A reversible infinite HMM using normalised random measures

Copyright 2014 by the author(s). We present a nonparametric prior over reversible Markov chains. We use completely random measures, specifically gamma processes, to construct a countably infinite graph with weighted edges. By enforcing symmetry to make the edges undirected we define a prior over random walks on graphs that results in a reversible Markov chain. The resulting prior over infinite transition matrices is closely related to the hierarchical Dirichlet process but enforces reversibility. A reinforcement scheme has recently been proposed with similar properties, but the de Finetti measure is not well characterised. We take the alternative approach of explicitly constructing the mixing measure, which allows more straightforward and efficient inference at the cost of no longer having a closed form predictive distribution. We use our process to construct a reversible infinite HMM which we apply to two real datasets, one from epigenomics and one ion channel recording.

洞穴碳酸盐^230Th-^234U-^238U测年初始钍校正的等时线研究

IEECAS SKLLQG

Convergence and tracking analysis of a variable normalised LMF (XE-NLMF) algorithm

The least-mean-fourth (LMF) algorithm is known for its fast convergence and lower steady state error, especially in sub-Gaussian noise environments. Recent work on normalised versions of the LMF algorithm has further enhanced its stability and performance in both Gaussian and sub-Gaussian noise environments. For example, the recently developed normalised LMF (XE-NLMF) algorithm is normalised by the mixed signal and error powers, and weighted by a fixed mixed-power parameter. Unfortunately, this algorithm depends on the selection of this mixing parameter. In this work, a time-varying mixed-power parameter technique is introduced to overcome this dependency. A convergence analysis, transient analysis, and steady-state behaviour of the proposed algorithm are derived and verified through simulations. An enhancement in performance is obtained through the use of this technique in two different scenarios. Moreover, the tracking analysis of the proposed algorithm is carried out in the presence of two sources of nonstationarities: (1) carrier frequency offset between transmitter and receiver and (2) random variations in the environment. Close agreement between analysis and simulation results is obtained. The results show that, unlike in the stationary case, the steady-state excess mean-square error is not a monotonically increasing function of the step size. (c) 2007 Elsevier B.V. All rights reserved.

Aberrant brain responses to emotionally valent words is normalised after cognitive behavioural therapy in female depressed adolescents

AbstractBackground Depression in adolescence is debilitating with high recurrence in adulthood, yet its pathophysiological mechanism remains enigmatic. To examine the interaction between emotion, cognition and treatment, functional brain responses to sad and happy distractors in an affective go/no-go task were explored before and after Cognitive Behavioural Therapy (CBT) in depressed female adolescents, and healthy participants. Methods Eighty-two Depressed and 24 healthy female adolescents, aged 12 to 17 years, performed a functional magnetic resonance imaging (fMRI) affective go/no-go task at baseline. Participants were instructed to withhold their responses upon seeing happy or sad words. Among these participants, 13 patients had CBT over approximately 30 weeks. These participants and 20 matched controls then repeated the task. Results At baseline, increased activation in response to happy relative to neutral distractors was observed in the orbitofrontal cortex in depressed patients which was normalized after CBT. No significant group differences were found behaviourally or in brain activation in response to sad distractors. Improvements in symptoms (mean: 9.31, 95% CI: 5.35-13.27) were related at trend-level to activation changes in orbitofrontal cortex. Limitations In the follow-up section, a limited number of post-CBT patients were recruited. Conclusions To our knowledge, this is the first fMRI study addressing the effect of CBT in adolescent depression. Although a bias toward negative information is widely accepted as a hallmark of depression, aberrant brain hyperactivity to positive distractors was found and normalised after CBT. Research, assessment and treatment focused on positive stimuli could be a future consideration. Moreover, a pathophysiological mechanism distinct from adult depression may be suggested and awaits further exploration.

Bayesian model comparison with un-normalised likelihoods

Models for which the likelihood function can be evaluated only up to a parameter-dependent unknown normalizing constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and network analysis. However, Bayesian analysis of these models using standard Monte Carlo methods is not possible due to the intractability of their likelihood functions. Several methods that permit exact, or close to exact, simulation from the posterior distribution have recently been developed. However, estimating the evidence and Bayes’ factors for these models remains challenging in general. This paper describes new random weight importance sampling and sequential Monte Carlo methods for estimating BFs that use simulation to circumvent the evaluation of the intractable likelihood, and compares them to existing methods. In some cases we observe an advantage in the use of biased weight estimates. An initial investigation into the theoretical and empirical properties of this class of methods is presented. Some support for the use of biased estimates is presented, but we advocate caution in the use of such estimates.

Radiocarbon, isotope, biogenic, and 230Th measurements for sediment core RC10-196

The subarctic North Pacific Ocean holds a large CO2 reservoir that is currently isolated from the atmosphere by a low-salinity layer. It has recently been hypothesized that the reorganization of these high-CO2 waters may have played a crucial role in the degassing of carbon dioxide to the atmosphere during the last deglaciation. This reorganization would leave some imprint on paleo-productivity records. Here we present 230Th-normalized biogenic fluxes from an intermediate depth sediment core in the Northwest Pacific (RC10-196, 54.7°N, 177.1°E, 1007 m) and place them within the context of a synthesis of previously-published biogenic flux data from 49 deep-sea cores north of 20°N, ranging from 420 to 3968 m water depth. The 230Th-normalized opal, carbonate, and organic carbon fluxes from RC10-196 peak approximately 13,000 calendar years BP during the Bølling/Allerød (B/A) period. Our data synthesis suggests that biogenic fluxes were in general lowest during the last glacial period, increased somewhat in the Northwest Pacific during Heinrich Event 1, and reached a maximum across the entire North Pacific during the B/A period. We evaluate several mechanisms as possible drivers of deglacial change in biogenic fluxes in the North Pacific, including changes in preservation, sediment focusing, sea ice extent, iron inputs, stratification, and circulation shifts initiated in the North Atlantic and North Pacific. Our analysis suggests that while micronutrient sources likely contributed to some of the observed changes, the heterogeneity in timing of glaciogenic retreat and sea level make these mechanisms unlikely causes of region-wide contemporaneous peaks in export production. We argue that paleo-observations are most consistent with ventilation increases in both the North Pacific (during H1) and North Atlantic (during B/A) being the primary drivers of increases in biogenic flux during the deglaciation, as respectively they were likely to bring nutrients to the surface via increased vertical mixing and shoaling of the global thermocline.

(Supplement Table S2) Results of 230Th/U-dating

We compared the suitability of two skeletal materials of the Atlantic brain coral Diploria strigosa for 230Th/U-dating: the commonly used bulk material comprising all skeletal elements and the denser theca wall material. Eight fossil corals of presumably Last Interglacial age from Bonaire, southern Caribbean Sea, were investigated, and several sub-samples were dated from each coral. For four corals, both the ages and the activity ratios of the bulk material and theca wall agree within uncertainty. Three corals show significantly older ages for their bulk material than for their theca wall material as well as substantially elevated 232Th content and (230Th/238U) ratios. The bulk material samples of another coral show younger ages and lower (230Th/238U) ratios than the corresponding theca wall samples. This coral also contains a considerable amount of 232Th. The application of the available open-system models developed to account for post-depositional diagenetic effects in corals shows that none of the models can successfully be applied to the Bonaire corals. The most likely explanation for this observation is that the assumptions of the models are not fulfilled by our data set. Comparison of the theca wall and bulk material data enables us to obtain information about the open-system processes that affected the corals. The corals showing apparently older ages for their bulk material were probably affected by contamination with a secondary (detrital) phase. The most likely source of the detrital material is carbonate sand. The higher (230Th/232Th) ratio of this material implies that detrital contamination would have a much stronger impact on the ages than a contaminant with a bulk Earth (230Th/232Th) ratio and that the threshold for the commonly applied 232Th reliability criterion would be much lower than the generally used value of 1 ng g^-1. The coral showing apparently younger ages for its bulk material was probably influenced by more than one diagenetic process. A potential scenario is a combination of detrital contamination and U addition by secondary pore infillings. Our results show that the dense theca wall material of D. strigosa is generally less affected by post-depositional open-system behaviour and better suited for 230Th/U-dating than the bulk material. This is also obvious from the fact that all ages of theca wall material reflect a Last Interglacial origin (~125 ka), whereas the bulk material samples are either substantially older or younger. However, for some corals, the 230Th/U-ages and activity ratios of the bulk material and the theca wall samples are similar. This shows that strictly reliable 230Th/U-ages can also be obtained from bulk material samples of exceptionally well-preserved corals. However, the bulk material samples more frequently show elevated activity ratios and ages than the corresponding theca wall samples. Our findings should be generally applicable to brain corals (Mussidae) that are found in tropical oceans worldwide and may enable reliable 230Th/U-dating of fossil corals with similar skeletal architecture, even if their bulk skeleton is altered by diagenesis. The 230Th/U-ages we consider reliable (120-130 ka), along with a recently published age of 118 ka, provide the first comprehensive dating of the elevated lower reef terrace at Bonaire (118-130 ka), which is in agreement in timing and duration with other Last Interglacial records.

Radiocarbon ages and 230Th data of five sediment cores from the Björn and Gardar Drift, North Atlantic

In locations of rapid sediment accumulation receiving substantial amounts of laterally transported material the timescales of transport and accurate quantification of the transported material are at the focus of intense research. Here we present radiocarbon data obtained on co-occurring planktic foraminifera, marine haptophyte biomarkers (alkenones) and total organic carbon (TOC) coupled with excess Thorium-230 (230Thxs) measurements on four sediment cores retrieved in 1649-2879 m water depth from two such high accumulation drift deposits in the Northeast Atlantic, Björn and Gardar Drifts. While 230Thxs inventories imply strong sediment focussing, no age offsets are observed between planktic foraminifera and alkenones, suggesting that redistribution of sediments is rapid and occurs soon after formation of marine organic matter, or that transported material contains negligible amounts of alkenones. An isotopic mass balance calculation based on radiocarbon concentrations of co-occurring sediment components leads us to estimate that transported sediment components contain up to 12% of fossil organic matter that is free of or very poor in alkenones, but nevertheless appears to consist of a mixture of fresh and eroded fossil material. Considering all available constraints to characterize transported material, our results show that although focussing factors calculated from bulk sediment 230Thxs inventories may allow useful approximations of bulk redeposition, they do not provide a unique estimate of the amount of each laterally transported sediment component. Furthermore, our findings provide evidence that the occurrence of lateral sediment redistribution alone does not always hinder the use of multiple proxies but that individual sediment fractions are affected to variable extents by sediment focussing.