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Optimizing Sample Variance Fitting to A Priori Distributions

This study explores sample variance fitting by comparing data against prior distributions. It focuses on adjusting parameters such as horizontal stretch and vertical offset to maximize the fitting probability, thereby minimizing the variance. The approach incorporates large and small discrepancies in data to refine the model and ensure its accuracy. We analyze individual samples to compute means and standard errors, while justifying the fitting function and its parameters. The goal is to achieve a model that passes quality control by ensuring normalized residuals resemble random noise.

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Optimizing Sample Variance Fitting to A Priori Distributions

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  1. Sample variance fitting

  2. Comparing data to a priori distributions

  3. Comparing data to a priori distributions

  4. Sample variance fitting Example parameters 1) Horizontal stretch x1/2 2) Vertical offset y0

  5. Sample variance fitting Example parameters 1) Horizontal stretch x1/2 2) Vertical offset y0 Adjust parameters to maximize “probability”, i.e. minimize

  6. Sample variance fitting Big dys c2big Example parameters 1) Horizontal stretch x1/2 2) Vertical offset y0 Big dys c2big Small dys c2small Adjust parameters to maximize “probability”, i.e. minimize Adjust parameters to maximize “probability”, i.e. minimize

  7. Sample variance fitting Adjust parameters to maximize “probability”, i.e. minimize

  8. Sample variance fitting IF the fitting curve can be adjusted to be “correct,” Adjust parameters to maximize “probability”, i.e. minimize

  9. Sample variance fitting Big dys c2big Measure individual samples to construct sample meansand standard errors at various x 3) Is ? ( ) Justify fitting function and parameters. Do normalized residuals look plausibly like random noise? Big dys c2big Small dys c2small 5) IF pass QC, report 1 0 -1

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