Application of maximum entropy to statistical inference for inversion of data from a single track segment

Area of Science:

• Acoustics
• Statistical Inference
• Signal Processing

Background:

• Estimating maximum entropy (ME) constraints for statistical inference typically requires multiple data segments.
• Model mismatch, where propagation models incompletely represent acoustic processes, can lead to inaccuracies in parameter estimation.
• Inaccuracies can result in inversion solutions falling outside established uncertainty intervals (priors).

Purpose of the Study:

• To develop an approach for estimating ME constraints using only a single track segment of underwater acoustic data.
• To address and mitigate the effects of model mismatch on statistical inference in acoustic data analysis.
• To ensure that inferred parameter uncertainties encompass prior knowledge, even in the presence of model mismatch.

Main Methods:

• The proposed method estimates the ME constraint by ensuring the inferred uncertainty interval includes the prior uncertainty interval for a specific parameter.
• This involves determining a constraint value that accounts for model mismatch effects.
• The approach is validated using both simulated and measured underwater acoustic data.

Main Results:

• The new approach successfully estimates ME constraints from single track segments.
• The method effectively accounts for model mismatch, producing more reliable parameter estimates.
• Inferred uncertainty intervals were shown to encompass prior intervals, even when minimum cost solutions were outside the priors.

Conclusions:

• A novel method for estimating ME constraints from single acoustic track segments has been presented.
• This approach enhances statistical inference by robustly handling model mismatch.
• The findings are applicable to various scenarios involving model inaccuracies in underwater acoustics.