A nonparametric ensemble transform method for Bayesian inference

Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian inference is implemented. Sequential Monte Carlo methods rely on importance sampling combined with a resampling step, while EnKFs utilize a linear transformation of Monte Carlo samples based on the classic Kalman filter. While EnKFs have proven to be quite robust even for small ensemble sizes, they are not consistent since their derivation relies on a linear regression ansatz. In this paper, we propose another transform method, which does not rely on any a priori assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables. © 2013, Society for Industrial and Applied Mathematics

Online bayesian inference in some time-frequency representations of non-stationary processes

The use of Bayesian inference in the inference of time-frequency representations has, thus far, been limited to offline analysis of signals, using a smoothing spline based model of the time-frequency plane. In this paper we introduce a new framework that allows the routine use of Bayesian inference for online estimation of the time-varying spectral density of a locally stationary Gaussian process. The core of our approach is the use of a likelihood inspired by a local Whittle approximation. This choice, along with the use of a recursive algorithm for non-parametric estimation of the local spectral density, permits the use of a particle filter for estimating the time-varying spectral density online. We provide demonstrations of the algorithm through tracking chirps and the analysis of musical data.

How large is congressional dependence in agriculture. Bayesian inference about ‘scale’ and ‘scope’ in measuring a spatial externality

The political economy literature on agriculture emphasizes influence over political outcomes via lobbying conduits in general, political action committee contributions in particular and the pervasive view that political preferences with respect to agricultural issues are inherently geographic. In this context, ‘interdependence’ in Congressional vote behaviour manifests itself in two dimensions. One dimension is the intensity by which neighboring vote propensities influence one another and the second is the geographic extent of voter influence. We estimate these facets of dependence using data on a Congressional vote on the 2001 Farm Bill using routine Markov chain Monte Carlo procedures and Bayesian model averaging, in particular. In so doing, we develop a novel procedure to examine both the reliability and the consequences of different model representations for measuring both the ‘scale’ and the ‘scope’ of spatial (geographic) co-relations in voting behaviour.

Transreal logical space of all propositions

Transreal numbers provide a total semantics containing classical truth values, dialetheaic, fuzzy and gap values. A paraconsistent Sheffer Stroke generalises all classical logics to a paraconsistent form. We introduce logical spaces of all possible worlds and all propositions. We operate on a proposition, in all possible worlds, at the same time. We define logical transformations, possibility and necessity relations, in proposition space, and give a criterion to determine whether a proposition is classical. We show that proofs, based on the conditional, infer gaps only from gaps and that negative and positive infinity operate as bottom and top values.

Logical and epistemic foundationalism about grounding: the triviality of facts and principles

In this paper, I seek to undermine G.A. Cohen’s polemical use of a metaethical claim he makes in his article, ‘Facts and Principles’, by arguing that that use requires an unsustainable equivocation between epistemic and logical grounding. I begin by distinguishing three theses that Cohen has offered during the course of his critique of Rawls and contractualism more generally, the foundationalism about grounding thesis, the justice as non-regulative thesis, and the justice as all-encompassing thesis, and briefly argue that they are analytically independent of each other. I then offer an outline of the foundationalism about grounding thesis, characterising it, as Cohen does, as a demand of logic. That thesis claims that whenever a normative principle is dependent on a fact, it is so dependent in virtue of some other principle. I then argue that although this is true as a matter of logic, it, as Cohen admits, cannot be true of actual justifications, since logic cannot tell us anything about the truth as opposed to the validity of arguments. Facts about a justification cannot then be decisive for whether or not a given argument violates the foundationalism about grounding thesis. As long as, independently of actual justifications, theorists can point to plausible logically grounding principles, as I argue contractualists can, Cohen’s thesis lacks critical bite.

Robust inference in an heteroscedastic measurement error model

In this paper we deal with robust inference in heteroscedastic measurement error models Rather than the normal distribution we postulate a Student t distribution for the observed variables Maximum likelihood estimates are computed numerically Consistent estimation of the asymptotic covariance matrices of the maximum likelihood and generalized least squares estimators is also discussed Three test statistics are proposed for testing hypotheses of interest with the asymptotic chi-square distribution which guarantees correct asymptotic significance levels Results of simulations and an application to a real data set are also reported (C) 2009 The Korean Statistical Society Published by Elsevier B V All rights reserved

Inference From Aging Information

For many learning tasks the duration of the data collection can be greater than the time scale for changes of the underlying data distribution. The question we ask is how to include the information that data are aging. Ad hoc methods to achieve this include the use of validity windows that prevent the learning machine from making inferences based on old data. This introduces the problem of how to define the size of validity windows. In this brief, a new adaptive Bayesian inspired algorithm is presented for learning drifting concepts. It uses the analogy of validity windows in an adaptive Bayesian way to incorporate changes in the data distribution over time. We apply a theoretical approach based on information geometry to the classification problem and measure its performance in simulations. The uncertainty about the appropriate size of the memory windows is dealt with in a Bayesian manner by integrating over the distribution of the adaptive window size. Thus, the posterior distribution of the weights may develop algebraic tails. The learning algorithm results from tracking the mean and variance of the posterior distribution of the weights. It was found that the algebraic tails of this posterior distribution give the learning algorithm the ability to cope with an evolving environment by permitting the escape from local traps.

Improved likelihood inference for the shape parameter in Weibull regression

We obtain adjustments to the profile likelihood function in Weibull regression models with and without censoring. Specifically, we consider two different modified profile likelihoods: (i) the one proposed by Cox and Reid [Cox, D.R. and Reid, N., 1987, Parameter orthogonality and approximate conditional inference. Journal of the Royal Statistical Society B, 49, 1-39.], and (ii) an approximation to the one proposed by Barndorff-Nielsen [Barndorff-Nielsen, O.E., 1983, On a formula for the distribution of the maximum likelihood estimator. Biometrika, 70, 343-365.], the approximation having been obtained using the results by Fraser and Reid [Fraser, D.A.S. and Reid, N., 1995, Ancillaries and third-order significance. Utilitas Mathematica, 47, 33-53.] and by Fraser et al. [Fraser, D.A.S., Reid, N. and Wu, J., 1999, A simple formula for tail probabilities for frequentist and Bayesian inference. Biometrika, 86, 655-661.]. We focus on point estimation and likelihood ratio tests on the shape parameter in the class of Weibull regression models. We derive some distributional properties of the different maximum likelihood estimators and likelihood ratio tests. The numerical evidence presented in the paper favors the approximation to Barndorff-Nielsen`s adjustment.

Inference and local influence assessment in skew-normal null intercept measurement error model

In this article, we discuss inferential aspects of the measurement error regression models with null intercepts when the unknown quantity x (latent variable) follows a skew normal distribution. We examine first the maximum-likelihood approach to estimation via the EM algorithm by exploring statistical properties of the model considered. Then, the marginal likelihood, the score function and the observed information matrix of the observed quantities are presented allowing direct inference implementation. In order to discuss some diagnostics techniques in this type of models, we derive the appropriate matrices to assessing the local influence on the parameter estimates under different perturbation schemes. The results and methods developed in this paper are illustrated considering part of a real data set used by Hadgu and Koch [1999, Application of generalized estimating equations to a dental randomized clinical trial. Journal of Biopharmaceutical Statistics, 9, 161-178].

Epsilon Birnbaum-Saunders distribution family: properties and inference

In this paper we introduce a new extension for the Birnbaum-Saunder distribution based on the family of the epsilon-skew-symmetric distributions studied in Arellano-Valle et al. (J Stat Plan Inference 128(2):427-443, 2005). The extension allows generating Birnbaun-Saunders type distributions able to deal with extreme or outlying observations (Dupuis and Mills, IEEE Trans Reliab 47:88-95, 1998). Basic properties such as moments and Fisher information matrix are also studied. Results of a real data application are reported illustrating good fitting properties of the proposed model.

Improved likelihood inference in beta regression

We consider the issue of performing accurate small-sample likelihood-based inference in beta regression models, which are useful for modelling continuous proportions that are affected by independent variables. We derive small-sample adjustments to the likelihood ratio statistic in this class of models. The adjusted statistics can be easily implemented from standard statistical software. We present Monte Carlo simulations showing that inference based on the adjusted statistics we propose is much more reliable than that based on the usual likelihood ratio statistic. A real data example is presented.

Bayesian inference for a skew-normal IRT model under the centred parameterization

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is interest in studying latent variables. These latent variables are directly considered in the Item Response Models (IRM) and they are usually called latent traits. A usual assumption for parameter estimation of the IRM, considering one group of examinees, is to assume that the latent traits are random variables which follow a standard normal distribution. However, many works suggest that this assumption does not apply in many cases. Furthermore, when this assumption does not hold, the parameter estimates tend to be biased and misleading inference can be obtained. Therefore, it is important to model the distribution of the latent traits properly. In this paper we present an alternative latent traits modeling based on the so-called skew-normal distribution; see Genton (2004). We used the centred parameterization, which was proposed by Azzalini (1985). This approach ensures the model identifiability as pointed out by Azevedo et al. (2009b). Also, a Metropolis Hastings within Gibbs sampling (MHWGS) algorithm was built for parameter estimation by using an augmented data approach. A simulation study was performed in order to assess the parameter recovery in the proposed model and the estimation method, and the effect of the asymmetry level of the latent traits distribution on the parameter estimation. Also, a comparison of our approach with other estimation methods (which consider the assumption of symmetric normality for the latent traits distribution) was considered. The results indicated that our proposed algorithm recovers properly all parameters. Specifically, the greater the asymmetry level, the better the performance of our approach compared with other approaches, mainly in the presence of small sample sizes (number of examinees). Furthermore, we analyzed a real data set which presents indication of asymmetry concerning the latent traits distribution. The results obtained by using our approach confirmed the presence of strong negative asymmetry of the latent traits distribution. (C) 2010 Elsevier B.V. All rights reserved.

Bayesian Estimation of the Logistic Positive Exponent IRT Model

A Bayesian inference approach using Markov Chain Monte Carlo (MCMC) is developed for the logistic positive exponent (LPE) model proposed by Samejima and for a new skewed Logistic Item Response Theory (IRT) model, named Reflection LPE model. Both models lead to asymmetric item characteristic curves (ICC) and can be appropriate because a symmetric ICC treats both correct and incorrect answers symmetrically, which results in a logical contradiction in ordering examinees on the ability scale. A data set corresponding to a mathematical test applied in Peruvian public schools is analyzed, where comparisons with other parametric IRT models also are conducted. Several model comparison criteria are discussed and implemented. The main conclusion is that the LPE and RLPE IRT models are easy to implement and seem to provide the best fit to the data set considered.

Inference for a skew extension of the Grubbs model

In this paper, we discuss inferential aspects for the Grubbs model when the unknown quantity x (latent response) follows a skew-normal distribution, extending early results given in Arellano-Valle et al. (J Multivar Anal 96:265-281, 2005b). Maximum likelihood parameter estimates are computed via the EM-algorithm. Wald and likelihood ratio type statistics are used for hypothesis testing and we explain the apparent failure of the Wald statistics in detecting skewness via the profile likelihood function. The results and methods developed in this paper are illustrated with a numerical example.