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Belief Aggregation
Belief aggregation, also called risk aggregation, opinion aggregation or probabilistic opinion pooling, is a process in which different probability distributions, produced by different experts, are combined to yield a single probability distribution. Background Expert opinions are often uncertain. Rather than saying e.g. "it will rain tomorrow", a weather expert may say "it will rain with probability 70% and be sunny with probability 30%". Such a statement is called a belief. Different experts may have different beliefs; for example, a different weather expert may say "it will rain with probability 60% and be sunny with probability 40%". In other words, each expert has a subjeciive probability distribution over a given set of outcomes. A belief aggregation rule is a function that takes as input two or more probability distributions over the same set of outcomes, and returns a single probability distribution over the same space. Applications Documented applications of belief agg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prediction Of Volcanic Activity
Prediction of volcanic activity, and volcanic eruption forecasting, is an interdisciplinary monitoring and research effort to predict the time and severity of a volcano's eruption. Of particular importance is the prediction of hazardous eruptions that could lead to catastrophic loss of life, property, and disruption of human activities. Risk and uncertainty are central to forecasting and prediction, which are not necessarily the same thing in the context of volcanoes, where opinions have often played a role, and the prediction in time (forecasting) for an individual volcano is different from predicting eruption characteristics for apparently similar volcanoes. Both forecasting and prediction have processes based on past and present data. Seismic waves (seismicity) General principles of volcano seismology * Seismic activity (earthquakes and tremors) always occurs as volcanoes awaken and prepare to erupt and are a very important link to eruptions. Some volcanoes normally have co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Budget-proposal Aggregation
Budget-proposal aggregation (BPA) is a problem in social choice theory. A group has to decide on how to distribute its budget among several issues. Each group-member has a different idea about what the ideal budget-distribution should be. The problem is how to aggregate the different opinions into a single budget-distribution program. BPA is a special case of Participatory budgeting rule, participatory budgeting, with the following characteristics: # The issues are ''divisible'' and ''unbounded'' – each issue can be allocated any amount, as long as the sum of allocations equals the total budget. # Agents' preferences are given by single-peaked preferences over an ''ideal budget''. It is also a special case of fractional social choice (portioning), in which agents express their preferences by stating their ideal distribution, rather than by a ranking of the issues. Another sense in which aggregation in budgeting has been studied is as follows. Suppose a manager asks his worker ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sensor Fusion
Sensor fusion is a process of combining sensor data or data derived from disparate sources so that the resulting information has less uncertainty than would be possible if these sources were used individually. For instance, one could potentially obtain a more accurate location estimate of an indoor object by combining multiple data sources such as video cameras and WiFi localization signals. The term ''uncertainty reduction'' in this case can mean more accurate, more complete, or more dependable, or refer to the result of an emerging view, such as stereoscopic vision (calculation of depth information by combining two-dimensional images from two cameras at slightly different viewpoints). The data sources for a fusion process are not specified to originate from identical sensors. One can distinguish ''direct fusion'', ''indirect fusion'' and fusion of the outputs of the former two. Direct fusion is the fusion of sensor data from a set of heterogeneous or homogeneous sensors, soft s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scoring Rule
In decision theory, a scoring rule provides evaluation metrics for probabilistic forecasting, probabilistic predictions or forecasts. While "regular" loss functions (such as mean squared error) assign a goodness-of-fit score to a predicted value and an observed value, scoring rules assign such a score to a predicted probability distribution and an observed value. On the other hand, a scoring function provides a summary measure for the evaluation of point predictions, i.e. one predicts a property or Functional (mathematics), functional T(F), like the Expected value, expectation or the median. Scoring rules answer the question "how good is a predicted probability distribution compared to an observation?" Scoring rules that are (strictly) proper are proven to have the lowest expected score if the predicted distribution equals the underlying distribution of the target variable. Although this might differ for individual observations, this should result in a minimization of the expect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Assimilation
Data assimilation refers to a large group of methods that update information from numerical computer models with information from observations. Data assimilation is used to update model states, model trajectories over time, model parameters, and combinations thereof. What distinguishes data assimilation from other estimation methods is that the computer model is a dynamical model, i.e. the model describes how model variables change over time, and its firm mathematical foundation in Bayesian Inference. As such, it generalizes inverse methods and has close connections with machine learning. Data assimilation initially developed in the field of numerical weather prediction. Numerical weather prediction models are equations describing the evolution of the atmosphere, typically coded into a computer program. When these models are used for forecasting the model output quickly deviates from the real atmosphere. Hence, we use observations of the atmosphere to keep the model on track. Data ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aggregative Contingent Estimation Program
Aggregative Contingent Estimation (ACE) was a program of the Office of Incisive Analysis (OIA) at the Intelligence Advanced Research Projects Activity (IARPA). The program ran from June 2010 until June 2015. History The broad program announcement for ACE was published on June 30, 2010. ACE funded the Aggregative Contingent Estimation System (ACES) website and interface on July 15, 2011. They funded The Good Judgment Project some time around July 2011. ACE has been covered in ''The Washington Post' and ''Wired Magazine''. The program was concluded by late 2015. The program manager was future IARPA director Jason Gaverick Matheny. Goals and methods The official website says that the goals of ACE are "to dramatically enhance the accuracy, precision, and timeliness of intelligence forecasts for a broad range of event types, through the development of advanced techniques that elicit, weight, and combine the judgments of many intelligence analysts." The website claims that ACE seeks ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ensemble Forecasting
Ensemble forecasting is a method used in or within numerical weather prediction. Instead of making a single forecast of the most likely weather, a set (or ensemble) of forecasts is produced. This set of forecasts aims to give an indication of the range of possible future states of the atmosphere. Ensemble forecasting is a form of Monte Carlo analysis. The multiple simulations are conducted to account for the two usual sources of uncertainty in forecast models: (1) the errors introduced by the use of imperfect initial conditions, amplified by the chaotic nature of the equations of the atmosphere, which is often referred to as sensitive dependence on initial conditions; and (2) errors introduced because of imperfections in the model formulation, such as the approximate mathematical methods to solve the equations. Ideally, the verified future atmospheric state should fall within the predicted ensemble spread, and the amount of spread should be related to the uncertainty (error) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Majority Judgement
Majority judgment (MJ) is a single-winner voting system proposed in 2010 by Michel Balinski and Rida Laraki. It is a kind of highest median rule, a cardinal voting system that elects the candidate with the highest median rating. Voting process Voters grade as many of the candidates as they wish with regard to their suitability for office according to a series of grades. Balinski and Laraki suggest the options "Excellent, Very Good, Good, Acceptable, Poor, or Reject," but any scale can be used (e.g. the common letter grade scale). Voters can assign the same grade to multiple candidates. As with all highest median voting rules, the candidate with the highest median grade is declared winner. If more than one candidate has the same median grade, majority judgment breaks the tie by removing (one-by-one) any grades equal to the shared median grade from each tied candidate's column. This procedure is repeated until only one of the tied candidates is found to have the highest median ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dictatorship Mechanism
In social choice theory, a dictatorship mechanism is a degenerate voting rule or mechanism where the result depends on one person's. A serial dictatorship is similar, but also designates a series of "backup dictators", who break ties in the original dictator's choices when the dictator is indifferent. Formal definition Non-dictatorship is one of the necessary conditions in Arrow's impossibility theorem.''Game Theory'' Second Edition Guillermo Owen Ch 6 pp124-5 Axiom 5 Academic Press, 1982 In ''Social Choice and Individual Values'', Kenneth Arrow defines non-dictatorship as: :There is no voter i in such that, for every set of orderings in the domain of the constitution, and every pair of social states ''x'' and ''y'', ''x \succeq_i y'' implies x \succeq y. Unsurprisingly, a dictatorship is a rule that does not satisfy non-dictatorship. Anonymous voting rules automatically satisfy non-dictatorship (so long as there is more than one voter). Serial dictatorship When the dictator ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Median
The median of a set of numbers is the value separating the higher half from the lower half of a Sample (statistics), data sample, a statistical population, population, or a probability distribution. For a data set, it may be thought of as the “middle" value. The basic feature of the median in describing data compared to the Arithmetic mean, mean (often simply described as the "average") is that it is not Skewness, skewed by a small proportion of extremely large or small values, and therefore provides a better representation of the center. Median income, for example, may be a better way to describe the center of the income distribution because increases in the largest incomes alone have no effect on the median. For this reason, the median is of central importance in robust statistics. Median is a 2-quantile; it is the value that partitions a set into two equal parts. Finite set of numbers The median of a finite list of numbers is the "middle" number, when those numbers are liste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cumulative Distribution Function
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Every probability distribution Support (measure theory), supported on the real numbers, discrete or "mixed" as well as Continuous variable, continuous, is uniquely identified by a right-continuous Monotonic function, monotone increasing function (a càdlàg function) F \colon \mathbb R \rightarrow [0,1] satisfying \lim_F(x)=0 and \lim_F(x)=1. In the case of a scalar continuous distribution, it gives the area under the probability density function from negative infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables. Definition The cumulative distribution function of a real-valued random variable X is the function given by where the right-hand side represents the probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
