Maximum likelihood estimation on model fluorescence distributions that include light-assisted-collision loss recovers atom-number proportions in a tight optical tweezer with few-percent accuracy from about 600 test runs.
Statistics of weighted Poisson events and its applications
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abstract
The statistics of the sum of random weights where the number of weights is Poisson distributed has important applications in nuclear physics, particle physics and astrophysics. Events are frequently weighted according to their acceptance or relevance to a certain type of reaction. The sum is described by the compound Poisson distribution (CPD) which is shortly reviewed. It is shown that the CPD can be approximated by a scaled Poisson distribution (SPD). The SPD is applied to parameter estimation in situations where the data are distorted by resolution effects. It performs considerably better than the normal approximation that is usually used. A special Poisson bootstrap technique is presented which permits to derive confidence limits for observations following the CPD.
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Applications of maximum likelihood estimations for analyzing photon counts in few atom experiments
Maximum likelihood estimation on model fluorescence distributions that include light-assisted-collision loss recovers atom-number proportions in a tight optical tweezer with few-percent accuracy from about 600 test runs.