Information Content of Tracer Data With Respect to Steady-state Systems 185 



for any of the known values correspond to similar uncertainties along the 

 appropriate co-ordinates in the hyperspace. 



Thus, if all Aj,j and a^ are known exactly, a point in the hyperspace of n^ 

 dimensions specifies the model. If all the data are known to within a certain 

 statistical precision, the most likely model is estimated as a point in the n~ 

 dimensional space surrounded by a region that corresponds to the statistical 

 uncertainty. If some Aj^j or a_, are unknown, the corresponding dimensions in 

 the n^ dimensional hyperspace extend to the limits imposed by the relation that 

 all Xjj are positive. 



IV. UNIT OF UNCERTAINTY 



Based on the point of view presented, we can define a unit of uncertainty 

 to be a certain volume of the hyperspace. The size of the volume so defined is 

 arbitrary; it may correspond to a volume that is equivalent to the actual 

 standard deviation in the data, or to some convenient standard deviation that 

 may serve as a reference. The information necessary to define the system can 

 then be expressed as the number of binary choices, or bits of information, 

 necessary to reduce the total uncertainty space to the size of a defined unit. 



V. CONCLUSION 



The treatment presented provides a framework in which information in data 

 from tracer experiments on steady-state systems can be quantified in terms of a 

 compartmental system and its parameters. Before the information can be 

 quantified, however, a number of compartments has to be chosen for the system. 

 Unless this is known from independent sources, the method in choosing the 

 number of compartments is based on the minimum number of exponential terms 

 that 'reasonably' describe the data. This, at present, is by no means a unique 

 procedure. 



It was shown in this treatment that a model representing the system can be 

 expressed as a point in a generalized co-ordinate space, and that any uncertainty 

 in the system can be represented by a certain region in that space. The nature 

 of the uncertainty (whether incomplete data or statistical fluctuations in the data) 

 did not matter in the treatment. 



There is, however, one difference in the regions of the hyperspace corre- 

 sponding to these two sources of uncertainty. The difference is in the probability 

 that any model in the region represents the true system. In the case of incomplete 

 data, the probability density over the entire region is assumed constant; that is, 

 every model in the region is considered equally probable. In the case of statistical 

 fluctuations, however, a certain point or unit volume represents the most likely 

 model, and the rest of the points or unit volumes decrease in probability in a 

 manner governed by the statistics of the data. 



The region in the |A| hyperspace can serve to define the information content 

 in the data of the system as a whole or of each parameter of the system, namely 

 the turn-over rates, separately. The latter can be obtained by investigating their 

 values over the bounded region. 



One need not necessarily deal with all the dimensions of the hyperspace. One 

 can express the uncertainties in terms of a subspace whose dimensions are equal 



