A Bayesian approach to estimating the regression coefficients of a multinomial logit model

A Bayesian approach to estimation of the regression coefficients of a multinominal logit model with ordinal scale response categories is presented. A Monte Carlo method is used to construct the posterior distribution of the link function. The link function is treated as an arbitrary scalar function. Then the Gauss-Markov theorem is used to determine a function of the link which produces a random vector of coefficients. The posterior distribution of the random vector of coefficients is used to estimate the regression coefficients. The method described is referred to as a Bayesian generalized least square (BGLS) analysis. Two cases involving multinominal logit models are described. Case I involves a cumulative logit model and Case II involves a proportional-odds model. All inferences about the coefficients for both cases are described in terms of the posterior distribution of the regression coefficients. The results from the BGLS method are compared to maximum likelihood estimates of the regression coefficients. The BGLS method avoids the nonlinear problems encountered when estimating the regression coefficients of a generalized linear model. The method is not complex or computationally intensive. The BGLS method offers several advantages over Bayesian approaches. ^

(Table 1) Stratigraphic position, abundance, shape, color, and refractive indices of glass shards of selected samples from DSDP Leg 60 Holes vitric muds

Precisely determined refractive indices of glass shards from 32 ash-rich, volcaniclastic sediments, mostly turbidites interbedded with nonvolcanic sediments in the Mariana Trough, range from 1.480 to 1.585 (corresponding to SiO2 ca. 75 to 49%), with most in the range 1.500 to 1.540 (SiO2 ca. 70-62%) and a second, smaller mode between ca. 1.560 and 1.585 (57 to 49% SiO2). Shards are almost exclusively colorless from 1.480 to ca. 1.530, light brown with minor colorless and green tones between 1.530 and 1.560, and dominantly brown at higher refractive indices. Tubular pumice shards are more common at higher silica percentages and non- to poorly-vesicular cuniform shards at low SiO2 values, but there is no clear correlation between shape and composition of shards. About half of the samples have bimodal shard populations with silica differences ranging up to 20 percent; unimodal layers have a range of up to about 7 percent SiO2. Of 21 samples in which one type of shard dominates, seven have the main mode in the rhyolitic composition (>69% SiO2), eight in the intermediate range (56 to 69% SiO2), and five in mafic composition (SiO2 <53%). These unusually abundant mafic shards occur mainly in site survey piston cores, SP-IA and 4E, and in Holes 454, 456, 458, and 459B. These are the sites closest to the present arc. Hole 453, containing by far the most vitric tuff turbidites, shows a gradual increase in silica content of ash layers upward to the hole from Cores 36 to 19 (about 4.6 to 3.0 Ma). A drastic decrease in ash-rich beds in the younger (Pleistocene) part of this hole was noted by the shipboard party (see site chapter, Site 453) and was interpreted by them as indicating increasing distance from the arc volcanoes as the trough opened. The increase in silica in ashes from the early to the late Pliocene at Site 453 could be interpreted in the same way and might indicate that the trough started to open in early Pliocene time.

Permeability, overburden stress and friction coefficients of ODP Hole 190-1173A and 190-1174B

Permeability measured on three samples in a triaxial cell under effective confining pressure from 0.2 to 2.5 MPa ranges from 10**-18 to 10**-19 m**2. Overall, results indicate that permeability decreases with effective confining pressure up to 1.5 MPa; however, measurements at low effective pressure are too dispersed to yield a precise general relationship between permeability and pressure. When the effective pressure is increased from 1.5 to 2.5 MPa, permeability is roughly constant (~1-4 x 10**-19 m**2). Samples deformed in the triaxial cell developed slickenlined fractures, and permeability measurements were performed before and after failure. A permeability increase is observed when the sample fails under low effective confining pressure (0.2 MPa), but not under effective pressure corresponding to the overburden stress. Under isotropic stress conditions, permeability decrease related to fracture closure occurs at a relatively high effective pressure of ~1.5 MPa. Coefficients of friction on the fractures formed in the triaxial cell are ~0.4.

Discription of coastal shape at Bykovsky Peninsula

This article presents a comparison of sediment input by rivers and by coastal erosion into both the Laptev Sea and the Canadian Beaufort Sea (CBS). New data on coastal erosion in the Laptev Sea, which are based on field measurements and remote sensing information, and existing data on coastal erosion in the CBS as well as riverine sediment discharge into both the Laptev Sea and the CBS are included. Strong regional differences in the percentages of coastal erosion and riverine sediment supply are observed. The CBS is dominated by the riverine sediment discharge (64.45210**6 t/a) mainly of the Mackenzie River, which is the largest single source of sediments in the Arctic. Riverine sediment discharge into the Laptev Sea amounts to 24.10210**6 t/a, more than 70% of which are related to the Lena River. In comparison with the CBS, the Laptev Sea coast on average delivers approximately twice as much sediment mass per kilometer, a result of higher erosion rates due to higher cliffs and seasonal ice melting. In the Laptev Sea sediment input by coastal erosion (58.4210**6 t/a) is therefore more important than in the CBS and the ratio between riverine and coastal sediment input amounts to 0.4. Coastal erosion supplying 5.6210**6 t/a is less significant for the sediment budget of the CBS where riverine sediment discharge exceeds coastal sediment input by a factor of ca. 10.