Bayesian Credible Interval Research Articles

Uncovering interactions in multivariate contingency tables: a multi-level modelling exploratory approach

Much quantitative behavioural social science – a great deal of it exploratory in nature – involves the analysis of multivariate contingency tables, usually deploying logistic binomial and multinomial regression models with no exploration of interaction effects, despite arguments that this should be a crucial element of the analysis. This article builds on suggestions that the search for interaction effects should employ multi-level modelling strategies and outlines a procedure for modelling patterns in data sets with small numbers of observations in many, if not all, of their multivariate contingency table cells; all expected cells must be non-zero. The procedure produces precision-weighted estimates of the observed:expected rates for each and every cell, together with associated Bayesian credible intervals, and is illustrated using a large survey data set relating voting (and abstaining) at the 2015 UK general election to age, sex and educational qualifications. Crucially, while fine detail can be explored in the analysis, unreliable rates for particular subgroups are automatically down-weighted to what is happening generally. The identification of reliable differential rates then allows a simpler hybrid model that captures the main trends to be fitted and interpreted.

Bayesian Inference Supports the Use of Bypass Surgery Over Percutaneous Coronary Intervention To Reduce Mortality in Diabetic Patients with Multivessel Coronary Disease

Background: Coronary artery bypass graft (CABG) surgery may confer a survival advantage over percutaneous coronary intervention (PCI) in diabetic patients with multivessel coronary artery disease (CAD), but results of individual studies have been mixed. The primary aim of the current study was to compare mortality rates in diabetic patients with multivessel CAD randomized to either or CABG or PCI at 5 years or longest follow-up. Methods: Using a Bayesian approach, we updated a prior probability distribution elicited from 8 clinical trials (N=2024) with the likelihood obtained from the Future Revascularization Evaluation in Patients with Diabetes Mellitus: Optimal Management of Multivessel Disease (FREEDOM) (N=1460) to determine whether clinical trial evidence supports the underlying hypothesis that CABG is superior to PCI for diabetics with multivessel CAD. Results: A conjugate normal model comparing mortality rates favored the use of CABG (posterior mean odds ratio [OR] = 0.58, 95% Bayesian credible interval [BCI] = 0.48–0.71). Models weighted by the use of drug-eluting stents also favored the use of CABG over PCI (OR = 0.61, 95% BCI 0.48–0.78), as did models weighted by study age (OR=0.64, 95% BCI 0.52–0.80) or use of arterial conduits (OR=0.64, 95% BCI 0.51–0.81). The results were supported by a Bayesian hierarchical meta-analysis using a non-informative prior distribution (OR=0.55, 95% BCI 0.37–0.76). Conclusions: By integrating evidence from various studies, Bayesian methods directly support the underlying hypothesis that revascularization with CABG improves survival compared with PCI in diabetic patients with multivessel CAD.

Noninformative priors for the ratio of the shape parameters of two Weibull distributions

The Weibull distribution is one of the most widely used lifetime distributions in reliability engineering. Here, the noninformative priors for the ratio of the shape parameters of two Weibull models are introduced. The first criterion used is the asymptotic matching of the coverage probabilities of Bayesian credible intervals with the corresponding frequentist coverage probabilities. We develop the probability matching priors for the ratio of the shape parameters using the following matching criteria: quantile matching, matching of the distribution function, highest posterior density matching, and matching via inversion of the test statistics. We obtain one particular prior that meets all the matching criteria. Next, we derive the reference priors for different groups of ordering. Our findings show that some of the reference priors satisfy a first-order matching criterion and the one-at-a-time reference prior is a second-order matching prior. Lastly, we perform a simulation study and provide a real-world example.

Combined estimation for multi-measurements of branching ratio**Supported by National Nature Science Foundation of China (11275266) and Youth Innovation Promotion Association, CAS

A maximum likelihood method is used to deal with the combined estimation of multi-measurements of a branching ratio, where each result can be presented as an upper limit. The joint likelihood function is constructed using observed spectra of all measurements and the combined estimate of the branching ratio is obtained by maximizing the joint likelihood function. The Bayesian credible interval or upper limit of the combined branching ratio, is given in cases both with and without inclusion of systematic error.

Bayesian Wavelet Shrinkage of the Haar-Fisz Transformed Wavelet Periodogram.

It is increasingly being realised that many real world time series are not stationary and exhibit evolving second-order autocovariance or spectral structure. This article introduces a Bayesian approach for modelling the evolving wavelet spectrum of a locally stationary wavelet time series. Our new method works by combining the advantages of a Haar-Fisz transformed spectrum with a simple, but powerful, Bayesian wavelet shrinkage method. Our new method produces excellent and stable spectral estimates and this is demonstrated via simulated data and on differenced infant electrocardiogram data. A major additional benefit of the Bayesian paradigm is that we obtain rigorous and useful credible intervals of the evolving spectral structure. We show how the Bayesian credible intervals provide extra insight into the infant electrocardiogram data.

Statistical unfolding of elementary particle spectra: Empirical Bayes estimation and bias-corrected uncertainty quantification

We consider the high energy physics unfolding problem where the goal is to estimate the spectrum of elementary particles given observations distorted by the limited resolution of a particle detector. This important statistical inverse problem arising in data analysis at the Large Hadron Collider at CERN consists in estimating the intensity function of an indirectly observed Poisson point process. Unfolding typically proceeds in two steps: one first produces a regularized point estimate of the unknown intensity and then uses the variability of this estimator to form frequentist confidence intervals that quantify the uncertainty of the solution. In this paper, we propose forming the point estimate using empirical Bayes estimation which enables a data-driven choice of the regularization strength through marginal maximum likelihood estimation. Observing that neither Bayesian credible intervals nor standard bootstrap confidence intervals succeed in achieving good frequentist coverage in this problem due to the inherent bias of the regularized point estimate, we introduce an iteratively bias-corrected bootstrap technique for constructing improved confidence intervals. We show using simulations that this enables us to achieve nearly nominal frequentist coverage with only a modest increase in interval length. The proposed methodology is applied to unfolding the $Z$ boson invariant mass spectrum as measured in the CMS experiment at the Large Hadron Collider.

The Society of Thoracic Surgeons Composite Measure of Individual Surgeon Performance for Adult Cardiac Surgery: A Report of The Society of Thoracic Surgeons Quality Measurement Task Force

Previous composite performance measures of The Society of Thoracic Surgeons (STS) were estimated at the STS participant level, typically a hospital or group practice. The STS Quality Measurement Task Force has now developed a multiprocedural, multidimensional composite measure suitable for estimating the performance of individual surgeons. The development sample from the STS National Database included 621,489 isolated coronary artery bypass grafting procedures, isolated aortic valve replacement, aortic valve replacement plus coronary artery bypass grafting, mitral, or mitral plus coronary artery bypass grafting procedures performed by 2,286 surgeons between July 1, 2011, and June 30, 2014. Each surgeon's composite score combined their aggregate risk-adjusted mortality and major morbidity rates (each weighted inversely by their standard deviations) and reflected the proportion of case types they performed. Model parameters were estimated in a Bayesian framework. Composite star ratings were examined using 90%, 95%, or 98% Bayesian credible intervals. Measure reliability was estimated using various 3-year case thresholds. The final composite measure was defined as 0.81 × (1 minus risk-standardized mortality rate) + 0.19 × (1 minus risk-standardized complication rate). Risk-adjusted mortality (median, 2.3%; interquartile range, 1.7% to 3.0%), morbidity (median, 13.7%; interquartile range, 10.8% to 17.1%), and composite scores (median, 95.4%; interquartile range, 94.4% to 96.3%) varied substantially across surgeons. Using 98% Bayesian credible intervals, there were 207 1-star (lower performance) surgeons (9.1%), 1,701 2-star (as-expected performance) surgeons (74.4%), and 378 3-star (higher performance) surgeons (16.5%). With an eligibility threshold of 100 cases over 3 years, measure reliability was 0.81. The STS has developed a multiprocedural composite measure suitable for evaluating performance at the individual surgeon level.

Cervical disc arthroplasty with PRESTIGE LP disc versus anterior cervical discectomy and fusion: a prospective, multicenter investigational device exemption study.

OBJECT This study compared the safety and efficacy of treatment with the PRESTIGE LP cervical disc versus a historical control anterior cervical discectomy and fusion (ACDF). METHODS Prospectively collected PRESTIGE LP data from 20 investigational sites were compared with data from 265 historical control ACDF patients in the initial PRESTIGE Cervical Disc IDE study. The 280 investigational patients with single-level cervical disc disease with radiculopathy and/or myelopathy underwent arthroplasty with a low-profile artificial disc. Key safety/efficacy outcomes included Neck Disability Index (NDI), Neck and Arm Pain Numerical Rating Scale scores, 36-Item Short Form Health Survey (SF-36) score, work status, disc height, range of motion, adverse events (AEs), additional surgeries, and neurological status. Clinical and radiographic evaluations were completed preoperatively, intraoperatively, and at 1.5, 3, 6, 12, and 24 months postoperatively. Predefined Bayesian statistical methods with noninformative priors were used, along with the propensity score technique for controlling confounding factors. Analysis by independent statisticians confirmed initial statistical findings. RESULTS The investigational and control groups were mostly similar demographically. There was no significant difference in blood loss (51.0 ml [investigational] vs 57.1 ml [control]) or hospital stay (0.98 days [investigational] vs 0.95 days [control]). The investigational group had a significantly longer operative time (1.49 hours vs 1.38 hours); 95% Bayesian credible interval of the difference was 0.01-0.21 hours. Significant improvements versus preoperative in NDI, neck/arm pain, SF-36, and neurological status were achieved by 1.5 months in both groups and were sustained at 24 months. Patient follow-up at 24 months was 97.1% for the investigational group and 84.0% for the control group. The mean NDI score improvements versus preoperative exceeded 30 points in both groups at 12 and 24 months. SF-36 Mental Component Summary superiority was established (Bayesian probability 0.993). The mean SF-36 PCS scores improved by 14.3 points in the investigational group and by 11.9 points in the control group from baseline to 24 months postoperatively. Neurological success at 24 months was 93.5% in the investigational group and 83.5% in the control group (probability of superiority ~ 1.00). At 24 months, 12.1% of investigational and 15.5% of control patients had an AE classified as device or device/surgical procedure related; 14 (5.0%) investigational and 21 (7.9%) control patients had a second surgery at the index level. The median return-to-work time for the investigational group was 40 days compared with 60 days for the control group (p = 0.020 after adjusting for preoperative work status and propensity score). Following implantation of the PRESTIGE LP device, the mean angular motion was maintained at 12 months (7.9°) and 24 months (7.5°). At 24 months, 90.0% of investigational and 87.7% of control patients were satisfied with the results of surgery. PRESTIGE LP superiority on overall success (without disc height success), a composite safety/efficacy end point, was strongly supported with 0.994 Bayesian probability. CONCLUSIONS This device maintains mean postoperative segmental motion while providing the potential for biomechanical stability. Investigational patients reported significantly improved clinical outcomes compared with baseline, at least noninferior to ACDF, up to 24 months after surgery.

The effect of PAR and temperature on the photosynthetic performance of a freshwater red alga, Thorea gaudichaudii (Thoreales) from Kagoshima, Japan

The effect of photosynthetically active radiation (PAR) and temperature on the photosynthesis of an endangered freshwater red alga, Thorea gaudichaudii C. Agardh (Thoreales), was determined by laboratory and field measurements. This species was found in a freshwater spring habitat that was mostly shaded from direct sunlight and under almost undetectable seasonal fluctuations in water temperature (23.0 ± 0.31 °C, ±SD). A net oxygenic photosynthesis–PAR model revealed that the net photosynthetic rate quickly saturated, with a saturating PAR (E k) and compensation PAR (E c) of 12 μmol photons m−2 s−1 (9–16, 95 % Bayesian credible interval (BCI)) and 7 μmol photons m−2 s−1 (5–9, 95 % BCI), respectively. A temperature-dependent (i.e., 12–44 °C range) dome-shaped model of gross photosynthesis and dark respiration was fitted to reveal that the gross photosynthetic rate, 190 μg O2 gww −1 min−1 (175–208, 95 % BCI), was highest at 34.9 °C (33.5–36.0, 95 % BCI) and decreased sharply above this temperature. The dark respiration rate was also dome shaped in response to temperature, with a peak of 66 μg O2 gww −1 min−1 (59–76) at 32.2 °C (28.2–40.2) and then slow decay in rates at higher temperatures. In contrast, the effective quantum yield only gradually decreased with increases in PAR and the maximum quantum yield was weakly dome shaped with respect to temperature. Indeed, the highest value of maximum quantum yield of 0.596 (0.592–0.599, 95 % BCI) occurred at 24.1 °C (22.0–26.2, 95 % BCI). This species appears to be well adapted to the heavily shaded and relatively stable temperature conditions of its environment.

Noninformative priors for the common shape parameters of Weibull distributions

The Weibull distribution is widely used in survival analysis, reliability engineering, and failure analysis. In this paper, we develop noninformative priors such as probability matching priors for the common shape parameter of Weibull models using the asymptotic matching of coverage probabilities of Bayesian credible intervals with the corresponding frequentist coverage probabilities. Here, various matching criteria, such as quantile matching, matching of distribution function, highest posterior density matching, and matching via inversion of test statistics, are considered. Next, we derive the reference priors for groups of ordering. It also shows that most reference priors do not satisfy the first order matching criterion, but the one-at-a-time reference prior is the second order matching priors. A simulation study is performed and a real example is given.

Numeric score-based conditional and overall change-in-status indices for ordered categorical data.

Planned interventions and/or natural conditions often effect change on an ordinal categorical outcome (e.g., symptom severity). In such scenarios, it is sometimes desirable to assign a priori scores to observed changes in status, typically giving higher weight to changes of greater magnitude. We define change indices for such data based upon a multinomial model for each row of a c × c table, where the rows represent the baseline status categories. We distinguish an index designed to assess conditional changes within each baseline category from two others designed to capture overall change. One of these overall indices measures expected change across a target population. The other is scaled to capture the proportion of total possible change in the direction indicated by the data, so that it ranges from -1 (when all subjects finish in the least favorable category) to +1 (when all finish in the most favorable category). The conditional assessment of change can be informative regardless of how subjects are sampled into the baseline categories. In contrast, the overall indices become relevant when subjects are randomly sampled at baseline from the target population of interest, or when the investigator is able to make certain assumptions about the baseline status distribution in that population. We use a Dirichlet-multinomial model to obtain Bayesian credible intervals for the conditional change index that exhibit favorable small-sample frequentist properties. Simulation studies illustrate the methods, and we apply them to examples involving changes in ordinal responses for studies of sleep deprivation and activities of daily living.

An Efficient Method for Determining Capillary Pressure and Relative Permeability Curves from Spontaneous Imbibition Data

In this paper, a very efficient method, called single matrix block analyzer (SMBA), has been developed to determine relative permeability and capillary pressure curves from spontaneous imbibition (SI) data. SMBA mimics realistically the SI tests by appropriate boundary conditions modeling. In the proposed method, a cuboid with an identical core plug height is considered. The equal dimensions of the cuboid in x and y directions are set such that the cylindrical core plug and the cuboid have the same shape factor. Thus, by avoiding the difficulties of the cylindrical coordinates, a representative model for the core plug is established. Appropriate grid numbers in x-y and z directions are specified to the model. Furthermore, the rock and fluid properties of SI test are set in the SMBA. By supposing forms of the oil-water capillary pressure and relative permeability and comparing the oil recovery curves of SMBA and SI data, capillary pressure and relative permeability can be determined. The SMBA is demonstrated using three experimental data with different aging times. Suitable equations are employed to represent the capillary pressure and relative permeability curves. The genetic algorithm is used as the optimization tool. The obtained results, especially for capillary pressure, are in good agreement with the experimental data. Moreover, the Bayesian credible interval (P10 and P90) evaluated by the Neighborhood Bayes Algorithm (NAB) is quite satisfactory.

ESTIMATING THE GALACTIC MASS PROFILE IN THE PRESENCE OF INCOMPLETE DATA

A powerful method to measure the mass profile of a galaxy is through the velocities of tracer particles distributed through its halo. Transforming this kind of data accurately to a mass profile M(r), however, is not a trivial problem. In particular, limited or incomplete data may substantially affect the analysis. In this paper we develop a Bayesian method to deal with incomplete data effectively; we have a hybrid-Gibbs sampler that treats the unknown velocity components of tracers as parameters in the model. We explore the effectiveness of our model using simulated data, and then apply our method to the Milky Way using velocity and position data from globular clusters and dwarf galaxies. We find that in general, missing velocity components have little effect on the total mass estimate. However, the results are quite sensitive to the outer globular cluster Pal 3. Using a basic Hernquist model with an isotropic velocity dispersion, we obtain credible regions for the cumulative mass profile M(r) of the Milky Way, and provide estimates for the model parameters with 95 percent Bayesian credible intervals. The mass contained within 260 kpc is 1.37x10^12 solar masses, with a 95 percent credible interval of (1.27,1.51)x10^12 solar masses. The Hernquist parameters for the total mass and scale radius are 1.55 (+0.18/-0.13)x10^12 solar masses and 16.9 (+4.8/-4.1) kpc, where the uncertainties span the 95 percent credible intervals. The code we developed for this work, Galactic Mass Estimator (GME), will be available as an open source package in the R Project for Statistical Computing.

Disentangling the effects of climate, density dependence, and harvest on an iconic large herbivore's population dynamics.

Understanding the relative effects of climate, harvest, and density dependence on population dynamics is critical for guiding sound population management, especially for ungulates in arid and semiarid environments experiencing climate change. To address these issues for bison in southern Utah, USA, we applied a Bayesian state-space model to a 72-yr time series of abundance counts. While accounting for known harvest (as well as live removal) from the population, we found that the bison population in southern Utah exhibited a strong potential to grow from low density (β0 = 0.26; Bayesian credible interval based on 95% of the highest posterior density [BCI] = 0.19-0.33), and weak but statistically significant density dependence (β1 = -0.02, BCI = -0.04 to -0.004). Early spring temperatures also had strong positive effects on population growth (Pfat1 = 0.09, BCI = 0.04-0.14), much more so than precipitation and other temperature-related variables (model weight > three times more than that for other climate variables). Although we hypothesized that harvest is the primary driving force of bison population dynamics in southern Utah, our elasticity analysis indicated that changes in early spring temperature could have a greater relative effect on equilibrium abundance than either harvest or. the strength of density dependence. Our findings highlight the utility of incorporating elasticity analyses into state-space population models, and the need to include climatic processes in wildlife management policies and planning.

Speciation and genetic divergence of three species of charr from ancient Lake El'gygytgyn (Chukotka) and their phylogenetic relationships with other representatives of the genusSalvelinus

The diversity of phenotypically different and often reproductively isolated lacustrine forms of charrs of the genus Salvelinus represents a substantial problem for taxonomists and evolutionary biologists. Based on the analysis of variability of ten microsatellite loci and two fragments of mitochondrial DNA (control region and cyt-b gene), the evolutionary history of three charr species from Lake El’gygytgyn was reconstructed, and phylogenetic relationships between the main representatives of the genus were revealed. Three species from Lake El’gygytgyn were strongly reproductively isolated. Long-finned charr described previously as Salvethymus svetovidovi ,a n ancient endemic form in the lake, originated 3.5 Mya (95% Bayesian credible intervals: 1.7, 6.1). Placement of this species in the phylogenetic tree of Salvelinus was not determined strictly, but it should be located in the basal part of the clade Salvelinus alpinus – S. malma species complex. The origin of small-mouth charr S. elgyticus and Boganida charr S. boganidae in Lake El’gygytgyn was related to allopatric speciation. Their ancestors were represented by two glacial lineages of Taranets charr S. alpinus taranetzi from Asia. In Lake El’gygytgyn, these lineages entered into secondary contact postglacially. A revision of the main phylogenetic groups within the Salvelinus alpinus – S. malma complex is conducted. The Boganida charrs from Lakes El’gygytgyn and Lama (Taimyr) belong to different phylogenetic groups of Arctic charr and should not be regarded as a single species S. boganidae. Using the charrs from Lakes El’gygytgyn and Lama as a case study, we show that a model of sympatric speciation, which seemed more probable based on previous empirical evidence, was rejected by other data. © 2015 The Linnean Society of London, Biological Journal of the Linnean Society, 2015, 116 ,6 3–85. ADDITIONAL KEYWORDS: microsatellites – mitochondrial DNA – molecular dating – Salvelinus boganidae – Salvelinus elgyticus – Salvethymus svetovidovi – species complex – systematics.

Reflections on the Probability Space Induced by Moment Conditions with Implications for Bayesian Inference

Often a structural model implies that certain moment functions expressed in terms of data and model parameters follow a distribution. An assertion that moment functions follow a distribution logically implies a distribution on the arguments of the moment functions. This fact would appear to permit Bayesian inference on model parameters. The classic example is an assertion that the sample mean centered at a parameter and scaled by its standard error has Student’s t-distribution followed by an assertion that the sample mean plus and minus a critical value times the standard error is a Bayesian credibility interval for the parameter. This article studies the logic of such assertions. The main finding is that if the moment functions have one of the properties of a pivotal, then the assertion of a distribution on moment functions coupled with a proper prior does permit Bayesian inference. Without the semi-pivotal condition, the assertion of a distribution for moment functions either partially or completely specifies the prior. In this case, Bayesian inference may or may not be practicable depending on how much of the distribution of the constituents remains indeterminate after imposition of a noncontradictory prior. An asset pricing example that uses data from the U.S. economy illustrates the ideas.

Outcomes after multivessel or culprit-Vessel intervention for ST-elevation myocardial infarction in patients with multivessel coronary disease: a Bayesian cross-design meta-analysis.

During primary percutaneous coronary intervention (PCI), patients with ST-elevation myocardial infarction (STEMI) and multivessel coronary disease can undergo either multivessel intervention (MVI) or culprit-vessel intervention (CVI) only. Randomized controlled trials (RCTs) support the use of MVI, but cohort studies support the use of CVI. We developed Bayesian models that incorporated parameters for study type and study outcome after MVI or CVI. A total of 18 studies (4 RCTs, 3 matched cohort studies, and 11 unmatched observational studies) enrolled 48,398 patients with STEMI and multivessel CAD and reported outcomes after MVI or CVI-only at the time of primary PCI. Using a Bayesian hierarchical model, we found that the point estimates replicated previously reported trends, but the wide Bayesian credible intervals (BCI) excluded any plausible mortality difference between MVI versus CVI in all three study types: RCTs (odds ratio [OR] 0.60, 95% BCI 0.31-1.20), matched cohort studies (OR 1.37, 95% BCI 0.86-2.24), or unmatched cohort studies (OR 1.16, 95% BCI 0.70-1.89). Both the global summary (OR 1.10, 95% BCI 0.74-1.51) and a sensitivity analysis that weighted the RCTs 1-5 times as much as observational studies revealed no credible advantage of one PCI strategy over the other (OR 1.05, 95% BCI 0.64-1.48). Bayesian approaches contextualize the comparison of different strategies by study type and suggest that neither MVI nor CVI emerges as a preferred strategy in an analysis that accounts mortality differences.

Spatial distribution of schistosomiasis and treatment needs in sub-Saharan Africa: a systematic review and geostatistical analysis

Schistosomiasis affects more than 200 million individuals, mostly in sub-Saharan Africa, but empirical estimates of the disease burden in this region are unavailable. We used geostatistical modelling to produce high-resolution risk estimates of infection with Schistosoma spp and of the number of doses of praziquantel treatment needed to prevent morbidity at different administrative levels in 44 countries. We did a systematic review to identify surveys including schistosomiasis prevalence data in sub-Saharan Africa via PubMed, ISI Web of Science, and African Journals Online, from inception to May 2, 2014, with no restriction of language, survey date, or study design. We used Bayesian geostatistical meta-analysis and rigorous variable selection to predict infection risk over a grid of 1 155 818 pixels at 5 × 5 km, on the basis of environmental and socioeconomic predictors and to calculate the number of doses of praziquantel needed for prevention of morbidity. The literature search identified Schistosoma haematobium and Schistosoma mansoni surveys done in, respectively, 9318 and 9140 unique locations. Infection risk decreased from 2000 onwards, yet estimates suggest that 163 million (95% Bayesian credible interval [CrI] 155 million to 172 million; 18·5%, 17·6-19·5) of the sub-Saharan African population was infected in 2012. Mozambique had the highest prevalence of schistosomiasis in school-aged children (52·8%, 95% CrI 48·7-57·8). Low-risk countries (prevalence among school-aged children lower than 10%) included Burundi, Equatorial Guinea, Eritrea, and Rwanda. The numbers of doses of praziquantel needed per year were estimated to be 123 million (95% CrI 121 million to 125 million) for school-aged children and 247 million (239 million to 256 million) for the entire population. Our results will inform policy makers about the number of treatments needed at different levels and will guide the spatial targeting of schistosomiasis control interventions. European Research Council, China Scholarship Council, UBS Optimus Foundation, and Swiss National Science Foundation.

Illness and injury of travellers abroad: Finnish nationwide data from 2010 to 2012, with incidences in various regions of the world

The number of international tourist arrivals reached 1,000 million in 2012. Assessment of travellers' health problems has relied on proportionate morbidity data.Given the lack of data on number of visitors to each region, incidences have been impossible to calculate.This study, largest yet reporting travellers' health problems, is the first to present incidence of illness and injury. Data on Finnish travellers with health problems abroad during 2010 to 2012 were retrieved from the database of an assistance organisation,SOS International, covering 95% of those requiring aid abroad. The numbers were compared with those of Finnish travellers in the database of the Official Statistics of Finland. The SOS International database included 50,710 cases: infections constituted the most common health problem (60%), followed by injuries(14%), diseases of skin (5%), musculoskeletal system and connective tissue (5%), digestive tract (3%),and vascular system (2%). Gastroenteritis (23%) and respiratory infections (21%) proved the most frequent diagnoses. Overall incidence of illness or injury was high in Africa (97.9/100,000 travel days; 95% Bayesian credible interval (BCI): 53.1–145.5), southern Europe plus the eastern Mediterranean (92.3; 95% BCI: 75.4–110.1) and Asia (65.0; 95% BCI: 41.5–87.9). The data show significant differences between geographical regions, indicating the main risks and thus providing destination-specific tools for travelers' healthcare.

The effect of irradiance and temperature on the photosynthesis of a native alga Sargassum fusiforme (Fucales) from Kagoshima, Japan

:The effect of irradiance and temperature on the photosynthesis of a Japanese native brown alga, Sargassum fusiforme, was determined by using dissolved oxygen sensors and pulse amplitude–modulated fluorometry. In situ measurements of the effective quantum yield (ΦPSII) decreased as irradiance increased at 12:00 PM and recovered in the late afternoon, indicating that a proportionately greater number of reaction centres were closed. Likewise, laboratory measurement after 6 hours of exposure to low and high (300 and 1000 μmol photons m−2 s−1, respectively) irradiances showed a relatively greater decrease in ΦPSII at high irradiance, and both treatments recovered overnight. A model of the net photosynthesis–irradiance relationship determined at 20°C revealed that the net photosynthetic rate quickly increased at irradiances below the estimated saturation irradiance of 391 μmol photons m−2 s−1 [95% Bayesian credible interval (BCI) of 299–515 μmol photons m−2 s−1]. Gross photosynthesis and dark respiration rates determined over a range of temperatures (8–36°C) revealed that the maximal gross photosynthetic rate was 24.1 (BCI: 21.5–26.8) μg O2 gww−1 min−1 at 22.9°C (BCI: 19.8–25.8), and the dark respiration rate increased nonlinearly from a low of 0.5 μg O2 gww−1 min−1 at 8°C to a high of 8.9 μg O2 gww−1 min−1 at 36°C. The highest value of the quantum yield (Fv/Fm = ΦPSII at 0 μmol photons m−2 s−1) was estimated to occur at 22.9°C (BCI: 21.8–23.9) and was 0.72 (BCI: 0.70–0.73). The specimens examined appeared to be well adapted to the natural temperature range of the study site. Although the irradiances on the fronds were strong enough to induce a drop in quantum yield, our evidence clearly suggests that full recovery occurs overnight.