Related papers: On Model Selection in Cosmology
Based on the cosmological principle only, the method of describing the evolution of the Universe, called cosmography, is in fact a kinematics of cosmological expansion. The effectiveness of cosmography lies in the fact that it allows, based…
[Abridged] Some cosmological theories propose that the observable universe is a small part of a much larger universe in which parameters describing the low-energy laws of physics vary from region to region. How can we reasonably assess a…
Engineers are often faced with the decision to select the most appropriate model for simulating the behavior of engineered systems, among a candidate set of models. Experimental monitoring data can generate significant value by supporting…
Hypothesis testing and model choice are quintessential questions for statistical inference and while the Bayesian paradigm seems ideally suited for answering these questions, it faces difficulties of its own ranging from prior modelling to…
We review observational tests for the homogeneity of the Universe on large scales. Redshift and peculiar velocity surveys, radio sources, the X-Ray Background, the Lyman-$\alpha$ forest and the Cosmic Microwave Background are used to set…
It can be important in Bayesian analyses of complex models to construct informative prior distributions which reflect knowledge external to the data at hand. Nevertheless, how much prior information an analyst can elicit from an expert will…
Using the Bayesian theory of model comparison, a new cosmological model due to John and Joseph [M. V. John and K. Babu Joseph, Phys. Rev. D 61, 87304 (2000)] is compared with the standard \Omega_{\Lambda} \neq 0 cosmological model. Their…
Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…
Hierarchical models are increasingly used in many applications. Along with this increased use comes a desire to investigate whether the model is compatible with the observed data. Bayesian methods are well suited to eliminate the many…
Often the goal of model selection is to choose a model for future prediction, and it is natural to measure the accuracy of a future prediction by squared error loss. Under the Bayesian approach, it is commonly perceived that the optimal…
Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…
Linear models with a growing number of parameters have been widely used in modern statistics. One important problem about this kind of model is the variable selection issue. Bayesian approaches, which provide a stochastic search of…
This paper compares classical parametric methods with recently developed Bayesian methods for system identification. A Full Bayes solution is considered together with one of the standard approximations based on the Empirical Bayes paradigm.…
Consider the setting where there are B>1 candidate statistical models, and one is interested in model selection. Two common approaches to solve this problem are to select a single model or to combine the candidate models through model…
Comparisons are made for the amount of agreement of the composite likelihood information criteria and their full likelihood counterparts when making decisions among the fits of different models, and some properties of penalty term for…
Conventional likelihood-based information criteria for model selection rely on the distribution assumption of data. However, for complex data that are increasingly available in many scientific fields, the specification of their underlying…
Demographic studies of cosmic populations must contend with measurement errors and selection effects. We survey some of the key ideas astronomers have developed to deal with these complications, in the context of galaxy surveys and the…
Genetic algorithms are a powerful tool in optimization for single and multi-modal functions. This paper provides an overview of their fundamentals with some analytical examples. In addition, we explore how they can be used as a parameter…
A key science goal of upcoming dark energy surveys is to seek time evolution of the dark energy. This problem is one of {\em model selection}, where the aim is to differentiate between cosmological models with different numbers of…
We consider problems in model selection caused by the geometry of models close to their points of intersection. In some cases---including common classes of causal or graphical models, as well as time series models---distinct models may…