By Wiper M., Wilson S.
Listed here, we outline a version for fault detection through the beta trying out part of a software program layout venture. Given sampled info, we illustrate how you can estimate the failure expense and the variety of faults within the software program utilizing Bayesian statistical tools with a number of various past distributions. Secondly, given an appropriate fee functionality, we additionally express easy methods to optimise the period of one other attempt interval for every one of many previous distribution buildings thought of.
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Extra info for A Bayesian Analysis of Beta Testing
2 Recursions for L For the developments in this and subsequent sections it will be convenient to introduce a final piece of notation for the so-called Kalman gain matrices. These matrices arise naturally in formulae for both L and L−1 and, not surprisingly, appear in various signal and state vector prediction formulae that we will encounter in the next chapter. They are defined by K(t) = F (t)S(t|t − 1)H T (t)R −1 (t), t = 1, . , n. 17) via the relation M (t) = F (t) − K(t)H(t). With this notational preliminary, we can now give a detailed description of the form of L.
F (n−2) F (n − 2) · · · F (2)S(2|1)H T (2) ×F (n−1) F (n − 1) · · · F (2)S(2|1)H T (2) By extrapolating from what we have observed in these special cases we can determine that the diagonal and below diagonal blocks of ΣXε can be computed on a row-by-row basis by simply “updating” entries from previous rows through pre-multiplication by an appropriate F (·) matrix. That is, we can use the elements of the tth block row of ΣXε to evaluate all the (strictly) below diagonal blocks of the (t + 1)st row block through premultiplication by F (t).
T. 3. This two-stage approach can be perfectly satisfactory and we will see this reflected in some of the forward and backward recursions for computing signal and state vector estimators in Chapters 4 and 5. However, there are also cases where it would be more convenient to have the entire matrix ΣXε in hand after a single forward pass. One way to evaluate the entirety of ΣXε in a single recursion is to work forward from the upper left hand corner of the matrix in an L-shaped pattern. 2. Then the above diagonal blocks for the (t + 1)st column block are evaluated.