16 research outputs found
Quantum Measurement and Weak Values in Entropic Dynamics
The problem of measurement in quantum mechanics is studied within the
Entropic Dynamics framework. We discuss von Neumann and Weak measurements,
wavefunction collapse, and Weak Values as examples of bayesian and entropic
inference.Comment: Presented at MaxEnt 2016, the 36th International Workshop on Bayesian
Inference and Maximum Entropy Methods in Science and Engineering (July 10-15,
2016, Ghent, Belgium
Inferential Moments of Uncertain Multivariable Systems
This article expands the framework of Bayesian inference and provides direct
probabilistic methods for approaching inference tasks that are typically
handled with information theory. We treat Bayesian probability updating as a
random process and uncover intrinsic quantitative features of joint probability
distributions called inferential moments. Inferential moments quantify shape
information about how a prior distribution is expected to update in response to
yet to be obtained information. Further, we quantify the unique probability
distribution whose statistical moments are the inferential moments in question.
We find a power series expansion of the mutual information in terms of
inferential moments, which implies a connection between inferential theoretic
logic and elements of information theory. Of particular interest is the
inferential deviation, which is the expected variation of the probability of
one variable in response to an inferential update of another. We explore two
applications that analyze the inferential deviations of a Bayesian network to
improve decision-making. We implement simple greedy algorithms for exploring
sensor tasking using inferential deviations that generally outperform similar
greedy mutual information algorithms in terms of root mean squared error
between epistemic probability estimates and the ground truth probabilities they
are estimating
A Generalized Bayesian Approach to Model Calibration
In model development, model calibration and validation play complementary
roles toward learning reliable models. In this article, we expand the Bayesian
Validation Metric framework to a general calibration and validation framework
by inverting the validation mathematics into a generalized Bayesian method for
model calibration and regression. We perform Bayesian regression based on a
user's definition of model-data agreement. This allows for model selection on
any type of data distribution, unlike Bayesian and standard regression
techniques, that "fail" in some cases. We show that our tool is capable of
representing and combining least squares, likelihood-based, and Bayesian
calibration techniques in a single framework while being able to generalize
aspects of these methods. This tool also offers new insights into the
interpretation of the predictive envelopes (also known as confidence bands)
while giving the analyst more control over these envelopes. We demonstrate the
validity of our method by providing three numerical examples to calibrate
different models, including a model for energy dissipation in lap joints under
impact loading. By calibrating models with respect to the validation metrics
one desires a model to ultimately pass, reliability and safety metrics may be
integrated into and automatically adopted by the model in the calibration
phase
Entropic Updating of Probabilities and Density Matrices
We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probabilities and density matrices, respectively. From the same set of inferentially guided design criteria, both of the previously stated entropies are derived in parallel. This formulates a quantum maximum entropy method for the purpose of inferring density matrices in the absence of complete information
Theoretical Study of Variable Measurement Uncertainty h_I and Infinite Unobservable Entropy
This paper examines the statistical mechanical and thermodynamical consequences of variable phase-space volume element . Varying leads to variations in the amount of measured entropy of a system but the maximum entropy remains constant due to the uncertainty principle. By taking an infinite unobservable entropy is attained leading to an infinite unobservable energy per particle and an unobservable chemical equilibrium between all particles. The amount of heat fluxing though measurement apparatus is formulated as a function of for systems in steady state equilibrium as well as the number of measured particles or sub-particles so any system can be described as unitary or composite in number. Some example systems are given using variable