Inferences about the coefficient of correlation in the standard bivariate normal distribution

The study of the association between two random variables that have a joint normal distribution is of interest in applied statistics; for example, in statistical genetics. This article, targeted to applied statisticians, addresses inferences about the coefficient of correlation (ρ) in the bivariate normal and standard bivariate normal distributions using likelihood, frequentist, and Baycsian perspectives. Some results are surprising. For instance, the maximum likelihood estimator and the posterior distribution of ρ in the standard bivariate normal distribution do not follow directly from results for a general bivariate normal distribution. An example employing bootstrap and rejection sampling procedures is used to illustrate some of the peculiarities.

Changes in the distribution of income and the New Economic Model in Jamaica

Includes bibliography

Study on the Curcumin dynamics and distribution through living biofilms

Human oral cavity is colonized by a wide range of microorganisms, often organized in biofilms. These biofilms are responsible for the pathogenesis of caries and most periodontal diseases. A possible alternative to reduce biofilms is the photodynamic inactivation (PDI). The success of the PDI depends on different factors. The time required by the PS to remain in contact with the target cells prior to illumination is determinant for the technique's efficacy. This study aimed to assess the interaction between the PS and the biofilm prior to the PDI. We used confocal microscopy and FLIM to evaluate the interaction between the PS and the biofilm's microorganism during the pre-irradiation time (PIT). The study of this dynamics can lead to the understanding of why only some PSs are effective and why is necessary a long PIT for some microorganisms. Our results showed that are differences for each PIT. These differences can be the determinate for the efficacy of the PDI. We observed that the microorganism needs time to concentrate and/or transport the PS within the biofilm. We presented preliminary results for biofilms of Candida albicans and Streptococcus mutans in the presence of Curcumin and compared it with the literature. We observed that the effectiveness of the PDI might be directly correlated to the position of the PS with the biofilm. Further analyses will be conducted in order to confirm the potential of FLIM to assess the PS dynamics within the biofilms. © 2013 SPIE.

A bayesian analysis for the parameters of the exponential-logarithmic distribution

The exponential-logarithmic is a new lifetime distribution with decreasing failure rate and interesting applications in the biological and engineering sciences. Thus, a Bayesian analysis of the parameters would be desirable. Bayesian estimation requires the selection of prior distributions for all parameters of the model. In this case, researchers usually seek to choose a prior that has little information on the parameters, allowing the data to be very informative relative to the prior information. Assuming some noninformative prior distributions, we present a Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. Jeffreys prior is derived for the parameters of exponential-logarithmic distribution and compared with other common priors such as beta, gamma, and uniform distributions. In this article, we show through a simulation study that the maximum likelihood estimate may not exist except under restrictive conditions. In addition, the posterior density is sometimes bimodal when an improper prior density is used. © 2013 Copyright Taylor and Francis Group, LLC.

Bayesian inference for two-parameter gamma distribution assuming different noninformative priors

In this paper distinct prior distributions are derived in a Bayesian inference of the two-parameters Gamma distribution. Noniformative priors, such as Jeffreys, reference, MDIP, Tibshirani and an innovative prior based on the copula approach are investigated. We show that the maximal data information prior provides in an improper posterior density and that the different choices of the parameter of interest lead to different reference priors in this case. Based on the simulated data sets, the Bayesian estimates and credible intervals for the unknown parameters are computed and the performance of the prior distributions are evaluated. The Bayesian analysis is conducted using the Markov Chain Monte Carlo (MCMC) methods to generate samples from the posterior distributions under the above priors.

Parameter recovery for a skew-normal IRT model under a Bayesian approach: hierarchical framework, prior and kernel sensitivity and sample size

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353-365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R. B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362-1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis-Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271-275]. Our algorithm has only one Metropolis-Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146-178; R. J. Patz and B. W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342-366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599-607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models.

Cardiogoniometric parameters for detection of coronary artery disease at rest as a function of stenosis localization and distribution

Cardiogoniometry (CGM), a spatiotemporal electrocardiologic 5-lead method with automated analysis, may be useful in primary healthcare for detecting coronary artery disease (CAD) at rest. Our aim was to systematically develop a stenosis-specific parameter set for global CAD detection. In 793 consecutively admitted patients with presumed non-acute CAD, CGM data were collected prior to elective coronary angiography and analyzed retrospectively. 658 patients fulfilled the inclusion criteria, 405 had CAD verified by coronary angiography; the 253 patients with normal coronary angiograms served as the non-CAD controls. Study patients--matched for age, BMI, and gender--were angiographically assigned to 8 stenosis-specific CAD categories or to the controls. One CGM parameter possessing significance (P < .05) and the best diagnostic accuracy was matched to one CAD category. The area under the ROC curve was .80 (global CAD versus controls). A set containing 8 stenosis-specific CGM parameters described variability of R vectors and R-T angles, spatial position and potential distribution of R/T vectors, and ST/T segment alterations. Our parameter set systematically combines CAD categories into an algorithm that detects CAD globally. Prospective validation in clinical studies is ongoing.

A global historical ozone data set and prominent features of stratospheric variability prior to 1979

We present a vertically resolved zonal mean monthly mean global ozone data set spanning the period 1901 to 2007, called HISTOZ.1.0. It is based on a new approach that combines information from an ensemble of chemistry climate model (CCM) simulations with historical total column ozone information. The CCM simulations incorporate important external drivers of stratospheric chemistry and dynamics (in particular solar and volcanic effects, greenhouse gases and ozone depleting substances, sea surface temperatures, and the quasi-biennial oscillation). The historical total column ozone observations include ground-based measurements from the 1920s onward and satellite observations from 1970 to 1976. An off-line data assimilation approach is used to combine model simulations, observations, and information on the observation error. The period starting in 1979 was used for validation with existing ozone data sets and therefore only ground-based measurements were assimilated. Results demonstrate considerable skill from the CCM simulations alone. Assimilating observations provides additional skill for total column ozone. With respect to the vertical ozone distribution, assimilating observations increases on average the correlation with a reference data set, but does not decrease the mean squared error. Analyses of HISTOZ.1.0 with respect to the effects of El Niño–Southern Oscillation (ENSO) and of the 11 yr solar cycle on stratospheric ozone from 1934 to 1979 qualitatively confirm previous studies that focussed on the post-1979 period. The ENSO signature exhibits a much clearer imprint of a change in strength of the Brewer–Dobson circulation compared to the post-1979 period. The imprint of the 11 yr solar cycle is slightly weaker in the earlier period. Furthermore, the total column ozone increase from the 1950s to around 1970 at northern mid-latitudes is briefly discussed. Indications for contributions of a tropospheric ozone increase, greenhouse gases, and changes in atmospheric circulation are found. Finally, the paper points at several possible future improvements of HISTOZ.1.0.

Mapping material distribution in a heterogeneous sand tank by image analysis

Water flow and solute transport through soils are strongly influenced by the spatial arrangement of soil materials with different hydraulic and chemical properties. Knowing the specific or statistical arrangement of these materials is considered as a key toward improved predictions of solute transport. Our aim was to obtain two-dimensional material maps from photographs of exposed profiles. We developed a segmentation and classification procedure and applied it to the images of a very heterogeneous sand tank, which was used for a series of flow and transport experiments. The segmentation was based on thresholds of soil color, estimated from local median gray values, and of soil texture, estimated from local coefficients of variation of gray values. Important steps were the correction of inhomogeneous illumination and reflection, and the incorporation of prior knowledge in filters used to extract the image features and to smooth the results morphologically. We could check and confirm the success of our mapping by comparing the estimated with the designed sand distribution in the tank. The resulting material map was used later as input to model flow and transport through the sand tank. Similar segmentation procedures may be applied to any high-density raster data, including photographs or spectral scans of field profiles.

Late Pliocene stratigraphic distribution of Globoconella taxa in the North Atlantic

Quantitative records of Globorotalia puncticulata and Globorotalia inflata, the last two members of the Globorotalia (Globoconella) lineage, obtained from North Atlantic sediments collected at DSDP Site 552, ODP Site 659 and ODP Site 665, are used to examine fluctuations in the biogeographic distribution of these species in the Late Pliocene between 3 and 2 Ma. Abundance data indicate that prior to the expansion of Northern Hemisphere glaciation at about 2.5 Ma, Gr. puncticulata was an important component of the planktonic foraminiferal fauna and had a geographic distribution ranging from 2°N to at least 56°N in the North Atlantic. A previously undescribed 6 chambered variant of Gr. puncticulata is found at both Sites 659 and 665. The stratigraphic distribution of this morphotype is restricted, first occurring at 2.9 Ma and then disappearing when glacial intensity increased at 2.75 Ma (isotope stage 110). Similar declines in Gr. puncticulata abundances occurred during glacial isotope stages 102, 100, and 98 immediately prior to the extinction of Gr. puncticulata during glacial isotope stage 96. It appears that this extinction event was latitudinally diachronous within the North Atlantic, occurring earliest in the north at Site 552 (2.453 Ma), then at Site 659 (2.443 Ma) and later still in the Site 665 equatorial record (2.438 Ma). At Site 665 the first record of Gr. inflata occurs during glacial isotope stage 94 (2.416 Ma), shortly after the extinction of Gr. puncticulata. In the mid latitude North Atlantic there was a 340,000 year period following the disappearance of Gr. puncticulata when the Globoconella lineage was absent (the Gr. inflata gap). The Gr. inflata population found in the equatorial Atlantic must therefore have been introduced from the South Atlantic, probably by the South Equatorial Current. Faunal records from Sites 552 and 659 show that it was not until glacial isotope stage 78 (2.10 Ma) that Gr. inflata became widely established in the North Atlantic. Prior to this large-scale migration event, there were two limited colonisation events during glacial isotope stages 86 and 82 when Gr. inflata populations reached as far as Site 659 in the eastern North Atlantic. These incursions are believed to be reflect the entrainment of Gr. inflata within South Atlantic Central Water and the northward subsurface transport of individuals to the coastal upwelling zone off northwest Africa. It seems likely that the same mechanism was responsible for the re-establishment of the Globoconella lineage in the North Atlantic at 2.10 Ma, but in this instance additional factors, such as enhanced glacial circulation patterns and ecological changes within planktonic foraminiferal faunas, resulted in the successful expansion of Gr. inflata across the North Atlantic and the Mediterranean.

(Table 1) n-alkane distribution, and stable carbon and deuterium isotope ratios of DSDP Hole 10-94

Hydrology, source region, and timing of precipitation are important controls on the climate of the Great Plains of North America and the composition of terrestrial ecosystems. Moisture delivered to the Great Plains varies seasonally and predominately derives from the Gulf of Mexico/Atlantic Ocean with minor contributions from the Pacific Ocean and Arctic region. For this work, we evaluate long-term relationships for the past ~ 35 million years between North American hydrology, climate, and floral change, using isotopic records and average carbon chain lengths of higher plant n-alkanes from Gulf of Mexico sediments (DSDP Site 94). We find that carbon isotope values (d13C) of n-alkanes, corrected for variations in the d13C value of atmospheric CO2, provide minor evidence for contributions of C4 plants prior to the Middle Miocene. A sharp spike in C4 input is identified during the Middle Miocene Climatic Optimum, and the influence of C4 plants steadily increased during the Late Miocene into the Pleistocene - consistent with other North American records. Chain-length distributions of n-alkanes, indicative of the composition of higher plant communities, remained remarkably constant from 33 to 4 Ma. However, a trend toward longer chain lengths occurred during the past 4 million years, concurrent with an increase in d13C values, indicating increased C4 plant influence and potentially aridity. The hydrogen isotope values (dD) of n-alkanes are relatively invariant between 33 and 9 Ma, and then become substantially more negative (75 per mil) from 9 to 2 Ma. Changes in the plant community and temperature of precipitation can solely account for the observed variations in dD from 33 to 5 Ma, but cannot account for Plio-Pleistocene dD variations and imply substantial changes in the source region of precipitation and seasonality of moisture delivery. We posit that hydrological changes were linked to tectonic and oceanographic processes including the shoaling and closure of the Panamanian Seaway, amplification of North Atlantic Deep Water Production and an associated increase of meridional winds. The southerly movement of the Intertropical Convergence Zone near 4 Ma allowed for the development of a near-modern pressure/storm track system, driving increased aridity and changes in seasonality within the North American interior.

Distribution of Pliocene diatom faunas in the Northwest Pacific

High-resolution quantitative diatom data are tabulated for the early part of the late Pliocene ( 3.25 to 2.08 Ma ) at DSDP Site 580 in the northwestern Pacific. Sample spacing averages 11 k.y. between 3.1 and 2.8 Ma, but increases to 14 to 19 k.y. prior to 3.1 Ma and after 2.8 Ma. Q-mode factor analysis of the middle Pliocene assemblage reveals four factors which explain 92.4% of the total variance of the 47 samples studied between 3.25 and 2.55 Ma. Three of the factors are closely related to modern subarctic, transitional, and subtropical elements, while the fourth factor, which is dominated by Coscinodiscus marginatus and the extinct Pliocene species Neodenticula kamtschatica, appears to correspond to a middle Pliocene precursor of the subarctic water mass. Knowledge of the modern and generalized Pliocene paleoclimatic relationships of various diatom taxa is used to generate a paleoclimate curve ("Twt") based on the ratio of warm-water (subtropical) to cold-water diatoms with warm-water transitional taxa (Thalassionema nitzschioides, Thalassiosira oestrupii, and Coscinodiscus radiatus) factored into the equation at an intermediate (0.5) value. The "Twt" ratios at more southerly DSDP Sites 579 and 578 are consistently higher (warmer) than those at Site 580 throughout the Pliocene, suggesting the validity of the ratio as a paleoclimatic index. Diatom paleoclimatic data reveal a middle Pliocene (3.1 to 3.0 Ma) warm interval at Site 580 during which paleotemperatures may have exceeded maximum Holocene values by 3 °- 5.5 °C at least three times. This middle Pliocene warm interval is also recognized by planktic foraminifers in the North Atlantic, and it appears to correspond with generalized depleted oxygen isotope values suggesting polar warming. The diatom "Twt" curve for Site 580 compares fairly well with radiolarian and silicoflagellate paleoclimatic curves for Site 580, planktic foraminiferal sea-surface temperature estimates for the North Atlantic, and benthic oxygen isotope curves for late Pliocene, although higher resolution studies on paired samples are required to test the correspondence of these various paleoclimatic indices.

Distribution of Cycladophora davisiana davisiana in upper Pliocene and Pleistocene sediments of the North Atlantic and Labrador Sea

Upper Pliocene and Pleistocene abundance fluctuations of the radiolarian Cycladophora davisiana (Ehrenberg) davisiana (Petrushevskaya) are documented from North Atlantic (Site 609) and Labrador Sea (Site 646B) to provide the first long-term correlation of its abundance fluctuations to oxygen isotope stages 1-114. Also examined are temporal and regional fluctuations in abundances C. d. davisiana and the global dispersal routes of the species. The first occurrence of C. d. davisiana in the eastern North Atlantic Ocean (Site 609) occurred between 2.586 and 2.435 Ma (oxygen isotope stages 109.66-102.19). During the early Matuyama Chron, prior to oxygen isotope stage 63, C. d. davisiana abundances were less than 1% and never greater than 12%, while abundances of greater than 5% are found in stages 65.71-73, 74, and 83-84. The initial major abundance peak (35.7%) of C. d. davisiana was noted near the stage 63/62 boundary. Abundance peaks of greater than 15%, between oxygen isotope stages 35 and 63, are limited to stages 63.02, 58.07, 55.07-54.26, and 50.76-50.22. These represent the only such abundance peaks detected during the first c. 1.5 million years of the species within the North Atlantic. The character of C. d. davisiana abundance fluctuations in Site 609 changes after oxygen isotope stage 35; average abundances are greater (7.7% vs. 4.3%) and abundance maxima of more than 15% are more frequent. Many, but not all, peak abundances of C. d. davisiana occur in glacial stages (e.g., 8, 14, 18, 20, 26, 30, 34, 50, 54, and 58). Increased abundances of the species are also noted in weak interglacial stages (e.g., stages 3, 23, 39, and 41), and significant cool periods of robust interglacial periods (e.g., late stage 11). Sample spacing is adequate in some stages to note some rapid changes in abundance near stage transitions (e.g., stages 4/5, 25/26, 62/63). The sample density in Holes 609 and 611 and the upper portion of 646B is sufficient to detect a synchroneity of many abundance maxima and minima among sites. Some abundance peaks are undetected in one or more of the two holes, warranting further sampling to obtain a more accurate record of regional abundance fluctuations. Prior to stage 36, few ages of Hole 611 peaks are the same as those in the more precisely dated Hole 609. The highest abundances of C. d. davisiana were noted in Labrador Sea Hole 646B where the earliest known occurrence of the species is documented (3.08-2.99 Ma). C. d. davisiana is inferred to have evolved in the Labrador Sea (or Arctic), and migrated next through the Arctic into the North Pacific (2.62-2.64 Ma, stage 114) before migrating into the Norwegian Sea (2.63-2.53 Ma) and North Atlantic (2.59-2.44 Ma, stages 109-102). Additional migration of C. d. dauisiana into the southern South Atlantic (Site 704) occurred much later (2.06 Ma, stage 83).

Characteristics and distribution of Neogene turbidites at ODP Site 108-657

Numerous and variable silty-sandy siliciclastic turbidites were observed in Neogene pelagic sediments (late Miocene to Holocene) at Site 657: (1) thick-bedded, coarse-grained and thin-bedded, fine-grained turbidites; and (2) turbidites composed of eolian dune sand and shallow-water bioclasts or of fluvial-sand or mixed sandy component assemblages. The stratigraphic distribution of these turbidites indicates five periods during which climatic conditions and material sources change. Turbidite occurrence prior to 6.2 Ma (late Miocene) is sparse; the deposits contain coarse and fine-grained turbidites with quartz grains of eolian or mixed origin suggesting the existence of arid conditions at about 8.5 and 6.5 Ma. A coarse-grained turbidite of fluvial origin, recording a humid climate, occurs at about 6.2 Ma. During the early Pliocene, turbidites are frequent (15/Ma); they contain only fine-grained sequences comprising material of mixed origin, which indicates a more humid climate perhaps. The late Pliocene starts with rare coarse-grained turbidites of wind-transported sand while the uppermost Pliocene deposits show a higher frequency of fine-grained sequences (10/0.7 Ma) composed mainly of fluvial material. During the early Pleistocene, similar high turbidite frequency was observed (20/1.3 Ma) but with a total lack of eolian supply. During the last 0.7 Ma, the frequency decreases and the sequences are characterized by highly variable sediment components that could be related to strong variations of climatic conditions. The sedimentary characteristics of turbidites are mainly controlled by sediment source and climate. The frequency must be influenced by sea-level variations, by cyclic processes of climatic origin, and possibly by variations in the continental slope morphology. Clay mineral assemblages suggest a south Saharan source of terrigenous material during the late Miocene and the Pliocene and a northwest Saharan source during the Pleistocene.

Distribution of marine invertebrate larvae in the southern Kara Sea (Russian Arctic)

Within the generally oligotroph Arctic marine environment river outlets are favoured by many planktonic and benthic organisms due to their high input of organic carbon. The retention of pelagic larvae within nursery grounds and/or the ability to return to their parental grounds prior to settlement is one important factor for the persistence of benthic communities in such river influenced areas. The southern Kara Sea is strongly controlled by high freshwater inputs from the Ob and Yenisei Rivers, which create a pronounced bi-layered pycnocline with a warm fresh/brackish water layer on top and a cold high saline marine layer below. The dispersal of five meroplanktonic species and settled juveniles (the brittle star Ophiocten sericeum, and the polychaetes Micronephtys minuta, Nereimyra aphroditoides, Phyllodoce groenlandica and Prionospio cirrifera) in relation to the adult distribution patterns was investigated. For all apart from P. cirrifera the highest densities of larvae were found in the upper brackish water layer. To assess size-at-settlement, the body sizes of larvae and newly settled juveniles were estimated and compared. Dispersal patterns ranged from virtually no adaption to river run-off as in the common, stenohaline O. sericeum and M. minuta (7 ind./m**3, 459 µm) to local retention as in N. aphroditoides (7 ind./m**3, 541 µm) and P. groenlandica (0.5 ind./m**3, 1121 µm) retained by horizontal eddies created by the outflow. Adults of P. cirrifera, which were exclusively restricted to the estuary of the Yenisei River, showed a well adapted reproductive behaviour to ensure a high retention potential of their progenies. The larvae (1.5 ind./m**3, 1513 µm) were only present in the lower water layers, most probably taking advantage of the prevailing near bottom counter current retaining them within their hatching areas.