In order to estimate model parameters and circumvent possible dif-6 ficulties encountered with the likelihood function, we propose to replace the like-7 lihood in the formula of the posterior distribution by a function depending on a 8 contrast. The properties of the contrast-based (CB) posterior distribution and 9 MAP estimator are studied to understand what the consequences of incorporat-10 i...

The Bayesian Information Criterion (BIC) estimates the order of a Markov chain (with nite alphabet A) from observation of a sample path x 1 ; x 2 ; : : :; x n , as that value k = ^ k that minimizes the sum of the negative logarithm of the k-th order maximum likelihood and the penalty term jAj k (jAj?1) 2 log n: We show that ^ k equals the correct order of the chain, eventually almost surely as ...

In this paper, we consider the problem of estimating stress-strength reliability for inverse Weibull lifetime models having the same shape parameters but different scale parameters. We obtain the maximum likelihood estimator and its asymptotic distribution. Since the classical estimator doesn’t hold explicit forms, we propose an approximate maximum likelihood estimator. The asymptotic confidenc...

We consider the Bayesian inference of a random Gaussian vector in a linear model with a Gaussian model matrix. We derive the maximum a-posteriori (MAP) estimator for this model and show that it can be found using a simple line search over a unimodal function that can be efficiently evaluated. Next, we discuss the application of this estimator in the context of nearoptimal detection of near-Gaus...

Given a sample from a fully specified parametric model, let Zn be a given finite-dimensional statistic for example, an initial estimator or a set of sample moments. We propose to (re-)estimate the parameters of the model by maximizing the likelihood of Zn. We call this the maximum indirect likelihood (MIL) estimator. We also propose a computationally tractable Bayesian version of the estimator ...

This paper joins polynomial chaos theory with Bayesian estimation to recursively estimate the states and unknown parameters of asymptotically stable, linear, time invariant, state-space systems. This paper studies the proposed algorithms from a pole/zero locations perspective. The estimator has fixed pole locations that are independent of the estimation algorithm (and the estimated variables). ...

An important problem in learning Bayesian networks is assessing confidence on the learnt structure. Prior work in constraint-based algorithms focuses on estimating or controlling the False Discovery Rate (FDR) when identifying the skeleton (set of edges without regard of direction) of a network. We present a unified approach to estimation and control of the FDR of Bayesian network skeleton iden...

A Bayesian approach is presented for spatially adaptive nonparametric regression where the regression function is modelled as a mixture of splines. Each component spline in the mixture has associated with it a smoothing parameter which is defined over a local region of the covariate space. These local regions overlap such that individual data points may lie simultaneously in multiple regions. C...

This paper deals with the state estimation of dynamic systems. A recursive linear MMSE estimator is presented as an alternative to Kalman filtering . This estimator has the ability to cope with asynchronous measurements, and to process the data by sets of undefined sizes. It is particularly suitable for fault detection, because the decisions can be based on more data. This is an open door to ro...

Psychophysical experiments have demonstrated that the brain integrates information from multiple sensory cues in a near Bayesian optimal manner. The present study proposes a novel mechanism to achieve this. We consider two reciprocally connected networks, mimicking the integration of heading direction information between the dorsal medial superior temporal (MSTd) and the ventral intraparietal (...