In ‘inverse problems’ data from indirect measurements are used to estimate unknown parameters of physical systems. Uncertain data, (possibly vague) prior information on model parameters, and a physical theory relating the model parameters to the observations are the fundamental elements of any inverse problem. Using concepts from probability theory, a consistent formulation of inverse problems ...

For machine learning of an input-output function f from examples, we show it is possible to define an a priori probability density function on the hypothesis space to represent knowledge of the probability distribution of f , even when the hypothesis space H is large (i.e., nonparametric). This allows extension of maximum a posteriori (MAP) estimation methods nonparametric function estimation. ...

This paper proposes a novel merging algorithm in Gaussian mixture probability hypothesis density filter to track close proximity targets. The proposed algorithm is added after GM-PHD recursion, in a condition that more than one target has the same state. The weights of Gaussian components decide whether the components can be utilized to extract states, and the means and covariances of Gaussian ...

Quantitative analysis of the dynamics of tiny cellular and subcellular structures in time-lapse cell microscopy sequences requires the development of a reliable multi-target tracking method capable of tracking numerous similar targets in the presence of high levels of noise, high target density, maneuvering motion patterns and intricate interactions. The linear Gaussian jump Markov system proba...

Although knowing the time of the occurrence of the earthquakes is vital and helpful, unfortunately it is still unpredictable. By the way there is an urgent need to find a method to foresee this catastrophic event. There are a lot of methods for forecasting the time of earthquake occurrence. Another method for predicting that is to know probability density function of time interval between earth...

Conditional probability density functional theory (CP-DFT) determines the ground-state energy of a many-electron system by finding conditional from parallelizable series Kohn-Sham DFT calculations. By directly calculating densities, authors bypass need for an approximate exchange-correlation (XC) functional. CP-DFT is formally exact, but potentials are used in practice. We explore suitable appr...

This paper studies the problem of multiple vehicle cooperative localization with spatial registration in the formulation of the probability hypothesis density (PHD) filter. Assuming vehicles are equipped with proprioceptive and exteroceptive sensors (with biases) to cooperatively localize positions, a simultaneous solution for joint spatial registration and state estimation is proposed. For thi...