of sources of data are becoming available, introducing a variety of candidate explanatory variables for these models. Selection of an optimal combination of variables is thus becoming crucial. In a Bayesian setting, the posterior distribution of the models, based on the observed data, can be viewed as a relevant measure for the model evidence. The number of possible models increases exponentially in the number of candidate variables. Moreover, the space of models has numerous local extrema in terms of posterior model probabilities. To resolve these issues a novel MCMC algorithm for the search through the model space via efficient mode jumping for GLMMs is introduced. The algorithm is based on that marginal likelihoods can be efficiently calculated within each model. It is recommended that either exact expressions or precise approximations of marginal likelihoods are applied. The suggested algorithm is applied to simulated data, the famous U.S. crime data, protein activity data and epigenetic data and is compared to several existing approaches.

Markov chain Monte Carlo with the Integrated Nested Laplace Approximation

The Integrated Nested Laplace Approximation (INLA) has established itself as a widely used method for approximate inference on Bayesian hierarchical models which can be represented as a latent Gaussian model (LGM). INLA is based on producing an accurate approximation to the posterior marginal distributions of the parameters in the model and some other quantities of interest by using repeated approximations to intermediate distributions and integrals that appear in the computation of the posterior marginals. INLA focuses on models whose latent effects are a Gaussian Markov random field. For this reason, we have explored alternative ways of expanding the number of possible models that can be fitted using the INLA methodology. In this paper, we present a novel approach that combines INLA and Markov chain Monte Carlo (MCMC). The aim is to consider a wider range of models that can be fitted with INLA only when some of the parameters of the model have been fixed. We show how new values of these parameters can be drawn from their posterior by using conditional models fitted with INLA and standard MCMC algorithms, such as Metropolis–Hastings. Hence, this will extend the use of INLA to fit models that can be expressed as a conditional LGM. Also, this new approach can be used to build simpler MCMC samplers for complex models as it allows sampling only on a limited number of parameters in the model. We will demonstrate how our approach can extend the class of models that could benefit from INLA, and how the R-INLA package will ease its implementation. We will go through simple examples of this new approach before we discuss more advanced applications with datasets taken from the relevant literature. In particular, INLA within MCMC will be used to fit models with Laplace priors in a Bayesian Lasso model, imputation of missing covariates in linear models, fitting spatial econometrics models with complex nonlinear terms in the linear predictor and classification of data with mixture models. Furthermore, in some of the examples we could exploit INLA within MCMC to make joint inference on an ensemble of model parameters.

Multivariate spatial covariance models: a conditional approach

Multivariate geostatistics is based on modelling all covariances between all possible combinations of two or more variables at any sets of locations in a continuously indexed domain. Multivariate spatial covariance models need to be built with care, since any covariance matrix that is derived from such a model must be nonnegative-definite. In this article, we develop a conditional approach for spatial-model construction whose validity conditions are easy to check. We start with bivariate spatial covariance models and go on to demonstrate the approach’s connection to multivariate models defined by networks of spatial variables. In some circumstances, such as modelling respiratory illness conditional on air pollution, the direction of conditional dependence is clear. When it is not, the two directional models can be compared. More generally, the graph structure of the network reduces the number of possible models to compare. Model selection then amounts to finding possible causative links in the network. We demonstrate our conditional approach on surface temperature and pressure data, where the role of the two variables is seen to be asymmetric.

Early Quaternary sedimentary processes and palaeoenvironments in the central North Sea

ABSTRACTA number of elongate trough‐like features are observed in the early Quaternary succession of the central North Sea basin. A definitive model of formation for the features remains unclear but the troughs may aid in our understanding of the depositional environment of the early Quaternary. In total, 380 troughs were mapped over 11 000 km2 using continuous 3D seismic data and analysed in conjunction with well log data and understanding of the probable palaeogeographical context. The troughs were formed in a marine setting on the slope of a large clinoform set during a period of rapid progradation. The geometry and infill of the troughs, as well as the marine setting, strongly support a model of repeated density‐driven downslope flows which excavate and then infill the troughs perpendicular to the strike of the slope. A subset of the troughs are observed to form parallel to the strike in such a way that cannot be easily explained by downslope processes alone. A number of possible models are considered for the formation of these along‐slope troughs; here we conclude that the most likely scenario involves modification of the downslope flows by currents which divert the features along‐slope while maintaining the erosive nature of the flow.

Automating Analytics: Forecasting Time Series in Economics and Business

Abstract. With the growing ability of organizations in the public and private sector to collect large volumes of real-time data, the mounting pile of information presents specific challenges for storage, processing, and analysis. Many organizations do need data analysis for the purposes of planning and logistics. Likewise, governments and regulators will need analysis to support policy-making, implementation and controlling. All this leads to the importance of being able to generate large-scale analytics under (sometimes severe) resource constraints. This paper investigates a possible solution – automating analytics with a special focus on forecasting time series. Such approach has the benefit of being able to produce scalable forecasting of thousands of variables with relatively high accuracy for a short period of time and few resources. We first review the literature on time series forecasting with a particular focus on the M, M-2, and M-3 forecasting competition and outline a few major conclusions supported across different empirical studies. The paper then proceeds to explore the typical structure of a time-series variables using Bulgarian GDP growth and show how the ARIMA modeling with a seasonal component can be used to fit economic data of this class. We also review some major approaches to automating forecasting and outline the benefits of selecting the optimal model from a large set of ARIMA alternatives using an information criterion. A possible approach to fit an automated forecasting algorithm on four crucial economic time series from the Bulgarian economy is demonstrated. We use data on GDP growth, inflation, unemployment, and interest rates and fit a large number of possible models. The best ones are selected by taking recourse to the Akaike Information Criterion. The optimal ARIMA models are studied and commented. Forecast accuracy metrics are presented and a few major conclusions and possible model applications are outlined. The paper concludes with directions for further research. Keywords. Automated analytics, Forecasting, Time series, ARIMA, Business forecasting. JEL. C22, C53, E37.

General modeling of saturated AC machines for industrial drives

Purpose – When magnetic saturation in ac machines is evolved, the theory of main flux saturation in d-q axes remains the best. Because of its simplicity, it is the most used in either motoring or generating mode for synchronous or asynchronous machines. Although, it is considered as a global way of introducing the iron saturation, compared to other methods, today, its fidelity has no contest in predicting complex ac machine operations. For this purpose, the aims of this paper consists of modeling these machines whatever the state-space variables values are taking into account the magnetic saturation. Two unified procedures are proposed. The first one deals with a common approach to establishing a complete and detailed model synthesis in d-q axes. The second also presents a unified approach to introducing magnetic saturation of the iron core in the characteristic equations. The analysis takes the salient pole synchronous machine as a general case of study. Then the approaches are extended to undamped and smooth air gap synchronous machines as well as induction machines. The paper aims to discuss these issues. Design/methodology/approach – The present paper, which is a first part of a work under study dealing with a unified method to derive multiple models of saturated ac machines, is intended to the description of an alternative method and its application for induction and synchronous machines. It mainly consists of the following parts: first, after writing the stator and rotor space vector d-q equations, the number of possible models is immediately discussed. By considering the currents and fluxes as state-space variables, 14 models are obtained for AC induction machine (IM and SM). They are classified into three families, current (three), flux (three) and mixed models (eight). Second, in order to easily introduce the magnetic saturation in the 14 developed models, a method is presented. It consists of just elaborating the model with the winding currents as state variables, then deriving all the other models from it. Third, to emphasize the influence of the presence of magnetic saturation, in each model, each inductance along the d and q axes is written with a fundamental expression which exists with or without saturation and an additional one due purely to saturation. Hence the additional terms can be studied and quantified in an easy way or simply removed when linear case is assumed. Fourth, adopting such strategy to write the different coefficients of the models had led to the definition of common saturation factors. In turn, the definition of common saturation factors had allowed the definition of different groups of models within each family. Fifth, an alternative to evaluate the static and dynamic saturation coefficients is also proposed. It is shown that by proper fitting of the experimental magnetizing curve, all saturation coefficients can be written only in terms of which is simply the magnitudes ratio of the magnetizing flux and current. Sixth, although the theory of the main flux saturation is now admitted, an investigation was carried out on a self-excited induction generator and the build-up of voltage and current phases of a standalone alternator, to prove the equivalence between the all developed models. Findings – The number of models based on the state-space variables choice, of a saturated ac machine, is reviewed. A simple method consisting of elaborating just the winding currents model, with magnetic saturation and deriving all the other models from it, is presented. In this study special interest was particularly focussed on either novel models or existing models cited in the literature but cannot be obtained by other approaches. In all cases, if the differential equations of the machine are formulated in terms of a set of variables other than the winding currents, a noticeable reduction in the size of equations may be obtained and consequently less time computing. The approach seems to be able to derive any possible model whatever the state-space variables and the type of the ac machine and hence can be classified as a general approach. Practical implications – The experiments of synchronous and induction machine transients prove the validity of the method. Originality/value – By suitable choice of state-space characteristic vectors among the fluxes and the currents, a synthesis of AC machine models in d-q axes is established. To introduce magnetic saturation in each model, an approach-based uniquely on the elaboration of the winding currents model is exposed and applied. In addition, the analysis gives a detailed classification of all found models taking into account the state variables nature as well as the cross-coupling coefficient considered as a saturation factor. The study is completed with a simple alternative to evaluate all saturation factors by just calculating the static magnetizing inductance.

About the discovery of an explicit model to monitor blood pressure in a non-invasive way

Purpose: The objective of the study was to identify an explicit model to indirectly monitor blood pressure by using the electrocardiography and heart rate variability parameters, and the plethysmography. Those latter signals can be monitored through wearable non-invasive sensors, namely an electrocardiography sensor and a finger pulse oximeter sensor. The developed model was included in a real-time mobile monitoring system to realize a wearable continuous non-invasive arterial pressure monitor. Context: Continuous non-invasive arterial pressure methods can be used to continuously measure arterial blood pressure in real time and without any need for patient's body cannulation. Currently there is a high request for accurate and easy-to-use continuous non-invasive arterial pressure systems. Consequently, an increasing focus on these devices exists. Several non-invasive approaches to blood pressure have been attempted, some of which are described in [1]. Methods: The explicit model was developed under the form of a function by combining heart rate variability parameters and plethysmography measurements. We decided to avail ourselves of a Genetic Programming technique for this regression problem because it can automatically find an explicit model for the relationship between the independent variables and a dependent one, in this case one between the systolic and the diastolic blood pressure values. Therefore, once hypothesized the existence of a nonlinear relationship between heart activity, and thus electrocardiography and heart rate variability parameters, plethysmography and blood pressure values, and chosen a fitness function, we found, from among the huge number of possible models, the one that best describes the fundamental features of this relationship.

Dynamic model averaging in large model spaces using dynamic Occam׳s window

Bayesian model averaging has become a widely used approach to accounting for uncertainty about the structural form of the model generating the data. When data arrive sequentially and the generating model can change over time, Dynamic Model Averaging (DMA) extends model averaging to deal with this situation. Often in macroeconomics, however, many candidate explanatory variables are available and the number of possible models becomes too large for DMA to be applied in its original form. We propose a new method for this situation which allows us to perform DMA without considering the whole model space, but using a subset of models and dynamically optimizing the choice of models at each point in time. This yields a dynamic form of Occam׳s window. We evaluate the method in the context of the problem of nowcasting GDP in the Euro area. We find that its forecasting performance compares well with that of other methods.

An improved convergence rate of A-P reconstruction algorithm and application in signal processing

This paper presents a reconstruction formula in general shift-invariant signal spaces that improve the rate of A-P iterative algorithm. We use the algorithm to show reconstruction of signals from weighted samples and also show that there is better convergence than the old one. We study the algorithm with emphasis on its implementation in field of signal processing, which the signal spaces is sufficiently large to accommodate a large number of possible models. Numerical examples results are furnished to illustrate our results.

On the Geometric Structures with n Points and k Distances

In this paper the geometric structures M(n, k) containing n points in R3 having k distinct distances are investigated. We will show that up to similarity there exist uncountable models M(n, k) and up to pseudo-equivalence the number of possible models for M(n, k) is finite.

Disease Mapping and Regression with Count Data in the Presence of Overdispersion and Spatial Autocorrelation: A Bayesian Model Averaging Approach

This paper applies the generalised linear model for modelling geographical variation to esophageal cancer incidence data in the Caspian region of Iran. The data have a complex and hierarchical structure that makes them suitable for hierarchical analysis using Bayesian techniques, but with care required to deal with problems arising from counts of events observed in small geographical areas when overdispersion and residual spatial autocorrelation are present. These considerations lead to nine regression models derived from using three probability distributions for count data: Poisson, generalised Poisson and negative binomial, and three different autocorrelation structures. We employ the framework of Bayesian variable selection and a Gibbs sampling based technique to identify significant cancer risk factors. The framework deals with situations where the number of possible models based on different combinations of candidate explanatory variables is large enough such that calculation of posterior probabilities for all models is difficult or infeasible. The evidence from applying the modelling methodology suggests that modelling strategies based on the use of generalised Poisson and negative binomial with spatial autocorrelation work well and provide a robust basis for inference.

Variability in color working memory precision reflects inherent stimulus properties

State of the art visual working memory models suggest that resources are not only continuous, but also variable across items and trials. The cause of trial-to-trial variability remains unknown, with several possibilities proposed (e.g., doubly stochastic neural representation). One important possibility is that variation is due to the particular stimulus values presented in a trial. To explore this possibility, Experiment 1 used delayed estimation for color, testing participants at a memory load of one, probing each of 180 colors ten times. We found clear differences among these colors in average recall precision. Experiment 2 replicated a study by van de Berg et al. (2012), and fit their variable-precision model to the results. We averaged the model’s precision estimates for each color, and correlated these averages with the values obtained in Experiment 1. The correlation was highly significant, both overall and for each memory load, suggesting that differences among stimulus values account for a large proportion of the trial-to-trial variance. Experiment 3 investigated one reason why responses for certain colors might be more precise than for others. Participants were asked to identify the most prototypical example of each of seven colors by marking a color wheel. The least frequent selections served as good proxies for color category boundaries. We averaged the trial-to-trial variance estimates within each category for Experiment 1; these estimates correlated significantly with estimates derived in the same way for each color category at each memory load in Experiment 2. These results again suggest that trial variability is stimulus driven, perhaps reflecting categorical effects in color perception. This has important implications for modeling visual working memory, primarily, via the opportunity to account for trial variability with independent estimates of stimulus perception. We discuss a number of possible models employing such an approach. Meeting abstract presented at VSS 2013