Mathematical Basis for Physical Inference

Research output: Contribution to journalJournal articlepeer-review

Standard

Mathematical Basis for Physical Inference. / Tarantola, Albert; Mosegaard, Klaus.

In: arXiv, 20.09.2000.

Research output: Contribution to journalJournal articlepeer-review

Harvard

Tarantola, A & Mosegaard, K 2000, 'Mathematical Basis for Physical Inference', arXiv. <http://arxiv.org/pdf/math-ph/0009029v1>

APA

Tarantola, A., & Mosegaard, K. (2000). Mathematical Basis for Physical Inference. arXiv. http://arxiv.org/pdf/math-ph/0009029v1

Vancouver

Tarantola A, Mosegaard K. Mathematical Basis for Physical Inference. arXiv. 2000 Sep 20.

Author

Tarantola, Albert ; Mosegaard, Klaus. / Mathematical Basis for Physical Inference. In: arXiv. 2000.

Bibtex

@article{1310527a242147498ef422d32f935ad7,
title = "Mathematical Basis for Physical Inference",
abstract = " While the axiomatic introduction of a probability distribution over a space is common, its use for making predictions, using physical theories and prior knowledge, suffers from a lack of formalization. We propose to introduce, in the space of all probability distributions, two operations, the OR and the AND operation, that bring to the space the necessary structure for making inferences on possible values of physical parameters. While physical theories are often asumed to be analytical, we argue that consistent inference needs to replace analytical theories by probability distributions over the parameter space, and we propose a systematic way of obtaining such {"}theoretical correlations{"}, using the OR operation on the results of physical experiments. Predicting the outcome of an experiment or solving {"}inverse problems{"} are then examples of the use of the AND operation. This leads to a simple and complete mathematical basis for general physical inference. ",
keywords = "math-ph, math.MP",
author = "Albert Tarantola and Klaus Mosegaard",
note = "24 pages, 4 figures",
year = "2000",
month = sep,
day = "20",
language = "English",
journal = "arXiv",
publisher = "arxiv.org",

}

RIS

TY - JOUR

T1 - Mathematical Basis for Physical Inference

AU - Tarantola, Albert

AU - Mosegaard, Klaus

N1 - 24 pages, 4 figures

PY - 2000/9/20

Y1 - 2000/9/20

N2 - While the axiomatic introduction of a probability distribution over a space is common, its use for making predictions, using physical theories and prior knowledge, suffers from a lack of formalization. We propose to introduce, in the space of all probability distributions, two operations, the OR and the AND operation, that bring to the space the necessary structure for making inferences on possible values of physical parameters. While physical theories are often asumed to be analytical, we argue that consistent inference needs to replace analytical theories by probability distributions over the parameter space, and we propose a systematic way of obtaining such "theoretical correlations", using the OR operation on the results of physical experiments. Predicting the outcome of an experiment or solving "inverse problems" are then examples of the use of the AND operation. This leads to a simple and complete mathematical basis for general physical inference.

AB - While the axiomatic introduction of a probability distribution over a space is common, its use for making predictions, using physical theories and prior knowledge, suffers from a lack of formalization. We propose to introduce, in the space of all probability distributions, two operations, the OR and the AND operation, that bring to the space the necessary structure for making inferences on possible values of physical parameters. While physical theories are often asumed to be analytical, we argue that consistent inference needs to replace analytical theories by probability distributions over the parameter space, and we propose a systematic way of obtaining such "theoretical correlations", using the OR operation on the results of physical experiments. Predicting the outcome of an experiment or solving "inverse problems" are then examples of the use of the AND operation. This leads to a simple and complete mathematical basis for general physical inference.

KW - math-ph

KW - math.MP

M3 - Journal article

JO - arXiv

JF - arXiv

ER -

ID: 261066199