Sets of probability distributions, independence, and convexity

This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli's discussion of "convex Bayesianism" (in particular their proposals concerning E-admissibility, independence, and convexity). The paper offers an organized review of the literature on independence for sets of probability distributions; new results on graphoid properties and on the justification of "strong independence" (using exchangeability) are presented. Finally, the connection between Kyburg and Pittarelli's results and recent developments on the axiomatization of non-binary preferences, and its impact on "complete" independence, are described.

Detection of one slowly exchanging substrate water molecule in the S3 state of photosystem II.

The exchangeability of the substrate water molecules at the catalytic site of water oxidation in photosystem II has been probed by isotope-exchange measurements using mass spectrometric detection of flash-induced oxygen evolution. A stirred sample chamber was constructed to reduce the lag time between injection of H2(18)O and the detecting flash by a factor of more than 1000 compared to the original experiments by R. Radmer and O. Ollinger [(1986) FEBS Lett. 195, 285-289]. Our data show that there is a slow (t1/2 approximately 500 ms, 10 degrees C) and a fast (t1/2 <25 ms, 10 degrees C) exchanging substrate water molecule in the S3 state of photosystem II. The slow exchange is coupled with an activation energy of about 75 kJ/mol and is discussed in terms of a terminal manganese oxo ligand, while the faster exchanging substrate molecule may represent a water molecule not directly bound to the manganese center.

On The Dirichlet Distribution

The Dirichlet distribution is a multivariate generalization of the Beta distribution. It is an important multivariate continuous distribution in probability and statistics. In this report, we review the Dirichlet distribution and study its properties, including statistical and information-theoretic quantities involving this distribution. Also, relationships between the Dirichlet distribution and other distributions are discussed. There are some different ways to think about generating random variables with a Dirichlet distribution. The stick-breaking approach and the Pólya urn method are discussed. In Bayesian statistics, the Dirichlet distribution and the generalized Dirichlet distribution can both be a conjugate prior for the Multinomial distribution. The Dirichlet distribution has many applications in different fields. We focus on the unsupervised learning of a finite mixture model based on the Dirichlet distribution. The Initialization Algorithm and Dirichlet Mixture Estimation Algorithm are both reviewed for estimating the parameters of a Dirichlet mixture. Three experimental results are shown for the estimation of artificial histograms, summarization of image databases and human skin detection.

Shifting Processes with Cyclically Exchangeable Increments at Random

International audience

Evidence that risk adjustment is unnecessary in estimates of the User cost of money

Investors value the special attributes of monetary assets (e.g., exchangeability, liquidity, and safety) and pay a premium for holding them in the form of a lower return rate -- The user cost of holding monetary assets can be measured approximately by the difference between the returns on illiquid risky assets and those of safer liquid assets -- A more appropriate measure should adjust this difference by the differential risk of the assets in question -- We investigate the impact that time non-separable preferences has on the estimation of the risk-adjusted user cost of money -- Using U.K. data from 1965Q1 to 2011Q1, we estimate a habit-based asset pricing model with money in the utility function and find that the risk adjustment for risky monetary assets is negligible -- Thus, researchers can dispense with risk adjusting the user cost of money in constructing monetary aggregate indexes