Objective Bayesian Analysis of an Exponential Regression Model with Constrained Parameters Applied to Animal Digestibility

In animal digestibility the proportion of degraded food along the time has usually been modeled as a normal random variable with mean a function of the time and the following three parameters: the proportion of degraded food almost instantaneously, remaining proportion of food to be degraded, and velocity of degradation. The estimation of these parameters has been carried out mainly from a frequentist viewpoint by using the asymptotic distribution of the maximum likelihood estimator. This may give inadmissible estimates, such as values outside of the range of the parameters. This drawback could not appear if a Bayesian approach were adopted. In this article an objective Bayesian analysis is developed and illustrated on real and simulated data.     

Sufficient Reduction in Multivariate Surveillance

The relation between change points in multivariate surveillance is important but seldom considered. The sufficiency principle is here used to clarify the structure of some problems, to find efficient methods, and to determine appropriate evaluation metrics. We study processes where the changes occur simultaneously or with known time lags. The surveillance of spatial data is one example where known time lags can be of interest. A general version of a theorem for the sufficient reduction of processes that change with known time lags is given. A simulation study illustrates the benefits or the methods based on the sufficient statistics.     

A characterization based on conditional expectations

We obtain the necessary and sufficient conditions so that any real function (x) is the conditional expectation E(h(X)/X≥x) of a random variable X with continuous distribution function, where h is a given real, continuous and strictly monotonic function.     

Nonparametric product partition models for multiple change-points analysis

ABSTRACT

We propose an extension of parametric product partition models. We name our proposal nonparametric product partition models because we associate a random measure instead of a parametric kernel to each set within a random partition. Our methodology does not impose any specific form on the marginal distribution of the observations, allowing us to detect shifts of behaviour even when dealing with heavy-tailed or skewed distributions. We propose a suitable loss function and find the partition of the data having minimum expected loss. We then apply our nonparametric procedure to multiple change-point analysis and compare it with PPMs and with other methodologies that have recently appeared in the literature. Also, in the context of missing data, we exploit the product partition structure in order to estimate the distribution function of each missing value, allowing us to detect change points using the loss function mentioned above. Finally, we present applications to financial as well as genetic data.     

A class of bivariate regression models for discrete and/or continuous responses

ABSTRACT

A general class of models for discrete and/or continuous responses is proposed in which joint distributions are constructed via the conditional approach. It is assumed that the distributions of one response and of the other response given the first one belong to exponential family of distributions. Furthermore, the marginal means are related to the covariates by link functions and a dependency structure between the responses is inserted into the model. Estimation methods, diagnostic analysis and a simulation study considering a Bernoulli-exponential model, a particular case of the class, are presented. Finally, this model is used in a real data set.     

Spatial Matching of Multiple Configurations of Points with a Bioinformatics Application

In this article, we present a general model to deal with the problem of matching multiple objects or configurations of points from a Bayesian point of view. We study both labeled and non labeled cases. Our model generalizes, in terms of non singular affine transformations and multiple configurations, previous two-terms matching models. As a practical application in Bioinformatics, we consider data from a microarray experiment of gorilla, bonobo, and human-cultured fibroblasts. We find out the matchings and the best affine transformation between the projections of genes on a two-dimensional space, obtained by a multidimensional scaling technique.     

Convergence of non-linear functionals of smoothed empirical processes and kernel density estimates

We consider regularizations by convolution of the empirical process and study the asymptotic behaviour of non-linear functionals of this process. Using a result for the same type of non-linear functionals of the Brownian bridge, shown in a previous paper [4], and a strong approximation theorem, we prove several results for the p-deviation in estimation of the derivatives of the density. We also study the asymptotic behaviour of the number of crossings of the smoothed empirical process defined by Yukich [17] and of a modified version of the Kullback deviation.     

On the recoding of continuous and bounded indexes to a binomial form: an application to quality-of-life scores

The statistical analysis of patient-reported outcomes (PROs) as endpoints has shown to be of great practical relevance. The resulting scores or indexes from the questionnaires used to measure PROs could be treated as continuous or ordinal. The goal of this study is to propose and evaluate a recoding process of the scores, so that they can be treated as binomial outcomes and, therefore, analyzed using logistic regression with random effects. The general methodology of recoding is based on the observable values of the scores. In order to obtain an optimal recoding, the evaluation of the recoding method is tested for different values of the parameters of the binomial distribution and different probability distributions of the random effects. We illustrate, evaluate and validate the proposed method of recoding with the Short Form-36 (SF-36) Survey and real data. The optimal recoding approach is very useful and flexible. Moreover, it has a natural interpretation, not only for ordinal scores, but also for questionnaires with many dimensions and different profiles, where a common method of analysis is desired, such as the SF-36.     

Symbolic correlation integral

This paper aims to introduce the concept of symbolic correlation integral SC that is extensively used in many scientific fields. The new correlation integral SC avoids the noisy parameter 𝜀 of the classical correlation integral, defined by Grassberger and Procaccia (n class="ref-lnk">nk="_i108" href="#">1983n class="ref-overlay scrollable-ref rs_skip">n class="ref-close" tabindex="0">n>n class="ref-icon">n> n class="hlFld-ContribAuthor">Grassberger, n class="NLM_given-names">P.n>n>, n class="hlFld-ContribAuthor">Procaccia, n class="NLM_given-names">I.n>n> (n class="NLM_year">1983n>). n class="NLM_article-title">Measuring the strangeness of strange attractors.n> Physica D: Nonlinear Phenomena 9(1–2):n class="NLM_fpage">189n>–n class="NLM_lpage">208n>.n class="ref-links">n class="xlinks-container">[Crossref], [Web of Science ®]n> n class="googleScholar-container">, [Google Scholar]n>n>n>n>) and extensively used for constructing correlation-integral-based statistics, as in the BDS test. Once the free parameter 𝜀 disappears, it is possible to construct a nonparametric powerful test for independence that can also be used as a diagnostic tool for model selection. The symbolic correlation integral is also extended to deal with multivariate models, and a test for causality is proposed as an example of the theoretical power of the new concept. With extensive Monte Carlo simulations, the paper shows the good size and power performance of symbolic correlation-integral-based tests.