Fixed-Width Output Analysis for Markov Chain Monte Carlo

Markov chain Monte Carlo is a method of producing a correlated sample in order to estimate features of a complicated target distribution via simple ergodic averages. A fundamental question in MCMC applications is when should the sampling stop? That is, when are the ergodic averages good estimates of the desired quantities? We consider a method that stops the MCMC sampling the first time the width of a confidence interval based on the ergodic averages is less than a user-specified value. Hence calculating Monte Carlo standard errors is a critical step in assessing the output of the simulation. In particular, we consider the regenerative simulation and batch means methods of estimating the variance of the asymptotic normal distribution. We describe sufficient conditions for the strong consistency and asymptotic normality of both methods and investigate their finite sample properties in a variety of examples.

Age determination and grain size distribution of sediment core GeoB3375-1

The palaeoclimatic conditions during the Last Glacial Maximum (LGM) of southern South America and especially latitudinal shifts of the southern westerly wind belt are still discussed controversially. Longer palaeoclimatic records covering the Late Quaternary are rare. A particularly sensitive area to Late Quaternary climatic changes is the Norte Chico, northern Chile, because of its extreme climatic gradients. Small shifts of the present climatic zonation could cause significant variations of the terrestrial sedimentary environment which would be recorded in marine terrigenous sediments. To unveil the history of shifting climatic zones in northern Chile, we present a sedimentological study of a marine sediment core (GeoB 3375-1) from the continental slope off the Norte Chico (27.5°S). Sedimentological investigations include bulk- and silt grain-size determinations by sieving, Atterberg separation, and detailed SediGraph analyses. Additionally, clay mineralogical parameters were obtained by X-ray diffraction methods. The 14C-dated core, covering the time span from approximately 10,000 to 120,000 cal. yr B.P., consists of hemipelagic sediments. Terrigenous sedimentological parameters reveal a strong cyclicity, which is interpreted in terms of variations of sediment provenance, modifications of the terrestrial weathering regimes, and modes of sediment input to the ocean. These interpretations imply cyclic variations between comparatively arid climates and more humid conditions with seasonal precipitation for northern Chile (27.5°S) through the Late Quaternary. The cyclicity of the terrigenous sediment parameters is strongly dominated by precessional cycles. For the palaeoclimatic signal, this means that more humid conditions coincide with maxima of the precession index, as e.g. during the LGM. Higher seasonal precipitation for this part of Chile is most likely derived from frontal winter rain of the Southern Westerlies. Thus, the data presented here favour not only an equatorward shift of this atmospheric circulation system during the LGM, but also precession-controlled latitudinal movements throughout the Late Quaternary. Precessional forcing of latitudinal movements of the westerly atmospheric circulation system may be conceivable through teleconnections to the Northern Hemisphere monsoonal system in the Atlantic Ocean region.

Distribution of planktonic foraminifera in the Southern Ocean (maps)

There are about 30 species of planktonic Foraminifera, as contrasted with the more than 4200 benthic species in the oceans of the world. Most of the planktonic species belong to the families Globigerinidae and Globorotaliidae. Of the 30 species, 9 occur in Antarctic and Subantarctic waters; however, none of these cold-water species are restricted to the Southern Ocean, except possibly the newly recognized Globorotalia cavernula (Be, 1967b). These species are distributed in broad zones of similar temperature in both the Northern and Southern Hemispheres. Hence, it is not possible to refer to these species as endemic to the Antarctic or Subantarctic, although some of them do appear in very high concentrations of 10 specimens/m**3 or more in the Antarctic regions. The plankton samples upon which the accompanying maps are based were collected between 1960 and 1965 on the research vessels Eltanin of the National Science Foundation (U.S. Antarctic Research Program), and Vema and Conrad of the Lamont Geological Observatory. All surface (0 m to 10 m) and vertical (0 m to 300 m) tows were obtained with plankton nets of uniform mesh size and material (NITEX202 = 202 µm mesh-aperture width) and were provided with flowmeters for quantitative readings of amounts of water filtered.