With no explanation, label text_A→text_B with either "not_related" or "related".
text_A: A lion is a mammal.
text_B: Probability bounds analysis -LRB- PBA -RRB- is a collection of methods of uncertainty propagation for making qualitative and quantitative calculations in the face of uncertainties of various kinds .. It is used to project partial information about random variables and other quantities through mathematical expressions .. For instance , it computes sure bounds on the distribution of a sum , product , or more complex function , given only sure bounds on the distributions of the inputs .. Such bounds are called probability boxes , and constrain cumulative probability distributions -LRB- rather than densities or mass functions -RRB- .. cumulative probability distributions. cumulative distribution function. densities. probability density function. mass functions. probability mass function. This bounding approach permits analysts to make calculations without requiring overly precise assumptions about parameter values , dependence among variables , or even distribution shape .. bounding. upper and lower bounds. Probability bounds analysis is essentially a combination of the methods of standard interval analysis and classical probability theory .. interval analysis. interval analysis. probability theory. probability theory. Probability bounds analysis gives the same answer as interval analysis does when only range information is available .. interval analysis. interval analysis. It also gives the same answers as Monte Carlo simulation does when information is abundant enough to precisely specify input distributions and their dependencies .. Monte Carlo simulation. Monte Carlo simulation. Thus , it is a generalization of both interval analysis and probability theory .. interval analysis. interval analysis. probability theory. probability theory. The diverse methods comprising probability bounds analysis provide algorithms to evaluate mathematical expressions when there is uncertainty about the input values , their dependencies , or even the form of mathematical expression itself .. The calculations yield results that are guaranteed to enclose all possible distributions of the output variable if the input p-boxes were also sure to enclose their respective distributions .. p-boxes. probability box. In some cases , a calculated p-box will also be best-possible in the sense that. the bounds could be no tighter without excluding some of the possible. distributions .. P-boxes are usually merely bounds on possible distributions .. The bounds often also enclose distributions that are not themselves possible .. For instance , the set of probability distributions that could result from adding random values without the independence assumption from two -LRB- precise -RRB- distributions is generally a proper subset of all the distributions enclosed by the p-box computed for the sum .. subset. subset. That is , there are distributions within the output p-box that could not arise under any dependence between the two input distributions .. The output p-box will , however , always contain all distributions that are possible , so long as the input p-boxes were sure to enclose their respective underlying distributions .. p-boxes. probability box. This property often suffices for use in risk analysis and other fields requiring calculations under uncertainty .. risk analysis. Probabilistic risk assessment
not_related.