By Chen S.

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**Additional resources for Accuracy of MSI testing in predicting germline mutations of MSH2 and MLH1 a case study in Bayesian m**

**Example text**

K ( i ) } are called the diameters of those partitions and the number d i u m T = m a z { d i u m T ( i ) , i = 1,2} is called the diameter of T. , lc(2)). , r } and by a function f and let { T k } be a sequence of partitions of the square [O,u] x [O,a] whose diameters tend to zero and for any k , S ( T k ) 3 { s j } and curd(Tk(i)) = r(lc(i)). Below z E G and qn,o = q0,+ = 2 for all n. The following three propositions were established in 7. 1. Iff is continuous and bounded then x QK((t2,n - t 2 , n - i ) ( t i , k - t ~ , k - l ) ,q n - i , k - i , q n , k - i , q n - l , k , qn,k)dqn,k, The statement will be still valid if QR is substituted by QE.

Iff is continuous and bounded then x QK((t2,n - t 2 , n - i ) ( t i , k - t ~ , k - l ) ,q n - i , k - i , q n , k - i , q n - l , k , qn,k)dqn,k, The statement will be still valid if QR is substituted by QE. 2. 3. There exists such a probability S: o n C([O,u] x [0,a ],G ) that f o r any bounded continuous function f the following identity holds where The measure S: is equivalent to the Wiener measure W , and the corresponding Radon-Nykodim density is defined by & dS: dWX -(q) = c2e-: J," s," scal(~(tl,tz))dtldtz+B J," J," I l m ( q ( t 1 , t z ) ) l l Z d t 1 d t 2 where c;' = Proofs can be obtained using a theorem for measures, on a semiring of rectangles of the Euclidian plane, taking values in a commutative group of operators, which is similar to the famous Chernoff theorem lo (see also and estimates from 4).

To give a meaning to a2(x) we notice that for E SO + =o thus, as a distribution on SO, We remark at this point that if we try to extend this construction to higher powers of the delta function by working in SOthen the above limit becomes infinity. As we will see in the subsequent sections, a space of smoother functions is needed and that will cause the derivatives of the delta function to appear. 6), let F be the extension of limn++m ft(x) to all of S. 7) where $J E S is arbitrary with $(O) = 1.