On the relation between plausibility logic and the maximum-entropy principle: a numerical study

What is the relationship between plausibility logic and the principle of maximum entropy? When does the principle give unreasonable or wrong results? When is it appropriate to use the rule `expectation = average'? Can plausibility logic give the same answers as the principle, and better answers if those of the principle are unreasonable? To try to answer these questions, this study offers a numerical collection of plausibility distributions given by the maximum-entropy principle and by plausibility logic for a set of fifteen simple problems: throwing dice.Comment: 24 pages of main text and references, 8 pages of tables, 7 pages of additional reference

A Multifrequency Analysis of the Polarized Diffuse Galactic Radio Emission at Degree Scales

The polarized diffuse Galactic radio emission, mainly synchrotron emission, is expected to be one of the most relevant source of astrophysical contamination at low and moderate multipoles in cosmic microwave background polarization anisotropy experiments at frequencies lower then 50 to 100 GHz. We present here preliminary results based on a recent analysis of the Leiden surveys covering about 50% of the sky at low as well as at middle and high Galactic latitudes. By implementing specific interpolation methods to deal with these data, which show a large variation of the sampling across the sky, we produce maps of the polarized diffuse Galactic synchrotron component at frequencies between 408 and 1411 MHz with pixel sizes larger or equal to about 0.92 degrees. We derive the angular power spectrum of this component for the whole covered region and for three patches in the sky significantly oversampled with respect to the average and at different Galactic latitudes. We find multipole spectral indices typically ranging between about -3 and about -1, according to the considered frequency and sky region. At frequencies higher or equal to 610 MHz, the frequency spectral indices observed in the considered sky regions are about -3.5, compatible with an intrinsic frequency spectral index of about -5.8 and a depolarization due to Faraday rotation with a rotation measure RM of about 15 radians per square meter. This implies that the observed angular power spectrum of the polarized signal is about 85% or 20% of the intrinsic one at 1411 MHz or 820 MHz respectively.Comment: 6 pages, 5 figures. to appear in S.Cecchini et al., Astrophysical Polarized Backgrounds, AIP Conf. Proceeding

Factors Affecting Biodiversity Protection in the Mediterranean Basin

Earth’s biodiversity includes all extant species; however, species are not evenly distributed across the planet. Species tend to be clustered in densely populated areas known as “biodiversity hotspots;” species which inhabit only a single area are also termed “endemic,” and tend to be highly vulnerable to population-reducing changes in their environment. Biodiversity hotspots are considered priorities for conservation if the area has a high rate of endemism as well as a notable and continual habitat loss (Noss et al., 2015). Preventing biodiversity loss is a complex and multi-level decision-making process about setting priorities and defining clear biodiversity protection areas. Biodiversity loss, or the loss of entire species or sub-populations in an area, can be driven by multiple processes, including land use changes, climate change, and the introduction of invasive species (Plexida et al. 2018). The Mediterranean Basin is one such hotspot, transecting multiple countries surrounding the Mediterranean Sea, including European, Middle Eastern, and North African countries with different systems of government and cultural perceptions of environmental resources and biodiversity. Furthermore, the basin is one the most species-rich biodiversity hotspots on Earth in terms of endemic vascular plants and has high rates of endemism for amphibians and fish, as well as being an important migration corridor for many bird species (Cuttelod et al., 2008). The hotspot is at high risk for continued biodiversity loss due to 53 several human-driven factors including population increase and government-level environmental policies (Grainger, 2003)

The Laplace-Jaynes approach to induction

An approach to induction is presented, based on the idea of analysing the context of a given problem into `circumstances'. This approach, fully Bayesian in form and meaning, provides a complement or in some cases an alternative to that based on de Finetti's representation theorem and on the notion of infinite exchangeability. In particular, it gives an alternative interpretation of those formulae that apparently involve `unknown probabilities' or `propensities'. Various advantages and applications of the presented approach are discussed, especially in comparison to that based on exchangeability. Generalisations are also discussed.Comment: 38 pages, 1 figure. V2: altered discussion on some points, corrected typos, added reference

Numerical Bayesian state assignment for a three-level quantum system. I. Absolute-frequency data; constant and Gaussian-like priors

This paper offers examples of concrete numerical applications of Bayesian quantum-state-assignment methods to a three-level quantum system. The statistical operator assigned on the evidence of various measurement data and kinds of prior knowledge is computed partly analytically, partly through numerical integration (in eight dimensions) on a computer. The measurement data consist in absolute frequencies of the outcomes of N identical von Neumann projective measurements performed on N identically prepared three-level systems. Various small values of N as well as the large-N limit are considered. Two kinds of prior knowledge are used: one represented by a plausibility distribution constant in respect of the convex structure of the set of statistical operators; the other represented by a Gaussian-like distribution centred on a pure statistical operator, and thus reflecting a situation in which one has useful prior knowledge about the likely preparation of the system. In a companion paper the case of measurement data consisting in average values, and an additional prior studied by Slater, are considered.Comment: 23 pages, 14 figures. V2: Added an important note concerning cylindrical algebraic decomposition and thanks to P B Slater, corrected some typos, added reference

Numerical Bayesian quantum-state assignment for a three-level quantum system. II. Average-value data with a constant, a Gaussian-like, and a Slater prior

This paper offers examples of concrete numerical applications of Bayesian quantum-state assignment methods to a three-level quantum system. The statistical operator assigned on the evidence of various measurement data and kinds of prior knowledge is computed partly analytically, partly through numerical integration (in eight dimensions) on a computer. The measurement data consist in the average of outcome values of N identical von Neumann projective measurements performed on N identically prepared three-level systems. In particular the large-N limit will be considered. Three kinds of prior knowledge are used: one represented by a plausibility distribution constant in respect of the convex structure of the set of statistical operators; another one represented by a prior studied by Slater, which has been proposed as the natural measure on the set of statistical operators; the last prior is represented by a Gaussian-like distribution centred on a pure statistical operator, and thus reflecting a situation in which one has useful prior knowledge about the likely preparation of the system. The assigned statistical operators obtained with the first two kinds of priors are compared with the one obtained by Jaynes' maximum entropy method for the same measurement situation. In the companion paper the case of measurement data consisting in absolute frequencies is considered.Comment: 10 pages, 4 figures. V2: added "Post scriptum" under Conclusions, slightly changed Acknowledgements, and corrected some spelling error