Comparison of three expert elicitation methods for logistic regression on predicting the presence of the threatened brush-tailed rock-wallaby petrogale penicillata

Numerous expert elicitation methods have been suggested for generalised linear models (GLMs). This paper compares three relatively new approaches to eliciting expert knowledge in a form suitable for Bayesian logistic regression. These methods were trialled on two experts in order to model the habitat suitability of the threatened Australian brush-tailed rock-wallaby (Petrogale penicillata). The first elicitation approach is a geographically assisted indirect predictive method with a geographic information system (GIS) interface. The second approach is a predictive indirect method which uses an interactive graphical tool. The third method uses a questionnaire to elicit expert knowledge directly about the impact of a habitat variable on the response. Two variables (slope and aspect) are used to examine prior and posterior distributions of the three methods. The results indicate that there are some similarities and dissimilarities between the expert informed priors of the two experts formulated from the different approaches. The choice of elicitation method depends on the statistical knowledge of the expert, their mapping skills, time constraints, accessibility to experts and funding available. This trial reveals that expert knowledge can be important when modelling rare event data, such as threatened species, because experts can provide additional information that may not be represented in the dataset. However care must be taken with the way in which this information is elicited and formulated.

Raman spectroscopic study of the antimonate mineral bahianite Al5Sb35+O14(OH)2

Raman spectroscopy has been used to characterise the antimonate mineral bahianite Al5Sb35+O14(OH)2 , a semi-precious gem stone. The mineral is characterised by an intense Raman band at 818 cm-1 assigned to Sb3O1413- stretching vibrations. Other lower intensity bands at 843 and 856 cm-1 are also assigned to this vibration and this concept suggests the non-equivalence of SbO units in the structure. Low intensity Raman bands at 669 and 682 cm-1 are probably assignable to the OSbO antisymmetric stretching vibrations. Raman bands at 1756, 1808 and 1929 cm-1 may be assigned to δ SbOH deformation modes, whilst Raman bands at 3462 and 3495 cm-1 are assigned to AlOH stretching vibrations. Complexity in the low wave number region is attributed to the composition of the mineral.

Raman spectroscopic study of the phosphate mineral Churchite-(Y) YPO4.2H2O

Raman spectroscopy has been used to study the rare earth mineral churchite-(Y) of formula (Y,REE)(PO4) •2H2O. The mineral contains yttrium and depending on the locality, a range of rare earth metals. The Raman spectra of two churchite-(Y) mineral samples from Jáchymov and Medvědín in the Czech Republic were compared with the Raman spectra of churchite-(Y) downloaded from the RRUFF data base. The Raman spectra of churchite-(Y) are characterized by an intense sharp band at 975 cm-1 assigned to the ν1 (PO4)3- symmetric stretching mode. A lower intensity band observed at around 1065 cm-1 is attributed to the ν3 (PO43-) antisymmetric stretching mode. The (PO43-) bending modes are observed at 497 cm-1 (ν2) and 563 cm-1(ν4). Some small differences in the band positions between the four churchite-(Y) samples from four different localities were found. These differences are possible to explain as different compositions of the churchite-(Y) minerals.

Raman spectroscopic study of the antimonate mineral lewisite (Ca,Fe,Na)2(Sb,Ti)2O6(O,OH)7

The mineral lewisite, (Ca,Fe,Na)2(Sb,Ti)2O6(O,OH)7 an antimony bearing mineral has been studied by Raman spectroscopy. A comparison is made with the Raman spectra of other minerals including bindheimite, stibiconite and roméite. The mineral lewisite is characterised by an intense sharp band at 517 cm-1 with a shoulder at 507 cm-1 assigned to SbO stretching modes. Raman bands of medium intensity for lewisite are observed at 300, 356 and 400 cm-1. These bands are attributed to OSbO bending vibrations. Raman bands in the OH stretching region are observed at 3200, 3328, 3471 cm-1 with a distinct shoulder at 3542 cm-1. The latter is assigned to the stretching vibration of OH units. The first three bands are attributed to water stretching vibrations. The observation of bands in the 3200 to 3500 cm-1 region suggests that water is involved in the lewisite structure. If this is the case then the formula may be better written as Ca, Fe2+, Na)2(Sb, Ti)2(O,OH)7 •xH2O.

Raman spectroscopic study of the antimonate mineral brizziite NaSbO3

Raman spectra of antimonate mineral brizziite NaSbO3 were studied and related to the structure of the mineral. Two sharp bands at 617 and 660 cm-1 are attributed to the SbO3- symmetric stretching mode. The reason for two symmetric stretching vibrations depends upon the bonding of the SbO3- units. The band at 617 cm-1 is assigned to bonding through the Sb and the 660 cm-1 to bonding through the oxygen. The low intensity band at 508 cm-1 is ascribed to the SbO antisymmetric stretching vibration. Low intensity bands were found at 503, 526 and 578 cm-1. Sharp Raman bands observed at 204, 230, 307 and 315 cm-1are assigned to OSbO bending modes. Raman spectroscopy enables a better understanding of the molecular structure of the mineral brizziite.

An application of near-infrared and mid-infrared spectroscopy to the study of selected minerals

Near-infrared spectroscopy is a somewhat unutilised technique for the study of minerals. The technique has the ability to determine water content, hydroxyl groups and transition metals. In this paper we show the application of NIR spectroscopy to the study of selected minerals. The structure and spectral properties of two Cu-tellurite minerals graemite and teineite are compared with bismuth containing tellurite mineral smirnite by the application of NIR and IR spectroscopy. The position of Cu2+ bands and their splitting in the electronic spectra of tellurites are in conformity with octahedral geometry distortion. The spectral pattern of smirnite resembles graemite and the observed band at 10855 cm-1 with a weak shoulder at 7920 cm-1 is identified as due to Cu2+ ion. Any transition metal impurities may be identified by their bands in this spectral region. Three prominent bands observed in the region of 7200-6500 cm-1 are the overtones of water whilst the weak bands observed near 6200 cm-1in tellurites may be attributed to the hydrogen bonding between (TeO3)2- and H2O. The observation of a number of bands centred at around 7200 cm-1 confirms molecular water in tellurite minerals. A number of overlapping bands in the low wavenumbers 4500-4000 cm-1 is the result of combinational modes of (TeO3)2−ion. The appearance of the most intense peak at 5200 cm-1 with a pair of weak bands near 6000 cm-1 is a common feature in all the spectra and is related to the combinations of OH vibrations of water molecules, and bending vibrations ν2 (δ H2O). Bending vibrations δ H2O observed in the IR spectra shows a single band for smirnite at 1610 cm-1. The resolution of this band into number of components is evidenced for non-equivalent types of molecular water in graemite and teineite. (TeO3)2- stretching vibrations are characterized by three main absorptions at 1080, 780 and 695 cm-1.

Delay distribution based robust H∞ control of networked control systems with uncertainties

Network induced delay in networked control systems (NCS) is inherently non-uniformly distributed and behaves with multifractal nature. However, such network characteristics have not been well considered in NCS analysis and synthesis. Making use of the information of the statistical distribution of NCS network induced delay, a delay distribution based stochastic model is adopted to link Quality-of-Control and network Quality-of-Service for NCS with uncertainties. From this model together with a tighter bounding technology for cross terms, H∞ NCS analysis is carried out with significantly improved stability results. Furthermore, a memoryless H∞ controller is designed to stabilize the NCS and to achieve the prescribed disturbance attenuation level. Numerical examples are given to demonstrate the effectiveness of the proposed method.

Raman spectroscopic study of the mineral finnemanite Pb5(As3+O3)3Cl

The arsenite minerals finnemanite Pb5(As3+O3)3Cl been studied by Raman spectroscopy. The most intense Raman band at 871 cm-1 is assigned to the ν1 (AsO3)3- symmetric stretching vibration. Three Raman bands at 898, 908 and 947 cm-1 are assigned to the ν3 (AsO3)3- antisymmetric stretching vibration. The observation of multiple antisymmetric stretching vibrations suggest that the (AsO3)3- units are not equivalent in the molecular structure of finnemanite. Two Raman bands at 383 and 399 cm-1 are assigned to the ν2 (AsO3)3- bending modes. DFT calculations enabled the position of AsO32- symmetric stretching mode at 839 cm-1, the antisymmetric stretching mode at 813 cm-1, and the deformation mode at 449 cm-1 to be calculated. Raman bands are observed at 115, 145, 162, 176, 192, 216 and 234 cm-1 as well. The two most intense bands are observed at 176 and 192 cm-1. These bands are assigned to PbCl stretching vibrations and result from transverse/ longitudinal splitting. The bands at 145 and 162 cm-1 may be assigned to Cl-Pb-Cl bending modes.

Raman spectroscopic study of the arsenite minerals leiteite ZnAs2O4 , reinerite Zn3(AsO3)2 and cafarsite Ca5(Ti,Fe,Mn)7(AsO3)12.4H2O

The selected arsenite minerals leiteite, reinerite and cafarsite have been studied by Raman spectroscopy. DFT calculations enabled the position of AsO22- symmetric stretching mode at 839 cm-1, the antisymmetric stretching mode at 813 cm-1, and the deformation mode at 449 cm-1 to be calculated. The Raman spectrum of leiteite shows bands at 804 and 763 cm-1 assigned to the As2O42- symmetric and antisymmetric stretching modes. The most intense Raman band of leiteite is the band at 457 cm-1 and is assigned to the ν2 As2O42- bending mode. A comparison of the Raman spectrum of leiteite is made with the arsenite minerals reinerite and cafarsite.

Raman spectroscopic study of the multi-anion mineral dixenite CuMn2+14Fe3+(AsO3)5(SiO4)2(AsO4)(OH)6

The mixed anion mineral dixenite has been studied by Raman spectroscopy, complimented with infrared spectroscopy. The Raman spectrum of dixenite shows bands at 839 and 813 cm-1 assigned to the (AsO3)3- symmetric and antisymmetric stretching modes. The most intense Raman band of dixenite is the band at 526 cm-1 and is assigned to the ν2 AsO33- bending mode. DFT calculations enabled the position of AsO22- symmetric stretching mode at 839 cm-1, the antisymmetric stretching mode at 813 cm-1, and the deformation mode at 449 cm-1 to be calculated. Raman bands at 1026 and 1057 cm-1 are assigned to the SiO42- symmetric stretching vibrations and at 1349 and 1386 cm-1 to the SiO42- antisymmetric stretching vibrations. Both Raman and infrared spectra indicate the presence of water in the structure of dixenite. This brings into question the commonly accepted formula of dixenite as CuMn2+14Fe3+(AsO3)5(SiO4)2(AsO4)(OH)6. The formula may be better written as CuMn2+14Fe3+(AsO3)5(SiO4)2(AsO4)(OH)6•xH2O.