A. NONLINEAR MAP INTERVAL ESTIMATION We shall consider two problems related to the equations specifying the nonlinear interval estimator. In the first part, we shall discuss a method for solving these equations which involves the optimum nonlinear realizable filter. In the second part, we shall present a technique for determining the optimum nonlinear realizable filter from the equations specif...

This work proposed a real-time 3D map building system based on the visual odometry information derived from a Multi-Camera hardware. The accurate odometry information and images derived from the proposed intuitive Multi-Camera hardware, so called Multi-Camera Unit (MCU), are used as an input for the 3D map building process which cooperates the FastSLAM algorithm as a map and path estimator. Exp...

The Liu estimator has consistently been demonstrated to be an attractive shrinkage method for reducing the effects of multicollinearity. The Poisson regression model is a well-known model in applications when the response variable consists of count data. However, it is known that multicollinearity negatively affects the variance of the maximum likelihood estimator (MLE) of the Poisson regressio...

Inverse sampling design is generally considered to be appropriate technique when the population is divided into two subpopulations, one of which contains only few units. In this paper, we derive the Horvitz-Thompson estimator for the population mean under inverse sampling designs, where subpopulation sizes are known. We then introduce an alternative unbiased estimator, corresponding to post-st...

Dynamic mode decomposition (DMD) is an efficient tool for decomposing spatio-temporal data into a set of low-dimensional modes, yielding the oscillation frequencies and growth rates physically significant modes. In this paper, we propose novel DMD model that can be used dynamical systems affected by multiplicative noise. We first derive maximum posteriori (MAP) estimator data-based linear syste...

We derive analytical expressions for the bias of the Jarzynski free-energy estimator from N nonequilibrium work measurements, for a generic work distribution. To achieve this, we map the estimator onto the random energy model in a suitable scaling limit parametrized by (logN)/μ, where μ measures the width of the lower tail of the work distribution, and then compute the finite-N corrections to t...

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...

We study the effect of imperfect subtraction of the Sunyaev-Zel’dovich effect (SZE) using a robust and non-parametric method to estimate the SZE residual in the Planck channels. We include relativistic corrections to the SZE, and present a simple fitting formula for the SZE temperature dependence for the Planck channels. We show how the relativistic corrections constitute a serious problem for ...

The paper aims at contrasting two different ways of incorporating a-priori information in parameter estimation, i.e. hard-constrained and soft-constrained estimation. Hardconstrained estimation can be interpreted, in the Bayesian framework, as Maximum A-posteriori Probability (MAP) estimation with uniform prior distribution over the constraining set, and amounts to a constrained Least-Squares (...