Magnetic Resonance Diffusion Tensor Imaging (MR–DTI) is a noninvasive in vivo method capable of examining the structure of human brain, providing information about the position and orientation of the neural tracts. After a short introduction to the principles of MR–DTI, this paper describes the steps of the proposed neural tract visualization technique based on the DTI data. The cornerstone of the algorithm is a texture diffusion procedure modeled mathematically by the problem for the Allen–Cahn...

Most published research on the comparison between medical treatment options merely compares the results (effectiveness and cost) obtained for each treatment group. The present work proposes the incorporation of other patient characteristics into the analysis. Most of the studies carried out in this context assume normality of both costs and effectiveness. In practice, however, the data are not always distributed according to this assumption. Alternative models have to be developed.In this paper,...

The problem of approximating mixtures of distributions has received considerable attention recently. In this paper we consider problems of estimating the mixing proportions of a finite mixture from a Bayesian perspective. The problems which arise from this methodology are basically approximations of finite measures of distributions. We propose two approximating methods and prove that under certain conditions both methods are asymptotically equivalent to a third method, which turns out to be simpler...

En el presente artículo se utiliza el método de maximización de la información desconocida para deducir las distribuciones inicial y final de referencia cuando se trata de hacer inferencias sobre el coeficiente de correlación de una población normal bivariante.

Testing that some regression coefficients are equal to zero is an important problem in many applications. Homoscedasticity is not necessarily a realistic condition in this setting and, as a consequence, no frequentist test there exist. Approximate tests have been proposed. In this paper a Bayesian analysis of this problem is carried out, from a default Bayesian model choice perspective. Explicit expressions for intrinsic priors are provided, and it is shown that the corresponding Bayes factor is...

Dans Bernard & Charron (1996), nous avons proposé une nouvelle méthode, l'Analyse Implicative Bayésienne (AIB), pour l'étude des dépendances orientées entre deux variables binaires, méthode qui permet de conclure en terme de quasi-implication entre modalités des variables. Nous étendons ici cette méthode au cas d'un tableau de contingence A × B quelconque avec le problème de la mesure du degré de quasi-adéquation des données à un modèle logique donné. Au niveau descriptif, la méthode repose...

La réussite à l'épreuve A implique-t-elle, approximativement, la réussite à l'épreuve B ? Parmi les indices descriptifs proposés pour mesurer de telles dépendances orientées, nous considérons l'indice H de Loevinger, qui s'exprime simplement en termes des taux de liaison entre modalités. A partir de cet indice, nous définissons les notions de quasi-implication, de quasi-équivalence et de quasi-indépendance dans un tableau de contingence 2 x 2. Cependant, les méthodes inductives correspondantes,...

This paper presents in a simple and unified framework the Least-Squares approximation of posterior expectations. Particular structures of the sampling process and of the prior distribution are used to organize and to generalize previous results. The two basic structures are obtained by considering unbiased estimators and exchangeable processes. These ideas are applied to the estimation of the mean. Sufficient reduction of the data is analysed when only the Least-Squares approximation is involved....

In this paper the likelihood function is considered to be the primary source of the objectivity of a Bayesian method. The necessity of using the expected behaviour of the likelihood function for the choice of the prior distribution is emphasized. Numerical examples, including seasonal adjustment of time series, are given to illustrate the practical utility of the common-sense approach to Bayesian statistics proposed in this paper.

For inferences from random-effect models Lee and Nelder (1996) proposed to use hierarchical likelihood (h-likelihood). It allows influence from models that may include both fixed and random parameters. Because of the presence of unobserved random variables h-likelihood is not a likelihood in the Fisherian sense. The Fisher likelihood framework has advantages such as generality of application, statistical and computational efficiency. We introduce an extended likelihood framework and discuss why...

Real valued $M$-estimators ${\widehat{\theta }}_n:=min{\sum }_1^n\rho (Y_i-\tau \left(\theta \right))$ in a statistical model with observations $Y_i\sim F_{{\theta }_0}$ are replaced by ${ℝ}^p$-valued $M$-estimators ${\widehat{\beta }}_n:=min{\sum }_1^n\rho (Y_i-\tau \left(u\left(z_i^T\beta \right)\right))$ in a new model with observations $Y_i\sim F_{u\left(z_i^t{\beta }_0\right)}$, where $z_i\in {ℝ}^p$ are regressors, ${\beta }_0\in {ℝ}^p$ is a structural parameter and $u:ℝ\to ℝ$ a structural function of the new model. Sufficient conditions for the consistency of ${\widehat{\beta }}_n$ are derived, motivated by the sufficiency conditions for the simpler “parent estimator” ${\widehat{\theta }}_n$. The result is a general method of consistent estimation in a class of nonlinear (pseudolinear) statistical problems. If...

En este trabajo se acomete una generalización de la definición de Shannon-Lindley para la información esperada proporcionada por un experimento que presupone la existencia de estratificación en el espacio muestral. Ante la evidente dificultad de cálculo de la información esperada en la situación planteada -dificultad que se deriva de la existencia de un vector como parámetro de interés y de un resultado muestral que es un conjunto de muestras obtenidas de poblaciones distintas- en este artículo...

We consider a deconvolution problem of estimating a signal blurred with a random noise. The noise is assumed to be a stationary Gaussian process multiplied by a weight function function εh where h ∈ L2(R1) and ε is a small parameter. The underlying solution is assumed to be infinitely differentiable. For this model we find asymptotically minimax and Bayes estimators. In the case of solutions having finite number of derivatives similar results were obtained in [G.K. Golubev and R.Z. Khasminskii,...

The problems of minimax mutual prediction are considered for binomial and multinomial random variables and for sums of limited random variables with unknown distribution. For the loss function being a linear combination of quadratic losses minimax mutual predictors are determined where the parameters of predictors are obtained by numerical solution of some equations.

The problem of minimax mutual prediction is considered for multinomial random variables with the loss function being a linear combination of quadratic losses connected with prediction of particular variables. The basic parameter of the minimax mutual predictor is determined by numerical solution of some equation.