Optimum Nonlinear Signal Detection and Estimation in the Presence of Ultrasonic Speckle

1992 ◽  
Vol 14 (3) ◽  
pp. 249-275 ◽  
Author(s):  
Constantine Kotropoulos ◽  
Ioannis Pitas
Keyword(s):  
Decision Rules ◽  
Random Variable ◽  
Optimal Decision ◽  
Posteriori Probability ◽  
Unified Approach ◽  
A Posteriori Probability ◽  
Ultrasonic Speckle ◽  
Ml Estimator ◽  
Nonlinear Signal ◽  
Speckle Filtering

A unified approach to the design of nonlinear filters for speckle suppression in ultrasound B-mode images is presented. The detection of the (lesion) signal is formulated as a binary hypothesis-testing problem. The structure of the optimal decision rules is derived both in the case where the lesion signal is assumed either a constant or random variable. In the case of a constant signal, the maximum likelihood (ML) estimator and the optimal L-estimator are derived. In the case of a random lesion signal, the maximum a posteriori probability estimator of the lesion signal has also been found. Experimental results verify the superiority of the proposed ML-estimator and the L-estimator over the straightforward choice of an arithmetic mean for speckle filtering in simulated tissue mimicking phantom ultrasound B-mode images.

scholarly journals МЕТОД АВТОМАТИЧЕСКОЙ КЛАСТЕРИЗАЦИИ ДАННЫХ ДИСТАНЦИОННОГО ЗОНДИРОВАНИЯ

2019 ◽  
pp. 64-75
Author(s):  
Ирина Карловна Васильева ◽  
Анатолий Владиславович Попов
Keyword(s):  
A Priori ◽  
Decision Rules ◽  
Remote Sensing Data ◽  
Statistical Characteristics ◽  
Posteriori Probability ◽  
Training Procedure ◽  
A Posteriori Probability ◽  
Good Convergence ◽  
Empirical Distributions ◽  
Automatic Clustering

The subject matter of the article is the methods of automatic clustering of remote sensing data under conditions of a priori uncertainty regarding the number of observed object classes and the statistical characteristics of the signatures of classes. The aim is to develop a method for approximating multimodal empirical distributions of observational data to construct decision rules for pixel-by-pixel statistical classification procedures, as well as to investigate the effectiveness of this method for automatically classifying objects on synthesized and real images. The tasks to be solved are: to develop and implement a procedure for splitting a mixture of basic distributions, while ensuring the following requirements: the absence of a preliminary data analysis stage in order to select optimal initial approximations; a good convergence of the method and the ability to automatically refine the list of classes by combining indistinguishable or poorly distinguishable components of the mixture into a single cluster; to synthesize test images with a specified number of objects and known data distributions for each object; to evaluate the effectiveness of the developed method for automatic classification by the criterion of the probability of correct recognition; to evaluate the results of automatic clustering of real images. The methods used are methods of stochastic simulation, methods of approximation of empirical distributions, statistical methods of recognition, methods of probability theory and mathematical statistics. The following results have been obtained. A method for automatic splitting of a mixture of Gaussian distributions to construct decision thresholds according to the maximal a posteriori probability criterion was proposed. The results of the automatic forming the list of classes and their probabilistic descriptions, as well as the results of the clustering both test images and satellite ones are given. It is shown that the developed method is quite effective and can be used to determine the number of objects’ classes as well as their stochastic characteristics’ mathematical description for pattern recognition tasks and cluster analysis. Conclusions. The scientific novelty of the results obtained is that the proposed approach makes it possible directly during the “unsupervised” training procedure to evaluate the distinguishability of classes and exclude indistinguishable objects from the list of classes.

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.

scholarly journals Stochastic Comparative Statics in Markov Decision Processes

2021 ◽  
Author(s):  
Bar Light
Keyword(s):  
Markov Decision Processes ◽  
Dynamic Pricing ◽  
Optimization Problems ◽  
Transition Probability ◽  
Random Variable ◽  
Comparative Statics ◽  
Decision Processes ◽  
Optimal Decision ◽  
Initial State ◽  
Markov Decision

In multiperiod stochastic optimization problems, the future optimal decision is a random variable whose distribution depends on the parameters of the optimization problem. I analyze how the expected value of this random variable changes as a function of the dynamic optimization parameters in the context of Markov decision processes. I call this analysis stochastic comparative statics. I derive both comparative statics results and stochastic comparative statics results showing how the current and future optimal decisions change in response to changes in the single-period payoff function, the discount factor, the initial state of the system, and the transition probability function. I apply my results to various models from the economics and operations research literature, including investment theory, dynamic pricing models, controlled random walks, and comparisons of stationary distributions.

Bank's Portfolio Management under Uncertainty

1992 ◽  
Vol 36 (2) ◽  
pp. 30-38
Author(s):  
Subarna K. Samanta ◽  
Ali H. Mohamad-Zadeh
Keyword(s):  
Inventory Management ◽  
Commercial Bank ◽  
Expected Utility ◽  
Portfolio Management ◽  
Decision Rules ◽  
Optimal Decision ◽  
Net Income ◽  
Major Objective ◽  
Excess Reserves

The major objective of this paper is to derive a set of optimal decision rules (for asset or inventory management) for a commercial bank operating under uncertain circumstances (subject to stochastic deposit loss). The bank is assumed to be maximizing the expected utility derived from it's net income. This objective is realized by the marginal conditions of the model. It shows how and under what conditions, the banker should expand loans at the expense of securities and/or excess reserves and how he adjusts to de-regulations and how the change in uncertainty about the deposit loss affects him.

Sign in / Sign up

Export Citation Format

Share Document