Higher Order Cumulants and Inference for a Class of Filtered Poisson Processes
Bibliographic record
Abstract
Spectral methods are useful in the analysis of time series and point process data in Zd or Rd. Parameter estimates based on these often have a limiting Gaussian distribution, whose limiting variance depends upon integrals of the second, third and fourth order spectral densities. The effective evaluation of these spectral density integrals is needed. In image analysis (d = 2), these integrals are very time consuming to evaluate. This paper considers a particular class of integrated or filtered Poisson processes. Using higher order cumulants, one can identify parameters up to a certain order. In some parametric cases these identify all the parameters of the process. In such cases it would then be possible to construct and hence simulate a filtered Poisson process for the estimator functional has the same asymptotics. Simulation or bootstrapping this process is a more efficient way of estimating or approximating the distribution of the parameter estimate. This paper demonstrates the validity for such a method. Specific examples of scanning fluorescence correlation spectroscopy (S–FCS) and image correlation spectroscopy (ICS) are discussed and used as motivating examples. In these cases one can obtain estimates of an object that previously could only inferred indirectly.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.009 | 0.035 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".