OBJECTIVE FUNCTIONS FOR OCEAN ACOUSTIC INVERSION DERIVED BY LIKELIHOOD METHODS

2000 ◽  
Vol 08 (02) ◽  
pp. 259-270 ◽  
Author(s):  
CHRISTOPH F. MECKLENBRÄUKER ◽  
PETER GERSTOFT
Keyword(s):  
Inverse Problem ◽  
Objective Function ◽  
Likelihood Function ◽  
Point Of View ◽  
Single Frequency ◽  
Posteriori Probability ◽  
A Posteriori ◽  
Objective Functions ◽  
Unknown Parameters ◽  
A Posteriori Probability

Selection of a suitable objective function is an integral part of the inverse problem, and poor selection can have a strong influence on the inverse result. Objective functions are here derived for many practical occasions such as for single frequency and broadband, with and without knowledge of source strength, and with and without the received signal phase. These objective functions are all derived from a unified approach based on maximum likelihood and additive Gaussian noise models. The assumptions for the objective function are thus clear and the resulting estimator has good properties. From a Bayesian point of view, the solution to the inverse problem is the a posteriori probability distribution of the unknown parameters, which can be found from the likelihood function. Thus using objective functions based on likelihood functions facilitates computing the a posteriori distributions.

scholarly journals Level Set Segmentation of Medical Images Based on Local Region Statistics and Maximum a Posteriori Probability

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Wenchao Cui ◽  
Yi Wang ◽  
Tao Lei ◽  
Yangyu Fan ◽  
Yan Feng
Keyword(s):  
Objective Function ◽  
Level Set ◽  
Bias Field ◽  
Posteriori Probability ◽  
Maximum A Posteriori ◽  
A Posteriori ◽  
Image Domain ◽  
A Posteriori Probability ◽  
Global Criterion ◽  
Field Estimation

This paper presents a variational level set method for simultaneous segmentation and bias field estimation of medical images with intensity inhomogeneity. In our model, the statistics of image intensities belonging to each different tissue in local regions are characterized by Gaussian distributions with different means and variances. According to maximum a posteriori probability (MAP) and Bayes’ rule, we first derive a local objective function for image intensities in a neighborhood around each pixel. Then this local objective function is integrated with respect to the neighborhood center over the entire image domain to give a global criterion. In level set framework, this global criterion defines an energy in terms of the level set functions that represent a partition of the image domain and a bias field that accounts for the intensity inhomogeneity of the image. Therefore, image segmentation and bias field estimation are simultaneously achieved via a level set evolution process. Experimental results for synthetic and real images show desirable performances of our method.

scholarly journals Uncertainty Quantification in Epidemiological Models for COVID-19 Pandemic

2020 ◽  
Author(s):  
Leila Taghizadeh ◽  
Ahmad Karimi ◽  
Clemens Heitzinger
Keyword(s):  
Inverse Modeling ◽  
Posteriori Probability ◽  
Model Parameters ◽  
Epidemiological Models ◽  
Unknown Parameters ◽  
Protective Measures ◽  
A Posteriori Probability ◽  
Estimated Parameters ◽  
Forward And Inverse Modeling ◽  
Inversion Techniques

AbstractThe main goal of this paper is to develop the forward and inverse modeling of the Coronavirus (COVID-19) pandemic using novel computational methodologies in order to accurately estimate and predict the pandemic. This leads to governmental decisions support in implementing effective protective measures and prevention of new outbreaks. To this end, we use the logistic equation and the SIR system of ordinary differential equations to model the spread of the COVID-19 pandemic. For the inverse modeling, we propose Bayesian inversion techniques, which are robust and reliable approaches, in order to estimate the unknown parameters of the epidemiological models. We use an adaptive Markov-chain Monte-Carlo (MCMC) algorithm for the estimation of a posteriori probability distribution and confidence intervals for the unknown model parameters as well as for the reproduction number. Furthermore, we present a fatality analysis for COVID-19 in Austria, which is also of importance for governmental protective decision making. We perform our analyses on the publicly available data for Austria to estimate the main epidemiological model parameters and to study the effectiveness of the protective measures by the Austrian government. The estimated parameters and the analysis of fatalities provide useful information for decision makers and makes it possible to perform more realistic forecasts of future outbreaks.

Ensuring the secrecy of the radar

2021 ◽  
Author(s):  
S.G. Vorona ◽  
S.N. Bulychev
Keyword(s):  
Likelihood Function ◽  
Radio Pulse ◽  
A Priori ◽  
Detection Threshold ◽  
Posteriori Probability ◽  
Echo Signal ◽  
A Posteriori Probability ◽  
Advantages And Disadvantages ◽  
Radio Electronic ◽  
Unknown Signal

The article deals with the issue of stealth of radio-electronic means, energy and structural, radio-electronic masking and ways of its implementation. The structure of the unknown signal for exploration and its parameters, as well as the a posteriori probability of each signal associated with the a priori likelihood function and the cases of its solution. The advantages and disadvantages of broadband signals and their characteristics used in modern radars are considered. On the basis of which conclusions are drawn: LFM radio pulse and a single FCM pulse, used in target tracking modes, has high resolution capabilities in range and radial velocity. The ACF of the FCM pulse has side lobes that raise the target detection threshold, as a result of which radar targets with a weak echo signal can be missed. The considered signals do not provide energy and structural stealth of the radar operation.

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