A statistical approach to the resolution of point sources

SUMMARY The Rayleigh criterion in optics states that two point sources of equal intensity are 'barely resolved' when the maximum of the diffraction pattern of one source overlaps the first minimum of the diffraction pattern of the second source. Although useful for rough comparisons of optical systems, such a criterion does not take into account the randomness in the detection process and does not tell whether sources can actually be distinguished. We present a statistical approach that addressed these issues. From quantum optics, the photon counts in the pixels are independent Poisson random variables with means that depend on the distance 2theta between the sources. Resolving the sources corresponds to testing H0: theta =0 vs Ha: theta >0, under conditions that make the information number zero at theta =0. We define resolution as the (asymptotic) power function of the likelihood ratio test rather than as a single number. The asymptotic distribution of the test statistic is derived under H0 and under contiguous alternatives. The results are illustrated by an application to a sky survey to detect binary stars using the Hubble space telescope.     

WHO IS AFRAID OF THE FRIEDMAN RULE?

We explore the connection between optimal monetary policy and heterogeneity among agents in a standard monetary economy with two types of agents where the stationary distribution of money holdings is nondegenerate. Sans type-specific fiscal policy, we show that the zero-nominal-interest rate policy (the Friedman rule) does not maximize type-specific welfare; it may not maximize aggregate ex ante social welfare either. Indeed, one or, more surprisingly, both types may benefit if the central bank deviates from the Friedman rule. ( JEL E31, E51, E58)     

Crime, Crime News, and Crime Views

This paper compares police, newspaper, television, and publicimages of crime trends for the seven FBI index crimes over time,the relative frequency of occurrence of these offenses, andthe characteristics of persons committing them. Media presentationsof crime trends over time are found generally unrelated to trendsin police statistics. Newspaper presentation of the relativedistribution of crimes approximates police figures more closelythan does the television presentation. Public views of the relativedistribution of crimes but not of crime trends more closelyapproximate media presentations than police presentations. Television'simpact on public views of crime is apparently minor. Reasonsfor these findings and their implications for crime news reportingare discussed.