Decision analysis with approximate probabilities

This paper concerns decisions under uncertainty in which the probabilities of the states of nature are only approximately known. Decision problems involving three states of nature are studied. This is due to the fact that some key issues do not arise in two-state problems, while probability spaces with more than three states of nature are essentially impossible to graph. The primary focus is on two levels of probabilistic information. In one level, the three probabilities are separately rounded to the nearest tenth. This can lead to sets of rounded probabilities which add up to 0.9, 1.0, or 1.1. In the other level, probabilities are rounded to the nearest tenth in such a way that the rounded probabilities are forced to sum to 1.0. For comparison, six additional levels of probabilistic information, previously analyzed, were also included in the present analysis. A simulation experiment compared four criteria for decisionmaking using linearly constrained probabilities (Maximin, Midpoint, Standard Laplace, and Extended Laplace) under the eight different levels of information about probability. The Extended Laplace criterion, which uses a second order maximum entropy principle, performed best overall

Quantification of uncertainty in aerodynamic heating of a reentry vehicle due to uncertain wall and freestream conditions

The primary focus of this study is to demonstrate an efficient approach for uncertainty quantification of surface heat flux to the spherical non-ablating heatshield of a generic reentry vehicle due to epistemic and aleatory uncertainties that may exist in various parameters used in the numerical solution of hypersonic, viscous, laminar blunt-body flows with thermo-chemical non-equilibrium. Two main uncertainty sources were treated in the computational fluid dynamics (CFD) simulations: (1) aleatory uncertainty in the freestream velocity and (2) epistemic uncertainty in the recombination efficiency for a partially catalytic wall boundary condition. The Second-Order Probability utilizing a stochastic response surface obtained with Point-Collocation Non-Intrusive Polynomial Chaos was used for the propagation of mixed (aleatory and epistemic) uncertainties. The uncertainty quantication approach was validated on a stochastic model problem with mixed uncertainties for the prediction of stagnation point heat transfer with Fay-Riddell relation, which included the comparison with direct Monte Carlo sampling results. In the stochastic CFD problem, the uncertainty in surface heat transfer was obtained in terms of intervals at different probability levels at various locations including the stagnation point and the shoulder region. The mixed uncertainty results were compared to the results obtained with a purely aleatory uncertainty analysis to show the difference between two uncertainty quantication approaches. A global sensitivity analysis indicated that the velocity has a stronger contribution to the overall uncertainty in the stagnation point heat transfer for the range of input uncertainties considered in this study --Abstract, page iii

(R1503) Numerical Ultimate Survival Probabilities in an Insurance Portfolio Compounded by Risky Investments

Probability of ultimate survival is one of the central problems in insurance because it is a management tool that may be used to check on the solvency levels of the insurer. In this article, we numerically compute this probability for an insurer whose portfolio is compounded by investments arising from a risky asset. The uncertainty in the celebrated Cramér-Lundberg model is provided by a standard Brownian motion that is independent of the standard Brownian motion in the model for the risky asset. We apply an order four Block-by-block method in conjunction with the Simpson rule to solve the resulting Volterra integral equation of the second kind. The ultimate survival probability is arrived at by taking a linear combination of some two solutions to the Volterra equations. The several numerical examples show that the results are accurate and reliable. The method performs well even when the net profit condition is violated

Evaluation of the ultimate performances of a Ca+ single-ion frequency standard

We numerically evaluate the expected performances of an optical frequency standard at 729 nm based on a single calcium ion. The frequency stability is studied through the Allan deviation and its dependence on the excitation method (single Rabi pulse or two Ramsey pulses schemes) and the laser linewidth are discussed. The minimum Allan deviation that can be expected is estimated to $\sigma_y(\tau) \approx 2.5\times 10^{-15}/\sqrt{\tau}$ with $\tau$ the integration time. The frequency shifts induced by the environmental conditions are evaluated to minimize the uncertainty of the proposed standard by chosing the most suited environment for the ion. If using the odd isotope $^{43}$Ca$^{+}$ and a vessel cooled to 77 K, the expected relative shift is $-2 \times 10^{-16}$ with an uncertainty of $\pm 4\times10^{-16}$, mainly due to the quadrupole shift induced by the unknown static electric field gradient .Comment: soumis le 27/07/04 a Physics Letters

A Real Time Radio Spectrum Scanning Technique Based On The Bayesian Model And Its Comparison With The Frequentist Technique

The proliferation of mobile devices led to an exponential demand for wireless radio spectrum resources. The current fixed spectrum assignment has caused some portions of the radio spectrum to be heavily used whereas others to be scarcely used. This has resulted in underutilization of spectrum resources, and, hence has demanded the need for solutions to address the spectrum scarcity problem. Cognitive radio was proposed as one of the solutions. One of the techniques involved in cognitive radio is the dynamic spectrum access technique. This technique requires the identification of free channels in order to allow secondary users to exploit the spectrum resources. The process of identification of free channels is known as radio spectrum scanning, which is performed by sensing a particular channel in the radio spectrum to determine the presence or absence of a signal. In most of existing studies, the frequentist technique using energy detection with fixed threshold was used to scan the radio spectrum. However, this method comes with a major drawbacks. First, energy detection is unable to distinguish between signals and noise and suffer for high false detection rates. Second, energy detection has high false alarm probability. Finally, frequentist techniques are subject to uncertainty and do not provide real time monitoring/sensing. Therefore, the goal of this thesis is to develop a more efficient scanning technique that deals with uncertainty and scans the radio spectrum in real time and determines its occupancy levels. An enhanced spectrum scanning approach is developed using an efficient spectrum sensing technique: an uncertainty handling Bayesian model along with a Bayesian inferential approach. Two Bayesian models are developed: 1) a simplified model, and 2) an improved model to incorporate the Bayesian inferential approach to estimate the spectrum occupancy level. The performance evaluation of the proposed technique has been done using simulations as well as real experiments. For this purpose, two metrics were used: probability of detection and probability of false alarm. Furthermore, the efficiency of the proposed technique was compared to the efficiency of the frequentist technique, which uses only a spectrum sensing technique to identify the occupancy of the spectrum channels. As expected significant improvements in the spectrum occupancy measurements have been observed with the proposed Bayesian inference method

Configurational Information as Potentially Negative Entropy: The Triple Helix Model

Configurational information is generated when three or more sources of variance interact. The variations not only disturb each other relationally, but by selecting upon each other, they are also positioned in a configuration. A configuration can be stabilized and/or globalized. Different stabilizations can be considered as second-order variation, and globalization as a second-order selection. The positive manifestations and the negative selections operate upon one another by adding and reducing uncertainty, respectively. Reduction of uncertainty in a configuration can be measured in bits of information. The variables can also be considered as dimensions of the probabilistic entropy in the system(s) under study. The configurational information then provides us with a measure of synergy within a complex system. For example, the knowledge base of an economy can be considered as such a synergy in the otherwise virtual (that is, fourth) dimension of a regime

What do Bayesian methods offer population forecasters?

The Bayesian approach has a number of attractive properties for probabilistic forecasting. In this paper, we apply Bayesian time series models to obtain future population estimates with uncertainty for England and Wales. To account for heterogeneity found in the historical data, we add parameters to represent the stochastic volatility in the error terms. Uncertainty in model choice is incorporated through Bayesian model averaging techniques. The resulting predictive distributions from Bayesian forecasting models have two main advantages over those obtained using traditional stochastic models. Firstly, data and uncertainties in the parameters and model choice are explicitly included using probability distributions. As a result, more realistic probabilistic population forecasts can be obtained. Second, Bayesian models formally allow the incorporation of expert opinion, including uncertainty, into the forecast. Our results are discussed in relation to classical time series methods and existing cohort component projections. This paper demonstrates the flexibility of the Bayesian approach to simple population forecasting and provides insights into further developments of more complicated population models that include, for example, components of demographic change