 Next Article in Journal
The Mehler-Fock Transform in Signal Processing
Previous Article in Journal
Modeling Multi-Event Non-Point Source Pollution in a Data-Scarce Catchment Using ANN and Entropy Analysis
Open AccessArticle

# Assessing Probabilistic Inference by Comparing the Generalized Mean of the Model and Source Probabilities

1
Electrical and Computer Engineering Department, Boston University, Boston, MA 02215, USA
2
Raytheon Company, Woburn, MA 01808, USA
Academic Editor: Raúl Alcaraz Martínez
Entropy 2017, 19(6), 286; https://doi.org/10.3390/e19060286
Received: 31 May 2017 / Revised: 10 June 2017 / Accepted: 12 June 2017 / Published: 19 June 2017
(This article belongs to the Section Information Theory, Probability and Statistics)
An approach to the assessment of probabilistic inference is described which quantifies the performance on the probability scale. From both information and Bayesian theory, the central tendency of an inference is proven to be the geometric mean of the probabilities reported for the actual outcome and is referred to as the “Accuracy”. Upper and lower error bars on the accuracy are provided by the arithmetic mean and the −2/3 mean. The arithmetic is called the “Decisiveness” due to its similarity with the cost of a decision and the −2/3 mean is called the “Robustness”, due to its sensitivity to outlier errors. Visualization of inference performance is facilitated by plotting the reported model probabilities versus the histogram calculated source probabilities. The visualization of the calibration between model and source is summarized on both axes by the arithmetic, geometric, and −2/3 means. From information theory, the performance of the inference is related to the cross-entropy between the model and source distribution. Just as cross-entropy is the sum of the entropy and the divergence; the accuracy of a model can be decomposed into a component due to the source uncertainty and the divergence between the source and model. Translated to the probability domain these quantities are plotted as the average model probability versus the average source probability. The divergence probability is the average model probability divided by the average source probability. When an inference is over/under-confident, the arithmetic mean of the model increases/decreases, while the −2/3 mean decreases/increases, respectively. View Full-Text
Keywords:
Show Figures Figure 1

MDPI and ACS Style

Nelson, K.P. Assessing Probabilistic Inference by Comparing the Generalized Mean of the Model and Source Probabilities. Entropy 2017, 19, 286. https://doi.org/10.3390/e19060286

AMA Style

Nelson KP. Assessing Probabilistic Inference by Comparing the Generalized Mean of the Model and Source Probabilities. Entropy. 2017; 19(6):286. https://doi.org/10.3390/e19060286

Chicago/Turabian Style

Nelson, Kenric P. 2017. "Assessing Probabilistic Inference by Comparing the Generalized Mean of the Model and Source Probabilities" Entropy 19, no. 6: 286. https://doi.org/10.3390/e19060286

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

### Article Access Map by Country/Region

1
Search more from Scilit
Back to TopTop