تقرير
A tutorial on the Bayesian statistical approach to inverse problems
| العنوان: | A tutorial on the Bayesian statistical approach to inverse problems |
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| المؤلفون: | Waqar, Faaiq G., Patel, Swati, Simon, Cory M. |
| المصدر: | APL Machine Learning. 1, 041101 (2023) |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Statistics |
| مصطلحات موضوعية: | Statistics - Methodology, Computer Science - Machine Learning, Statistics - Applications, G.3 |
| الوصف: | Inverse problems are ubiquitous in the sciences and engineering. Two categories of inverse problems concerning a physical system are (1) estimate parameters in a model of the system from observed input-output pairs and (2) given a model of the system, reconstruct the input to it that caused some observed output. Applied inverse problems are challenging because a solution may (i) not exist, (ii) not be unique, or (iii) be sensitive to measurement noise contaminating the data. Bayesian statistical inversion (BSI) is an approach to tackle ill-posed and/or ill-conditioned inverse problems. Advantageously, BSI provides a "solution" that (i) quantifies uncertainty by assigning a probability to each possible value of the unknown parameter/input and (ii) incorporates prior information and beliefs about the parameter/input. Herein, we provide a tutorial of BSI for inverse problems, by way of illustrative examples dealing with heat transfer from ambient air to a cold lime fruit. First, we use BSI to infer a parameter in a dynamic model of the lime temperature from measurements of the lime temperature over time. Second, we use BSI to reconstruct the initial condition of the lime from a measurement of its temperature later in time. We demonstrate the incorporation of prior information, visualize the posterior distributions of the parameter/initial condition, and show posterior samples of lime temperature trajectories from the model. Our tutorial aims to reach a wide range of scientists and engineers. Comment: v0.0 |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1063/5.0154773 |
| URL الوصول: | http://arxiv.org/abs/2304.07610 |
| رقم الأكسشن: | edsarx.2304.07610 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1063/5.0154773 |
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