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Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
The formulas given in the previous section allow one to calculate the point estimates of α and β — that is, the coefficients of the regression line for the given set of data. However, those formulas do not tell us how precise the estimates are, i.e., how much the estimators α ^ {\displaystyle {\widehat {\alpha }}} and β ^ {\displaystyle ...
The response variable may be non-continuous ("limited" to lie on some subset of the real line). For binary (zero or one) variables, if analysis proceeds with least-squares linear regression, the model is called the linear probability model. Nonlinear models for binary dependent variables include the probit and logit model.
The one-factor-at-a-time method, [1] also known as one-variable-at-a-time, OFAT, OF@T, OFaaT, OVAT, OV@T, OVaaT, or monothetic analysis is a method of designing experiments involving the testing of factors, or causes, one at a time instead of multiple factors simultaneously.
Furthermore, probabilistic failure prediction based on MTBF implies the total absence of systematic failures (i.e., a constant failure rate with only intrinsic, random failures), which is not easy to verify. [4] Assuming no systematic errors, the probability the system survives during a duration, T, is calculated as exp^(-T/MTBF).
The term law of total probability is sometimes taken to mean the law of alternatives, which is a special case of the law of total probability applying to discrete random variables. [ citation needed ] One author uses the terminology of the "Rule of Average Conditional Probabilities", [ 4 ] while another refers to it as the "continuous law of ...
If the random variable can take on only a finite number of values, the "conditions" are that the variable can only take on a subset of those values. More formally, in the case when the random variable is defined over a discrete probability space, the "conditions" are a partition of this probability space.
Variance-based sensitivity analysis (often referred to as the Sobol’ method or Sobol’ indices, after Ilya M. Sobol’) is a form of global sensitivity analysis. [ 1 ] [ 2 ] Working within a probabilistic framework, it decomposes the variance of the output of the model or system into fractions which can be attributed to inputs or sets of inputs.