Bayesian adaptive estimation of arbitrary points on a psychometric function

Bayesian adaptive methods have been extensively used in psychophysics to estimate the point at which performance on a task attains arbitrary percentage levels, although the statistical properties of these estimators have never been assessed. We used simulation techniques to determine the small-sample properties of Bayesian estimators of arbitrary performance points, specifically addressing the issues of bias and precision as a function of the target percentage level. The study covered three major types of psychophysical task (yes-no detection, 2AFC discrimination and 2AFC detection) and explored the entire range of target performance levels allowed for by each task. Other factors included in the study were the form and parameters of the actual psychometric function Psi, the form and parameters of the model function M assumed in the Bayesian method, and the location of Psi within the parameter space. Our results indicate that Bayesian adaptive methods render unbiased estimators of any arbitrary point on psi only when M=Psi, and otherwise they yield bias whose magnitude can be considerable as the target level moves away from the midpoint of the range of Psi. The standard error of the estimator also increases as the target level approaches extreme values whether or not M=Psi. Contrary to widespread belief, neither the performance level at which bias is null nor that at which standard error is minimal can be predicted by the sweat factor. A closed-form expression nevertheless gives a reasonable fit to data describing the dependence of standard error on number of trials and target level, which allows determination of the number of trials that must be administered to obtain estimates with prescribed precision.

Verification of the indoor gps system by comparison with points calibrated using a network of laser tracker measurements

This paper details a method of determining the uncertainty of dimensional measurement for a three dimensional coordinate measurement machine. An experimental procedure was developed to compare three dimensional coordinate measurements with calibrated reference points. The reference standard used to calibrate these reference points was a fringe counting interferometer with the multilateration technique employed to establish three dimensional coordinates. This is an extension of the established technique of comparing measured lengths with calibrated lengths. Specifically a distributed coordinate measurement device was tested which consisted of a network of Rotary-Laser Automatic Theodolites (R-LATs), this system is known commercially as indoor GPS (iGPS). The method was found to be practical and able to establish that the expanded uncertainty of the basic iGPS system was approximately 1 mm at a 95% confidence level. © Springer-Verlag Berlin Heidelberg 2010.

(Table 1) Age control points and dating methods for sediment cores of the Sea of Okhotsk

Marine- and terrestrial-derived biomarkers (alkenones, brassicasterol, dinosterol, and long-chain n-alkanes), as well as carbonate, biogenic opal, and ice-rafted debris (IRD), were measured in two sediment cores in the Sea of Okhotsk, which is located in the northwestern Pacific rim and characterized by high primary productivity. Down-core profiles of phytoplankton markers suggest that primary productivity abruptly increased during the global Meltwater Pulse events 1A (about 14 ka) and 1B (about 11 ka) and stayed high in the Holocene. Spatial and temporal distributions of the phytoplankton productivity were found to be consistent with changes in the reconstructed sea ice distribution on the basis of the IRD. This demonstrates that the progress and retreat of sea ice regulated primary productivity in the Sea of Okhotsk with minimum productivity during the glacial period. The mass accumulation rates of alkenones, CaCO3, and biogenic opal indicate that the dominant phytoplankton species during deglaciation was the coccolithophorid, Emiliania huxleyi, which was replaced by diatoms in the late Holocene. Such a phytoplankton succession was probably caused by an increase in silicate supply to the euphotic layer, possibly associated with a change in surface hydrography and/or linked to enhanced upwelling of North Pacific Deep Water.

(Table S1) Tie-points used in age model construction for ODP Leg 172 sites

ix Ocean Drilling Program (ODP) sites, in the Northwest Atlantic have been used to investigate kinematic and chemical changes in the "Western Boundary Undercurrent" (WBUC) during the development of full glacial conditions across the Marine Isotope Stage 5a/4 boundary (~70,000 years ago). Sortable silt mean grain size(sort s) measurements are employed to examine changes in near bottom flow speeds, together with carbon isotopes measured in benthic foraminifera and % planktic foraminiferal fragmentation as proxies for changes in water-mass chemistry. A depth transect of cores, spanning 1.8-4.6 km depth, allows changes in both the strength and depth of the WBUC to be constrained across millennial scale events. Sort s measurements reveal that the flow speed structure of the WBUC during warm intervals ("interstadials") was comparable to modern (Holocene) conditions. However, significant differences are observed during cold intervals, with higher relative flow speeds inferred for the shallow component of the WBUC (~2 km depth) during all cold "stadial" intervals (including Heinrich Stadial 6), and a substantial weakening of the deep component (~3-4 km) during full glacial conditions. Our results therefore reveal that the onset of full glacial conditions was associated with a regime shift to a shallower mode of circulation (involving Glacial North Atlantic Intermediate Water) that was quantitatively distinct from preceding cold stadial events. Furthermore, our chemical proxy data show that the physical response of the WBUC during the last glacial inception was probably coupled to basin-wide changes in the water-mass composition of the deep Northwest Atlantic.

Age control points and sedimentation rates of ODP Hole 145-887B (Table 1)

Hole 887B of the Ocean Drilling Program (ODP) comprises a 44 m (750 kyr) long continuous section recovered from the Patton-Murray Rise, an elevated plateau that is largely isolated from turbidite deposition. The Patton-Murray area is centered under the Alaska Gyre, a region characterized by the domal upwelling of nutrient-rich waters. Marked increases in productivity and rapid settling of biogenic matter are suggested throughout the section by the episodic accumulation of diatomaceous oozes up to ~1 m thick that are accompanied by barium enrichments. Significant delta13Corg maxima in the major diatomaceous bands suggest that mixedlayer [CO2(aq)] may have been drawn down significantly during some of the productivity events. The episodes of enhanced productivity at Site 887 occur synchronously with short-lived minima in planktonic foram delta18O, suggesting a direct link to low salinity, or less likely, warming, events in the Gulf of Alaska. There is no obvious explanation for the events, but they may be related to seasonal incursions of meltwater from Alaska. We speculate that episodic input of meltwater- or dust-borne iron from Asian or Alaskan sources may have promoted the extraordinary diatom production events recorded in the sedimentary record.

(Table 1) Age control points and of sediment core MD01-2444

The marine isotopic stage 3 (MIS3) at Ocean Drilling Program (ODP) Site 1060 (Gulf Stream) shows both sharp onset and end of interstadials, the existence of very short lived warm events during stadials, and points to differences in detail between the sea surface temperature (SST) record from the western North Atlantic and the atmospheric temperature record inferred from d18O in Greenland ice. Investigating MIS3 and obtaining comparable data from other locations appears crucial. The eastern Atlantic provides well-documented records of climate changes. We have selected a core from off Portugal and use it to examine Dansgaard/Oeschger events (D/O) at centennial-scale resolution (139 years on average between two data points). We have obtained a faunal data set for core MD01-2444, 37°N, 10°W, 2600 m water depth and use a group of species (Globigerina bulloides + Globigerinita glutinata) as a proxy of upwelling intensity driven by trade winds intensity changes. We tentatively relate the variation of this group to a North Atlantic Oscillation-like phenomenon (NAO) off Portugal. We observe that it resembles the rainfall index in the Caribbean as recorded at ODP Site 1002 (Cariaco Basin) which traces the Intertropical Convergence Zone (ITCZ) location through changes of terrigenous inputs. The driest intervals (ITZC to the south) at Site 1002 correspond to intervals of increased upwelling in MD01-2444 as well as the driest periods identified during stadials on similar cores in the area. Because the ITZC to the south is consistent with an El Niño-Southern Oscillation (ENSO+) situation, our study suggests a positive correlation between ENSO-like conditions and NAO-like conditions at a millennial timescale. During interstadial intervals when increased wetness over Cariaco is recorded (ITCZ to the north) and the upwelling in MD01-2444 is decreased, we see from both SSTs and faunal tropical indicators that MD01-2444 site is warm. In addition, interstadials are equally warm through each so-called Bond cycle. This contrasts with the Greenland Ice Core Project (GRIP) record where interstadial peaks are successively cooler through each Bond cycle. This record confirms a link between tropical climate linked to ITCZ position and the climate of southern Europe at millennial timescales, in spite of showing a very good correlation with polar latitudes (GRIP) through d18O on Globigerina bulloides. In addition, because the warmest SSTs and the d18O on G. bulloides are so remarkably different, our work points to changes in seasonality as a strong control over the climatic pattern of the North Atlantic area and the marked influence of winter conditions.