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+function [extra, invhess] = fevbayes(net, y, a, x, t, x_test, invhess)
+%FEVBAYES Evaluate Bayesian regularisation for network forward propagation.
+%
+%	Description
+%	EXTRA = FEVBAYES(NET, Y, A, X, T, X_TEST) takes a network data
+%	structure  NET together with a set of hidden unit activations A from
+%	test inputs X_TEST, training data inputs X and T and outputs a matrix
+%	of extra information EXTRA that consists of error bars (variance) for
+%	a regression problem or moderated outputs for a classification
+%	problem. The optional argument (and return value)  INVHESS is the
+%	inverse of the network Hessian computed on the training data inputs
+%	and targets.  Passing it in avoids recomputing it, which can be a
+%	significant saving for large training sets.
+%
+%	This is called by network-specific functions such as MLPEVFWD which
+%	are needed since the return values (predictions and hidden unit
+%	activations) for different network types are in different orders (for
+%	good reasons).
+%
+%	See also
+%	MLPEVFWD, RBFEVFWD, GLMEVFWD
+%
+
+%	Copyright (c) Ian T Nabney (1996-2001)
+
+w = netpak(net);
+g = netderiv(w, net, x_test);
+if nargin < 7
+  % Need to compute inverse hessian
+  hess = nethess(w, net, x, t);
+  invhess = inv(hess);
+end
+
+ntest = size(x_test, 1);
+var = zeros(ntest, 1);
+for idx = 1:1:net.nout,
+  for n = 1:1:ntest,
+    grad = squeeze(g(n,:,idx));
+    var(n,idx) = grad*invhess*grad';  
+  end
+end
+
+switch net.outfn
+    case 'linear'
+	% extra is variance
+	extra = ones(size(var))./net.beta + var;
+    case 'logistic'
+	% extra is moderated output
+	kappa = 1./(sqrt(ones(size(var)) + (pi.*var)./8));
+	extra = 1./(1 + exp(-kappa.*a));
+    case 'softmax'
+	% Use extended Mackay formula; beware that this may not
+	% be very accurate
+	kappa = 1./(sqrt(ones(size(var)) + (pi.*var)./8));
+	temp = exp(kappa.*a);
+	extra = temp./(sum(temp, 2)*ones(1, net.nout));
+    otherwise
+	error(['Unknown activation function ', net.outfn]);
+end