Subclass Of Models Research Articles

Overdispersed Nonlinear Regression Models

In this paper we propose nonlinear regression models in the biparametric family of distributions. In this class of models we propose two new classes of overdispersed nonlinear regression models: the first, defined from the overdispersion family of distributionsproposed by Dey, Gelfand, and Peng (1994), and the second from a class of compound distributions. For these models, we develop a Bayesian method in which samples of the posterior distributions are obtained by applying an iterated Metropolis-Hastings algorithmobtained by assuming two groups of parameters, defined by the mean and dispersion regression structures. In the first subclass of models, to improve the performance of the iterated Metropolis-Hastings algorithm, we develop worked variables from the applicationof Fisher scoring algorithm, to build the kernel transition function. A Bayesian method to fit compound regression models is also proposed. Finally, we present an application to neonatal mortality dataset to illustrate the use of the proposed models and the perfor-mance of the Bayesian method to fit the proposed models.

Bayesian Modeling of Sequential Discoveries

We aim at modeling the appearance of distinct tags in a sequence of labeled objects. Common examples of this type of data include words in a corpus or distinct species in a sample. These sequential discoveries are often summarized via accumulation curves, which count the number of distinct entities observed in an increasingly large set of objects. We propose a novel Bayesian method for species sampling modeling by directly specifying the probability of a new discovery, therefore, allowing for flexible specifications. The asymptotic behavior and finite sample properties of such an approach are extensively studied. Interestingly, our enlarged class of sequential processes includes highly tractable special cases. We present a subclass of models characterized by appealing theoretical and computational properties, including one that shares the same discovery probability with the Dirichlet process. Moreover, due to strong connections with logistic regression models, the latter subclass can naturally account for covariates. We finally test our proposal on both synthetic and real data, with special emphasis on a large fungal biodiversity study in Finland. Supplementary materials for this article are available online.

Fixed-dimension renormalization group analysis of conserved surface roughening.

Conserved surface roughening represents a special case of interface dynamics where the total height of the interface is conserved. Recently, it was suggested [Caballero etal., Phys. Rev. Lett. 121, 020601 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.020601] that the original continuum model known as the Conserved Kardar-Parisi-Zhang (CKPZ) equation is incomplete, as additional nonlinearity is not forbidden by any symmetry in d>1. In this work, we perform detailed field-theoretic renormalization group (RG) analysis of a general stochastic model describing conserved surface roughening. Systematic power counting reveals additional marginal interaction at the upper critical dimension, which appears also in the context of molecular beam epitaxy. Depending on the origin of the surface particle's mobility, the resulting model shows two different scaling regimes. If the particles move mainly due to the gravity, the leading dispersion law is ω∼k^{2}, and the mean-field approximation describing a flat interface is exact in any spatial dimension. On the other hand, if the particles move mainly due to the surface curvature, the interface becomes rough with the mean-field dispersion law ω∼k^{4}, and the corrections to scaling exponents must be taken into account. We show that the latter model consist of two subclasses of models that are decoupled in all orders of perturbation theory. Moreover, our RG analysis of the general model reveals that the universal scaling is described by a rougher interface than the CKPZ universality class. The universal exponents are derived within the one-loop approximation in both fixed d and ɛ-expansion schemes, and their relation is discussed. We point out all important details behind these two schemes, which are often overlooked in the literature, and their misinterpretation might lead to inconsistent results.

Das Ophthalmoskopierphantom von Maurice Perrin im Spannungsfeld zwischen Militärmedizin und Ophthalmologie

Simulation phantoms are a subclass of models. They serve to learn a demanding (medical)skill. The l’oeil artificiel ophthalmoscopique, developed in 1866 by the French surgeonMaurice Perrin (1826–1889), is regarded as the first ophthalmoscopy phantom that comesquite close to imitating the natural conditions of the eye during mirroring. Such phantoms aredeveloped in order to support the learner to operate e. g. the hand-held-ophthalmoscope. Intensivepractice on the phantom gives the budding physician more confidence in the future use ofthe mirror in a real doctor-patient ophthalmoscopy situation. Perrin’s phantom was especiallyused to train military doctors in coping with the instrument and to analyse refractive errors.However, 19th century specialists showed only little interest in this kind of skill-training for theophthalmologist-to-be.

Gibbs-type Indian Buffet Processes

We investigate a class of feature allocation models that generalize the Indian buffet process and are parameterized by Gibbs-type random measures. Two existing classes are contained as special cases: the original two-parameter Indian buffet process, corresponding to the Dirichlet process, and the stable (or three-parameter) Indian buffet process, corresponding to the Pitman--Yor process. Asymptotic behavior of the Gibbs-type partitions, such as power laws holding for the number of latent clusters, translates into analogous characteristics for this class of Gibbs-type feature allocation models. Despite containing several different distinct subclasses, the properties of Gibbs-type partitions allow us to develop a black-box procedure for posterior inference within any subclass of models. Through numerical experiments, we compare and contrast a few of these subclasses and highlight the utility of varying power-law behaviors in the latent features.

Geodesic of nonlinear electrodynamics and stable photon orbits

We study the geodesics of charged black holes in polynomial Maxwell Lagrangians, a subclass of models within the nonlinear electrodynamics (NLED). Specifically, we consider black holes in Kruglov, power-law, and Ayon-Beato-Garcia models. Our exploration on the corresponding null bound states reveals that photon can orbit the extremal black holes in stable radii outside the corresponding horizon. The reason behind this is the well-known theorem that a photon in a NLED background propagates along its own {\it effective} geometry. This nonlinearity is able to shift the local minimum of the effective potential away from its corresponding outer horizon. For the null scattering states we obtain corrections to the weak deflection angle off the black holes. We rule out the power-law model to be physical since its deflection angle does not reduce to the Schwarzschild in the limit of the vanishing charge.

Phase-space structure analysis of self-gravitating collisionless spherical systems

In the mean field limit, isolated gravitational systems often evolve towards a steady state through a violent relaxation phase. One question is to understand the nature of this relaxation phase, in particular the role of radial instabilities in the establishment/destruction of the steady profile. Here, through a detailed phase-space analysis based both on a spherical Vlasov solver, a shell code, and a N-body code, we revisit the evolution of collisionless self-gravitating spherical systems with initial power-law density profiles ρ(r) ∝ rn, 0 ≤ n ≤ −1.5, and Gaussian velocity dispersion. Two sub-classes of models are considered, with initial virial ratios η = 0.5 (“warm”) and η = 0.1 (“cool”). Thanks to the numerical techniques used and the high resolution of the simulations, our numerical analyses are able, for the first time, to show the clear separation between two or three well-known dynamical phases: (i) the establishment of a spherical quasi-steady state through a violent relaxation phase during which the phase-space density displays a smooth spiral structure presenting a morphology consistent with predictions from self-similar dynamics, (ii) a quasi-steady-state phase during which radial instabilities can take place at small scales and destroy the spiral structure but do not change quantitatively the properties of the phase-space distribution at the coarse grained level, and (iii) relaxation to a non-spherical state due to radial orbit instabilities for n ≤ −1 in the cool case.

Signature change in loop quantum gravity: Two-dimensional midisuperspace models and dilaton gravity

Models of loop quantum gravity based on real connections have a deformed notion of general covariance, which leads to the phenomenon of signature change. This result is confirmed here in a general analysis of all midisuperspace models without local degrees of freedom. As a subclass of models, 2-dimensional theories of dilaton gravity appear, but a larger set of examples is possible based only on the condition of anomaly freedom. While the classical dilaton gravity models are the only such systems without deformed covariance, they do give rise to signature change when holonomy modifications are included.

An efficient Monte Carlo method for discrete variance contracts

We develop an efficient Monte Carlo method for the valuation of financial contracts on discretely realized variance. We work with a general stochastic volatility model that makes realized variance dependent on the full path of the asset price. The variance contract price is a high-dimensional integral over the fundamental sources of randomness. We identify a two-dimensional manifold that drives most of the uncertainty in realized variance, and we compute the contract price by combining precise integration over this manifold, implemented as fine stratification or deterministic sampling with quasirandom numbers, with conditional Monte Carlo on the remaining dimensions. For a subclass of models and a class of nonlinear payoffs, we derive approximate theoretical results that quantify the variance reduction achieved by our method. Numerical tests for the discretized versions of the widely used Hull–White and Heston models show that the algorithm performs significantly better than a standard Monte Carlo, even for fixed computational budgets.

A smooth subclass of graphical models for chain graph: towards measuring gender gaps

Recent gender literature shows a growing demand of sound statistical methods for analysing gender gaps, for capturing their complexity and for exploring the pattern of relationships among a collection of observable variables selected in order to disentangle the latent trait of gender equity. In this paper we consider parametric Hierarchical Marginal Models applying to binary and categorical data, as a promising statistical tool for gender studies. We explore the potential of Chain Graphical Models, by focusing on a special smooth sub-class of models known as Graphical Models of type II as recently developed (Nicolussi in Marginal parameterizations for conditional independence models and graphical models for categorical data, 2013) , i.e. an advanced methodology for untangling and highlighting any dependence/independence pattern between gender and a set of covariates of mixed nature, either categorical, ordinal or quantitative. With respect to traditional methodologies for treating categorical variables, such as Logistic Regression and Chi-Squared test for contingency table, the proposed model lead to a full multivariate analysis, allowing for isolating the effect of each dependent variable from all other response variables. At the same time, the resulting graph offers an immediate visual idea of the association pattern in the entire set of study variables. The empirical performance of the method is tested by using data from a recent survey about sexual harassment issues inside university, granted by the Equal Opportunities Committee of the University of Milano-Bicocca (Italy).

Chi-Square Mixture of Transformed/Inverse Transformed Gamma Family

In this study, we define the chi-square mixture of transformed gamma distribution which contained some special submodels namely, the chi-square mixture of gamma, Weibull, and exponential mixture distributions. Also, the chi-square mixture of inverse transformed gamma distribution is defined and a class of submodels are deduced, that is, the chi-square mixture of inverse gamma, inverse Weibull, and inverse exponential mixture distributions. For both classes, statistical properties are investigated, that is, mean, variance, skewness and kurtosis using $r$th raw moment. The limiting behavior and special cases are also given to established relationships.

Accelerated expansion from ghost-free bigravity: a statistical analysis with improved generality

We study the background cosmology of the ghost-free, bimetric theory of gravity. We perform an extensive statistical analysis of the model using both frequentist and Bayesian frameworks and employ the constraints on the expansion history of the Universe from the observations of supernovae, the cosmic microwave background and the large scale structure to estimate the model's parameters and test the goodness of the fits. We explore the parameter space of the model with nested sampling to find the best-fit chi-square, obtain the Bayesian evidence, and compute the marginalized posteriors and mean likelihoods. We mainly focus on a class of sub-models with no explicit cosmological constant (or vacuum energy) term to assess the ability of the theory to dynamically cause a late-time accelerated expansion. The model behaves as standard gravity without a cosmological constant at early times, with an emergent extra contribution to the energy density that converges to a cosmological constant in the far future. The model can in most cases yield very good fits and is in perfect agreement with the data. This is because many points in the parameter space of the model exist that give rise to time-evolution equations that are effectively very similar to those of the $\Lambda$CDM. This similarity makes the model compatible with observations as in the $\Lambda$CDM case, at least at the background level. Even though our results indicate a slightly better fit for the $\Lambda$CDM concordance model in terms of the $p$-value and evidence, none of the models is statistically preferred to the other. However, the parameters of the bigravity model are in general degenerate. A similar but perturbative analysis of the model as well as more data will be required to break the degeneracies and constrain the parameters, in case the model will still be viable compared to the $\Lambda$CDM.

On the polynomial complexity of the equivalence checking problem in algebraic models of programs

Algebraic models of programs are considered for which the decidability of the equivalence checking problem is proved. A new equivalence checking algorithm stemmed from the well-known Moore technique for finite state automata is introduced. It is shown that, for some subclasses of models, this algorithm is reduced to a polynomial-time equivalence checking procedure.

Estimating production frontiers and efficiency when output is a discretely distributed economic bad

This article studies the estimation of production frontiers and efficiency scores when the commodity of interest is an economic bad with a discrete distribution. Existing parametric econometric techniques (stochastic frontier methods) assume that output is a continuous random variable but, if output is discretely distributed, then one faces a scenario of model misspecification. Therefore a new class of econometric models has been developed to overcome this problem. The Delaporte subclass of models is studied in detail, and tests of hypotheses are proposed to discriminate among parametric models. In particular, Pearson’s chi-squared test is adapted to construct a new kernel-based consistent Pearson test. A Monte Carlo experiment evaluates the merits of the new model and methods, and these are used to estimate the frontier and efficiency scores of the production of infant deaths in England. Extensions to the model are discussed.

The dynamics of Lemaître–Tolman cosmologies

In this paper we give a coordinate-independent analysis of the dynamics of the spherically symmetric Lemaître–Tolman (LT) cosmologies, emphasizing their relation with the Friedmann–Lemaître (FL) cosmologies. We show that in general, ever-expanding LT cosmologies isotropize at late times, becoming asymptotic to the de Sitter universe or to the Milne universe, depending on whether or not a cosmological constant is present. The rate of isotropization depends significantly on whether Λ > 0 or Λ = 0. We introduce a dimensionless scalar representing the ratio of the Weyl curvature to the Ricci curvature, and show that in both cases it has a finite limit at late times, whose value determines the asymptotic spatial inhomogeneity in various physical quantities. We coin the phrase ‘residual inhomogeneity’ to describe these effects. We also identify the LT cosmologies for which the initial singularity is isotropic, and show that there is a subclass of models that are close-to-FL globally in time and in space.

Axion–dilaton cosmology and dark energy

We discuss a class of flat FRW cosmological models based onD = 4 axion–dilaton gravity universally coupled to cosmological background fluids. Inparticular, we investigate the possibility of recurrent acceleration, which was recentlyshown to be generically realized in a wide class of axion–dilaton models, but in theabsence of cosmological background fluids. We observe that, once we impose theexistence of radiation- and matter-dominated earlier stages of cosmic evolution, theaxion–dilaton dynamics is altered significantly with respect to the case of pureaxion–dilaton gravity. Explicit computations are done considering a universalmetric coupling between the dilaton and the matter fields. As a result we find thatduring the matter-dominated epoch the scalar fields remain either frozen, due tothe large expansion rate, or enter a cosmological scaling regime. In both cases,oscillations of the effective equation of state around the acceleration boundaryvalue are impossible. Models which enter an oscillatory stage in the low redshiftregime, on the other hand, are disfavored by observations. We also comment on theviability of the axion–dilaton system as a candidate for dynamical dark energy.In a certain subclass of models, an intermediate scaling regime is succeeded byeternal acceleration. We also briefly discuss the issue of dependence on initialconditions.

Droplet Shapes for a Class of Models in $$\mathbb{Z}^2 $$ at Zero Temperature

In this work we consider the Wulff construction at zero temperature for a class of Gibbs models and study the shape of the obtained droplets. Considering zero temperature we avoid all difficulties connected with the competition between energy and entropy. It allows us to study a quite wide class of models which provides a variety of shapes. The motivations of the study come from attempts to describe isotropic properties of some models on 2D lattice at zero temperature. The studied models are binary (the spin space is 0,1) with a ferromagnetic behavior such that the potential functions are not equal to zero only for some tiles with size 3×3. In fact, we study herein droplet shapes of a subclass of the ferromagnetic models with potential functions as mentioned above. This subclass of models is defined by a condition called regularity. We call the model classified here as having regular micro-boundaries. Several examples of non-regular models are also presented.

Scalar fields: from domain walls to nanotubes and fulerenes

In this work we review some features of topological defects in field theory models for real scalar fields. We investigate topological defects in models involving one and two or more real scalar fields. In models involving a single field we examine two different subclasses of models, which support one or more topological defects. In models involving two or more real scalar fields, we explore the presence of defects that live inside topological defects, and junctions and networks of defects. In the case of junctions of defects we investigte structures that simulate nanotubes and fulerenes. Our investigations may also be used to describe nonlinear properties of polymers, Langmuir films and optical solitons in fibers.

Cosmological Evolution of String Effective Gravitation with a Dilaton Potential and Higher-Loop Corrections. I

Cosmological evolution is investigated within the framework of low-energy string gravitation with higher-loop corrections to the dilaton coupling functions in the presence of a dilaton potential and a nongravitational source. It is shown that for homogeneous and isotropic models with a flat space, the cosmological system of equations reduces to an autonomous, third-order, dynamical system. Subclasses of models with a constant dilaton, which provide the basis for various cosmological mechanisms of dilaton stabilization, are considered. A class of solutions is distinguished with asymptotic scaling behavior of the energy density of the dilaton field.

Properties of optimal polynomial designs under smoothing spline models

This paper investigates the properties of G-optimal polynomial designs under smoothing spline models. A general formula is derived for the variance function of G-optimal polynomial designs and other designs with minimal support size. Moreover, it is shown by a sequence of propositions that G-optimal polynomial designs remain G-optimal under smoothing spline models for a subclass of models. The results are highlighted in the special cases of cubic and quintic smoothing splines.