Abstract
This paper presents formulations for the calibration of computational models according to random data. Uncertainty in the data might be caused by a poor metrology system, measurement noise, missing or uncontrollable input variables, or by the inability to directly measure the inputs and/or outputs of interest. The forward approach performs the calibration in the space of the model’s output thereby requiring repeated model simulations. Conversely, the inverse approach leverages an ensemble of solutions to an inverse problem in order to perform the calibration in the space of the model’s parameters. This approach not only has a lower computational cost but also allows for the identification of more suitable parameter model classes, which in turn yield better calibrated models. The proposed formulations are used to calibrate a radiation model that informs cancer risk projections for future outer space missions according to distinct datasets.
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Notes
- 1.
Chance-constrained programs such as (9) trade-off a reduction in the performance of a 100\(\alpha \)% of all possible outcomes for an improved performance for the remaining 100\((1-\alpha )\)%.
- 2.
The Least-Squares (LS) parameter point will be denoted as \(p_{\text {LS}}\) hereafter.
- 3.
If \(n_r\) samples of each \(\nu _i\) are available, the corresponding samples of \(L_p(\theta )\), \(\{ \sum _{i=1}^{n_m} \log \nu _i^{(j)}(\theta ) \}_{j=1}^{n_r}\), can be readily used to estimate the cost functions in (18) and (20). Using a piece-wise linear CDF in (9) and (20) makes gradient-based algorithms applicable.
- 4.
Each mutational frequency data point of [1], denoted as \(y_{i,\text {M}}\) for irradiation dose \(D_{i,\text {M}}\), is scaled according to \(y_{i,\text {M-scaled}} = y_{i,\text {M}} R(D_{i,\text {M}}, p_{\text {HG}})/ R(D_{i,\text {M}}, p_\text {M}),\) where \(p_{\text {HG}}\) and \(p_\text {M}\) are the LS regression estimates of the parameters associated with the Harderian gland tumor prevalence data of [2] and mutational frequency data of [1], respectively. Similarly, each chromosome aberration data point of [8], denoted as \(y_{i,\text {CA}}\) for irradiation dose \(D_{i,\text {CA}}\), is scaled according to \(y_{i,\text {CA-scaled}} = y_{i,\text {CA}} R(D_{i,\text {CA}}, p_{\text {HG}})/R(D_{i,\text {CA}}, p_{\text {CA}}),\) where \(p_{\text {CA}}\) is the LS regression estimate of the parameters associated with the chromosome aberration data of [8].
- 5.
Specifics on the setting used to compute the optimal \(\theta \) will be given in the notation used hereafter. In particular, the first subscript will refer to either the FML or the IML formulation, the second subscript will refer to either the Normal or the SN parameter model, and the superscript will refer to either the mean or the quantile cost function.
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Crespo, L.G., Slaba, T.C., Poignant, F.A., Kenny, S.P. (2022). Calibration of Radiation-Induced Cancer Risk Models According to Random Data. In: Ciucci, D., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2022. Communications in Computer and Information Science, vol 1602. Springer, Cham. https://doi.org/10.1007/978-3-031-08974-9_8
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