A categorical foundation for Bayesian probability

Given two measurable spaces $H$ and $D$ with countably generated $\sigma$-algebras, a perfect prior probability measure $P_H$ on $H$ and a sampling distribution $S: H \rightarrow D$, there is a corresponding inference map $I: D \rightarrow H$ which is unique up to a set of measure zero. Thus, given a data measurement $\mu: 1 \rightarrow D$, a posterior probability $\widehat{P_H}= I \circ \mu$ can be computed. This procedure is iterative: with each updated probability $P_H$, we obtain a new joint distribution which in turn yields a new inference map $I$ and the process repeats with each additional measurement. The main result uses an existence theorem for regular conditional probabilities by Faden, which holds in more generality than the setting of Polish spaces. This less stringent setting then allows for non-trivial decision rules (Eilenberg--Moore algebras) on finite (as well as non finite) spaces, and also provides for a common framework for decision theory and Bayesian probability.Comment: 15 pages; revised setting to more clearly explain how to incorporate perfect measures and the Giry monad; to appear in Applied Categorical Structure

Agricultural legacy, climate, and soil influence the restoration and carbon potential of woody regrowth in Australia

Opportunities for dual restoration and carbon benefits from naturally regenerating woody ecosystems in agricultural landscapes have been highlighted recently. The restoration capacity of woody ecosystems depends on the magnitude and duration of ecosystem modification, i.e., the ''agricultural legacy.'' However, this legacy may not influence carbon sequestration in the same way as restoration because carbon potential depends primarily on biomass accumulation, with little consideration of other attributes and functions of the ecosystem. Our present study simultaneously assesses the restoration and carbon potential of Acacia harpophylla regrowth, an extensive regrowth ecosystem in northeastern Australia. We used a landscape-scale survey of A. harpophylla regrowth to test the following hypotheses: (1) management history, in combination with climatic and edaphic factors, has long-term effects on stem densities, and (2) higher-density stands have lower restoration and carbon potential, which is also influenced by climatic and edaphic factors. We focused on the restoration of forest structure, which was characterized using stem density, aboveground biomass, stem heights, and stem diameters. Data were analyzed using multilevel models within the hierarchical Bayesian model (HBM) framework. We found strong support for both hypotheses. Repeated attempts at clearing Brigalow (A. harpophylla ecosystem) regrowth increases stem densities, and these densities remain high over the long term, particularly in high-rainfall areas and on gilgaied, high-clay soils (hypothesis 1). In models testing hypothesis 2, interactions between stem density and stand age indicate that higher-density stands have slower biomass accumulation and structural development in the long term. After accounting for stem density and stand age, annual rainfall had a positive effect on biomass accumulation and structural development. Other climate and soil variables were retained in the various models but had weaker effects. Spatial extrapolations of the HBMs indicated that the central and eastern parts of the study region are most suitable for biomass accumulation; however, these may not correspond to the areas that historically supported the highest biomass Brigalow forests. We conclude that carbon and restoration goals are largely congruent within areas of similar climate. At the regional scale, however, spatial prioritization of restoration and carbon projects may only be aligned where carbon benefits will be high. © 2010 by the Ecological Society of America

Interpreting ambiguous ‘trace’ results in Schistosoma mansoni CCA Tests: Estimating sensitivity and specificity of ambiguous results with no gold standard

Background The development of new diagnostics is an important tool in the fight against disease. Latent Class Analysis (LCA) is used to estimate the sensitivity and specificity of tests in the absence of a gold standard. The main field diagnostic for Schistosoma mansoni infection, Kato-Katz (KK), is not very sensitive at low infection intensities. A point-of-care circulating cathodic antigen (CCA) test has been shown to be more sensitive than KK. However, CCA can return an ambiguous ‘trace’ result between ‘positive’ and ‘negative’, and much debate has focused on interpretation of traces results. Methodology/Principle findings We show how LCA can be extended to include ambiguous trace results and analyse S. mansoni studies from both Côte d’Ivoire (CdI) and Uganda. We compare the diagnostic performance of KK and CCA and the observed results by each test to the estimated infection prevalence in the population. Prevalence by KK was higher in CdI (13.4%) than in Uganda (6.1%), but prevalence by CCA was similar between countries, both when trace was assumed to be negative (CCAtn: 11.7% in CdI and 9.7% in Uganda) and positive (CCAtp: 20.1% in CdI and 22.5% in Uganda). The estimated sensitivity of CCA was more consistent between countries than the estimated sensitivity of KK, and estimated infection prevalence did not significantly differ between CdI (20.5%) and Uganda (19.1%). The prevalence by CCA with trace as positive did not differ significantly from estimates of infection prevalence in either country, whereas both KK and CCA with trace as negative significantly underestimated infection prevalence in both countries. Conclusions Incorporation of ambiguous results into an LCA enables the effect of different treatment thresholds to be directly assessed and is applicable in many fields. Our results showed that CCA with trace as positive most accurately estimated infection prevalence

In-cell NMR in E. coli to Monitor Maturation Steps of hSOD1

In-cell NMR allows characterizing the folding state of a protein as well as posttranslational events at molecular level, in the cellular context. Here, the initial maturation steps of human copper, zinc superoxide dismutase 1 are characterized in the E. coli cytoplasm by in-cell NMR: from the apo protein, which is partially unfolded, to the zinc binding which causes its final quaternary structure. The protein selectively binds only one zinc ion, whereas in vitro also the copper site binds a non-physiological zinc ion. However, no intramolecular disulfide bridge formation occurs, nor copper uptake, suggesting the need of a specific chaperone for those purposes

Homocysteine levels in preterm infants: is there an association with intraventricular hemorrhage? A prospective cohort study.

BACKGROUND: The purpose of this study was to characterize total homocysteine (tHcy) levels at birth in preterm and term infants and identify associations with intraventricular hemorrhage (IVH) and other neonatal outcomes such as mortality, sepsis, necrotizing enterocolitis, bronchopulmonary dysplasia, and thrombocytopenia. METHODS: 123 infants \u3c 32 weeks gestation admitted to our Level III nursery were enrolled. A group of 25 term infants were enrolled for comparison. Two blood spots collected on filter paper with admission blood drawing were analyzed by a high performance liquid chromatography (HPLC) method. Statistical analysis included ANOVA, Spearman\u27s Rank Order Correlation and Mann-Whitney U test. RESULTS: The median tHcy was 2.75 micromol/L with an interquartile range of 1.34 - 4.96 micromol/L. There was no difference between preterm and term tHcy (median 2.76, IQR 1.25 - 4.8 micromol/L vs median 2.54, IQR 1.55 - 7.85 micromol/L, p = 0.07). There was no statistically significant difference in tHcy in 31 preterm infants with IVH compared to infants without IVH (median 1.96, IQR 1.09 - 4.35 micromol/L vs median 2.96, IQR 1.51 - 4.84 micromol/L, p = 0.43). There was also no statistically significant difference in tHcy in 7 infants with periventricular leukomalacia (PVL) compared to infants without PVL (median 1.55, IQR 0.25 - 3.45 micromol/L vs median 2.85, IQR 1.34 - 4.82 micromol/L, p = 0.07). Male infants had lower tHcy compared to female; prenatal steroids were associated with a higher tHcy. CONCLUSION: In our population of preterm infants, there is no association between IVH and tHcy. Male gender, prenatal steroids and preeclampsia were associated with differences in tHcy levels

Change Point Estimation in Monitoring Survival Time

Precise identification of the time when a change in a hospital outcome has occurred enables clinical experts to search for a potential special cause more effectively. In this paper, we develop change point estimation methods for survival time of a clinical procedure in the presence of patient mix in a Bayesian framework. We apply Bayesian hierarchical models to formulate the change point where there exists a step change in the mean survival time of patients who underwent cardiac surgery. The data are right censored since the monitoring is conducted over a limited follow-up period. We capture the effect of risk factors prior to the surgery using a Weibull accelerated failure time regression model. Markov Chain Monte Carlo is used to obtain posterior distributions of the change point parameters including location and magnitude of changes and also corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the risk-adjusted survival time CUSUM control charts for different magnitude scenarios. The proposed estimator shows a better performance where a longer follow-up period, censoring time, is applied. In comparison with the alternative built-in CUSUM estimator, more accurate and precise estimates are obtained by the Bayesian estimator. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered

Beyond the personal–anonymous divide: agency relations in powers of attorney in France in the eighteenth and nineteenth centuries

Powers of attorney are often interpreted as evidence of trust among the parties involved. We build a novel dataset of notarized powers of attorney, capturing a wide variety of agency relationships in four large French commercial cities in the eighteenth and nineteenth centuries, to test hypotheses on the relational basis of economic relationships. We find little support for the idea of a radical shift from personal to anonymous relationships during our period. Our results point to more nuanced transformations. The preference for proxies in the same occupation as the principal somewhat declined, while professional proxies emerged and principals used relational chains, especially involving notaries, to find proxies.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151849/1/ehr12784_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151849/2/ehr12784.pd

How Does Spatial Study Design Influence Density Estimates from Spatial Capture-Recapture Models?

When estimating population density from data collected on non-invasive detector arrays, recently developed spatial capture-recapture (SCR) models present an advance over non-spatial models by accounting for individual movement. While these models should be more robust to changes in trapping designs, they have not been well tested. Here we investigate how the spatial arrangement and size of the trapping array influence parameter estimates for SCR models. We analysed black bear data collected with 123 hair snares with an SCR model accounting for differences in detection and movement between sexes and across the trapping occasions. To see how the size of the trap array and trap dispersion influence parameter estimates, we repeated analysis for data from subsets of traps: 50% chosen at random, 50% in the centre of the array and 20% in the South of the array. Additionally, we simulated and analysed data under a suite of trap designs and home range sizes. In the black bear study, we found that results were similar across trap arrays, except when only 20% of the array was used. Black bear density was approximately 10 individuals per 100 km2. Our simulation study showed that SCR models performed well as long as the extent of the trap array was similar to or larger than the extent of individual movement during the study period, and movement was at least half the distance between traps. SCR models performed well across a range of spatial trap setups and animal movements. Contrary to non-spatial capture-recapture models, they do not require the trapping grid to cover an area several times the average home range of the studied species. This renders SCR models more appropriate for the study of wide-ranging mammals and more flexible to design studies targeting multiple species

BUGS in the Analysis of Biodiversity Experiments: Species Richness and Composition Are of Similar Importance for Grassland Productivity

The idea that species diversity can influence ecosystem functioning has been controversial and its importance relative to compositional effects hotly debated. Unfortunately, assessing the relative importance of different explanatory variables in complex linear models is not simple. In this paper we assess the relative importance of species richness and species composition in a multilevel model analysis of net aboveground biomass production in grassland biodiversity experiments by estimating variance components for all explanatory variables. We compare the variance components using a recently introduced graphical Bayesian ANOVA. We show that while the use of test statistics and the R2 gives contradictory assessments, the variance components analysis reveals that species richness and composition are of roughly similar importance for primary productivity in grassland biodiversity experiments