Presented at *Workshop on Maximum Entropy and Bayesian Methods*, July 9-13, 2000, Gif sur Yvette, France

## Inference from Rossi traces

Kenneth M. Hanson and Jane M. Booker

*Los Alamos National Laboratory*
### Abstract

In the Rossi technique for displaying a time-dependent signal, the horizontal sweep of an oscilloscope is driven sinusoidally in time and the vertical sweep is driven by the signal to be recorded. The major advantage of this unusual recording technique is that the trace is confined to the central region of the oscilloscope face, the region in which the linearity of the oscilloscope response in best. The sinusoid signal also provides a built-in time marker. The first step in interpreting Rossi traces is to read a photograph taken of the oscilloscope signal. The reading process amounts to tabulating the position of a succession of points manually placed on the Rossi trace by a technician. A typical aim of the analysis is to measure the time rate of change of the relative signal amplitude, called alpha, as a function of time. We will present an approach to analyzing Rossi traces that is grounded in calculating the likelihood of the points read from the film. This likelihood is evaluated by using a suitable model for the uncertainties in the readings of the film, based on the distance of the measured points to a predicted Rossi trace. Simple inferences about the uncertainties in the alpha curve are carried out using the curvature with respect to the model parameters of the log-posterior probability at the maximum-likelihood solution. Alternatively, more complete inferences are obtained by using the Markov chain Monte Carlo technique, which produces random samples from the posterior probability distribution expressed in terms of the parameters. These samples can be displayed in terms of the alpha curve to visualize its overall uncertainties.

**Keywords:** Rossi trace, Bayesian inference, Markov chain Monte Carlo

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Send e-mail to author at kmh@hansonhub.com