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ckn.m
function y = ckn(P,k)
determines the probability of the
occurrence of
k or more of the
n independent events whose probabilities are in row or
column vector
P (
k may be a row or column vector)
function y = ckn(P,k)
% CKN y = ckn(P,k) Probability of k or more successes% Version of 5/15/95
% Probabilities of k or more of n independent events% Uses the m-functions mintable, minprob, csort
n = length(P);m = length(k);
T = sum(mintable(n)); % The number of successes in each mintermpm = minprob(P); % The probability of each minterm
[t,p]= csort(T,pm); % Sorts and consolidates success numbers
% and adds corresponding probabilitiesfor i = 1:m % Sums probabilities for each k value
y(i) = sum(p(k(i)+1:n+1));end
parallel.m
function y = parallel(p)
determines the probability
of a parallel combination of the independent events whose probabilities are in row or columnvector
p .
function y = parallel(p)
% PARALLEL y = parallel(p) Probaaability of parallel combination% Version of 3/3/93
% Probability of parallel combination.% Individual probabilities in row matrix p.
y = 1 - prod(1 - p);
bayes.m produces a Bayesian reversal of conditional probabilities. The input consists of $P\left(E\right|{A}_{i})$ and $P\left({A}_{i}\right)$ for a disjoint class $\{{A}_{i}:1\le i\le n\}$ whose union contains E . The procedure calculates $P\left({A}_{i}\right|E)$ and $P\left({A}_{i}\right|{E}^{c})$ for $1\le i\le n$ .
% BAYES file bayes.m Bayesian reversal of conditional probabilities
% Version of 7/6/93% Input P(E|Ai) and P(Ai)
% Calculates P(Ai|E) and P(Ai|Ec)disp('Requires input PEA = [P(E|A1) P(E|A2) ... P(E|An)]')disp(' and PA = [P(A1) P(A2) ... P(An)]')disp('Determines PAE = [P(A1|E) P(A2|E) ... P(An|E)]')disp(' and PAEc = [P(A1|Ec) P(A2|Ec) ... P(An|Ec)]')PEA = input('Enter matrix PEA of conditional probabilities ');
PA = input('Enter matrix PA of probabilities ');PE = PEA*PA';
PAE = (PEA.*PA)/PE;PAEc = ((1 - PEA).*PA)/(1 - PE);
disp(' ')disp(['P(E) = ',num2str(PE),])disp(' ')
disp(' P(E|Ai) P(Ai) P(Ai|E) P(Ai|Ec)')disp([PEA; PA; PAE; PAEc]')disp('Various quantities are in the matrices PEA, PA, PAE, PAEc, named above')
odds.m The procedure calculates posterior odds for for a specified profile E . Assumes data have been entered by the procedure oddsf or oddsp .
% ODDS file odds.m Posterior odds for profile
% Version of 12/4/93% Calculates posterior odds for profile E
% Assumes data has been entered by oddsdf or oddsdpE = input('Enter profile matrix E ');
C = diag(a(:,E))'; % aa = a(:,E) is an n by n matrix whose ith columnD = diag(b(:,E))'; % is the E(i)th column of a. The elements on the
% diagonal are b(i, E(i)), 1<= i<= n
% Similarly for b(:,E)R = prod(C./D)*(p1/p2); % Calculates posterior odds for profile
disp(' ')disp(['Odds favoring Group 1: ',num2str(R),])if R>1
disp('Classify in Group 1')else
disp('Classify in Group 2')end
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