Investments viewed as growth processes

For modeling investment decision situations, we present a mathematical basis that views the cash flow sequences as growth processes. We first emphasize the pedagogical value of the basic model by showing that all traditionally established measures of worth (profitability) as well as the compound interest formulas of financial mathematics can actually be derived from it by simple algebraic manipulations. Then, we argue that the traditional measures fail to recognize the particularities of certain decision situations and point out the need for developing tailor made measures for each specific problem. We demonstrate, using real life examples, our approach for developing new measures and, by incorporating decision variables, practical optimization models from this mathematical basis. © 1995 Taylor & Francis Group, LLC

Including sparse noisy epicardial potential measurements into Bayesian inverse electrocardiography

Imposition of a priori constraints is needed to combat the ill-posedness of the inverse problem of electrocardiography. Solutions to this problem have not yet achieved clinical utility. Extra measurements from catheters inserted into cardiac veins, even though quite sparse, may help increase accuracy and robustness. In this paper, we study various Bayesian methods to incorporate sparse epicardial measurements in solutions to the inverse problem

A Bayesian approach to inclusion and performance analysis of using extra information in bioelectric inverse problems

Due to attenuation and spatial smoothing that occurs in the conducting media, the bioelectric inverse problem of estimating sources from remote measurements is ill-posed and solution requires regularization. Recent studies showed that employing Bayesian methods could help increase accuracy. The basic limitations are the availability of good a priori information about the solution, and the lack of a "good" error metric. In this paper, we employ Bayesian methods, and present the mathematical framework for incorporating additional information in the form of prior statistics, and extra measurements. We also use Bayesian error metrics to evaluate the reconstructions, and select prior models. We apply the methods to inverse electrocardiography problem. The results show that we can improve the reconstructions by including extra information, and Bayesian error metrics are useful in evaluating the results