Extreme lower probabilities

We consider lower probabilities on finite possibility spaces as models for the uncertainty about the state. These generalizations of classical probabilities can have some interesting properties; for example: k-monotonicity, avoiding sure loss, coherence, permutation invariance. The sets formed by all the lower probabilities satisfying zero or more of these properties are convex. We show how the extreme points and rays of these sets ─ the extreme lower probabilities ─ can be calculated and we give an illustration of our results

Extreme lower probabilities

We consider lower probabilities on finite possibility spaces as models for the uncertainty about the state. These generalizations of classical probabilities can have some interesting properties; for example: k-monotonicity, avoiding sure loss, coherence, permutation invariance. The sets formed by all the lower probabilities satisfying zero or more of these properties are convex. We show how the extreme points and rays of these sets ─ the extreme lower probabilities ─ can be calculated and we give an illustration of our results

Extreme lower probabilities

We consider lower probabilities on finite possibility spaces as models for the uncertainty about the state. These generalizations of classical probabilities can have some interesting properties; for example: k-monotonicity, avoiding sure loss, coherence, permutation invariance. The sets formed by all the lower probabilities satisfying zero or more of these properties are convex. We show how the extreme points and rays of these sets -- the extreme lower probabilities -- can be calculated and we give an illustration of our results

Quantile-based bias correction and uncertainty quantification of extreme event attribution statements

Extreme event attribution characterizes how anthropogenic climate change may have influenced the probability and magnitude of selected individual extreme weather and climate events. Attribution statements often involve quantification of the fraction of attributable risk (FAR) or the risk ratio (RR) and associated confidence intervals. Many such analyses use climate model output to characterize extreme event behavior with and without anthropogenic influence. However, such climate models may have biases in their representation of extreme events. To account for discrepancies in the probabilities of extreme events between observational datasets and model datasets, we demonstrate an appropriate rescaling of the model output based on the quantiles of the datasets to estimate an adjusted risk ratio. Our methodology accounts for various components of uncertainty in estimation of the risk ratio. In particular, we present an approach to construct a one-sided confidence interval on the lower bound of the risk ratio when the estimated risk ratio is infinity. We demonstrate the methodology using the summer 2011 central US heatwave and output from the Community Earth System Model. In this example, we find that the lower bound of the risk ratio is relatively insensitive to the magnitude and probability of the actual event.Comment: 28 pages, 4 figures, 3 table

Assessing statistical significance of periodogram peaks

The least-squares (or Lomb-Scargle) periodogram is a powerful tool which is used routinely in many branches of astronomy to search for periodicities in observational data. The problem of assessing statistical significance of candidate periodicities for different periodograms is considered. Based on results in extreme value theory, improved analytic estimations of false alarm probabilities are given. They include an upper limit to the false alarm probability (or a lower limit to the significance). These estimations are tested numerically in order to establish regions of their practical applicability.Comment: 7 pages, 6 figures, 1 table; To be published in MNRA

Seismic Hazard Assessment For Peninsular Malaysia Using Gumbel Distribution Method

This Paper Presents The Preliminary Study On Seismic Hazard Assessment Which Involved Developing Macrozonation Map For Two Hazard Levels, I.E. 10% And 2% Probabilities Of Exceedance In 50 Years For Bedrock Of Peninsular Malaysia. The Analysis Was Performed Using Statistic Theory Of Extreme Values From Gumbel. The Analysis Covered The Earthquake Data Processing (Such As Choosing A Consistent Magnitude To Be Used In The Analysis And Identifying Main Shock Events), And Selection Of Appropriate Attenuation Relationship. Results Showed That The Peak Ground Acceleration (PGA) Across The Peninsular Malaysia Range Between 10 And 25 Gal For 10% Probability Of Exceedance, And Between 15 And 35 Gal For 2% Probability Of Exceedance In 50 Years Hazard Levels. These Values Were Lower By About 50 To 65% Than Those Obtained From Deterministic Analysis

Dopamine D_1 Receptors and Nonlinear Probability Weighting in Risky Choice

Misestimating risk could lead to disadvantaged choices such as initiation of drug use (or gambling) and transition to regular drug use (or gambling). Although the normative theory in decision-making under risks assumes that people typically take the probability-weighted expectation over possible utilities, experimental studies of choices among risks suggest that outcome probabilities are transformed nonlinearly into subjective decision weights by a nonlinear weighting function that overweights low probabilities and underweights high probabilities. Recent studies have revealed the neurocognitive mechanism of decision-making under risk. However, the role of modulatory neurotransmission in this process remains unclear. Using positron emission tomography, we directly investigated whether dopamine D_1 and D_2 receptors in the brain are associated with transformation of probabilities into decision weights in healthy volunteers. The binding of striatal D_1 receptors is negatively correlated with the degree of nonlinearity of weighting function. Individuals with lower striatal D_1 receptor density showed more pronounced overestimation of low probabilities and underestimation of high probabilities. This finding should contribute to a better understanding of the molecular mechanism of risky choice, and extreme or impaired decision-making observed in drug and gambling addiction