Search

One regularity condition for the classical Cramer-Rao lower bound (CRLB) of an unbiased estimator to hold is that the support of the likelihood function (LF) should be independent of the parameter to be estimated. This has been shown to be too stringent and the CRLB has been shown to be valid for the case of parameter-dependent support as long as the LF is continuous at the boundary of its support. For the case where the LF is not continuous at the boundary of its support, a new modified CRLB — designated as the Cramer-Rao-Leibniz lower bound (CRLLB) as it relies on the Leibniz integral rule — has been presented for the scalar parameter and measurement case in [3]. The CRLLB for multidimensional parameter and measurements has been developed in [8]. The present work applies the multidimensional CRLLB to n-dimensional measurement noise with the raised fractional cosine and the truncated Laplace distributions inside an (n − 1)-sphere.

Lack of knowledge of the prior distribution in classification problems that operate on small data sets may make the application of Bayes' rule questionable. Uniform or arbitrary priors may provide classification answers that, even in simple examples, may end up contradicting our common sense about the problem. Entropic priors (EPs), via application of the maximum entropy (ME) principle, seem to provide good objective answers in practical cases leading to more conservative Bayesian inferences. EP are derived and applied to classification tasks when only the likelihood functions are available. In this paper, when inference is based only on one sample, we review the use of the EP also in comparison to priors that are obtained from maximization of the mutual information between observations and classes. This last criterion coincides with the maximization of the KL divergence between posteriors and priors that for large sample sets leads to the well-known reference (or Bernardo's) priors. Our comparison on single samples considers both approaches in prospective and clarifies differences and potentials. A combinatorial justification for EP, inspired by Wallis' combinatorial argument for entropy definition, is also included. The application of the EP to sequences (multiple samples) that may be affected by excessive domination of the class with the maximum entropy is also considered with a solution that guarantees posterior consistency. An explicit iterative algorithm is proposed for EP determination solely from knowledge of the likelihood functions. Simulations that compare EP with uniform priors on short sequences are also included.

We apply belief propagation to a Bayesian bipartite graph composed of discrete independent hidden variables and discrete visible variables. The network is the Discrete counterpart of Independent Component Analysis (DICA) and it is manipulated in a factor graph form for inference and learning. A full set of simulations is reported for character images from the MNIST dataset. The results show that the factorial code implemented by the sources contributes to build a good generative model for the data that can be used in various inference modes., Sumbitted for publication (May 2015)

Interaction analysis of ships mooring and maneuvering in harbors is pursued in this paper by using Bayesian probabilistic models. A number of ship-to-ship interactions are deduced from the navigation rules in port areas, and then used to train different Event-based Dynamic Bayesian Networks (E-DBNs). When data of two interacting ships are injected into the network, inference is performed in order to verify if the interaction between the vessels is known or not, and in the latter case actions to preserve the port safety can be taken. Results are drawn in the final part of the paper by including into the networks data provided by a simulator of realistic trajectories relative to an existing port.

We address the problem of modeling complex target behavior using a stochastic model that integrates object dynamics, statistics gathered from the environment and semantic knowledge about the scene. The method exploits prior knowledge to build point-wise polar histograms that provide the ability to forecast target motion to the most likely paths. Physical constraints are included in the model through a ray-launching procedure, while semantic scene segmentation is used to provide a coarser representation of the most likely crossable areas. The model is enhanced with statistics extracted from previously observed trajectories and with nearly-constant velocity dynamics. Information regarding the target's destination may also be included steering the prediction to a predetermined area. Our experimental results, validated in comparison to actual targets' trajectories, demonstrate that our approach can be effective in forecasting objects' behavior in structured scenes.

Human ability to foresee the near future plays a key role in everyone's life to prevent potentially dangerous situations. To be able to make predictions is crucial when people have to interact with the surrounding environment. Modeling such capability can lead to the design of automated warning systems and provide moving robots with an intelligent way of interaction with changing situation. In this work we focus on a typical urban human-scene where we aim at predicting an agent's behavior using a stochastic model. In this approach, we fuse the various factors that would contribute to a human motion in different contexts. Our method uses previously observed trajectories to build point-wise circular distributions that after combination, provide a statistical smooth prediction towards the most likely areas. More specifically, a ray-launching procedure, based on a semantic segmentation, gives a coarse scene representation for collision avoidance; a nearly-constant velocity dynamic model smooths the acceleration progression and knowledge of the agent's destination may further steer the path prediction. Experimental results in structured scenes, validate the effectiveness of the method in predicting paths in comparison to actual trajectories.