ABOUT A METHOD OF IMPROVING THE MAXIMUM
LIKELIHOOD ESTIMATES OF NUCLIDES ACTIVITIES

S.A. Tolstov, V.A. Muravsky

      Experimentally obtained    spectral    components,    containing
statistical noise,  are often used for nuclides activities  estimation
from  scintillation  g-spectra.  A  very  complicated  and rather slow
algorithm should be used to obtain  maximum  likelihood  estimates  of
activities in that case. However, if the spectral components are known
exactly,  one can apply a very fast converging iteration algorithm for
maximum  likelihood  activities  estimates.  But  application  of this
iteration algorithm will  give  biased  estimates  of  activities,  if
spectral components contain noise.  The appropriate correction factors
for diagonal elements of the matrix of a set  of  equations  for  that
iteration   algorithm  have  been  found  to  eliminate  bias  of  the
activities estimates. The estimates obtained by the new algorithm with
correction  are  not  biased and have practically the same variance as
estimates obtained from  the  likelihood  function  with  taking  into
account statistical noise in spectral components. The suggested method
can be used for improving estimates of least squares method also.