A new expiratory droplet investigation system (EDIS) was used to conduct the most comprehensive program of study to date, of the dilution corrected droplet size distributions produced during different respiratory activities. Distinct physiological processes were responsible for specific size distribution modes. The majority of particles for all activities were produced in one or more modes, with diameters below 0.8 m at average concentrations up to 0.75 cm −3 . These particles occurred at varying concentrations, during all respiratory activities, including normal breathing. A second mode at 1.8 m was produced during all activities, but at lower concentrations of up to 0.14 cm −3 . Speech produced additional particles in modes near 3.5 and 5 m. These two modes became most pronounced during sustained vocalization, producing average concentrations of 0.04 and 0.16 cm −3 , respectively, suggesting that the aerosolization of secretions lubricating the vocal chords is a major source of droplets in terms of number. For the entire size range examined of 0.3-20 m, average particle number concentrations produced during exhalation ranged from 0.1 cm −3 for breathing to 1.1 cm −3 for sustained vocalization. Non-equilibrium droplet evaporation was not detectable for particles between 0.5 and 20 m, implying that evaporation to the equilibrium droplet size occurred within 0.8 s.

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Size distributions of expiratory droplets expelled during coughing and speaking and the velocities of the expiration air jets of healthy volunteers were measured. Droplet size was measured using the interferometric Mie imaging (IMI) technique while the particle image velocimetry (PIV) technique was used for measuring air velocity. These techniques allowed measurements in close proximity to the mouth and avoided air sampling losses. The average expiration air velocity was 11.7 m/s for coughing and 3.9 m/s for speaking. Under the experimental setting, evaporation and condensation effects had negligible impact on the measured droplet size. The geometric mean diameter of droplets from coughing was 13.5 m and it was 16.0 m for speaking (counting 1-100). The estimated total number of droplets expelled ranged from 947 to 2085 per cough and 112-6720 for speaking. The estimated droplet concentrations for coughing ranged from 2.4 to 5.2 cm −3 per cough and 0.004-0.223 cm −3 for speaking.

Expert knowledge is used widely in the science and practice of conservation because of the complexity of problems, relative lack of data, and the imminent nature of many conservation decisions. Expert knowledge is substantive information on a particular topic that is not widely known by others. An expert is someone who holds this knowledge and who is often deferred to in its interpretation. We refer to predictions by experts of what may happen in a particular context as expert judgments. In general, an expert-elicitation approach consists of five steps: deciding how information will be used, determining what to elicit, designing the elicitation process, performing the elicitation, and translating the elicited information into quantitative statements that can be used in a model or directly to make decisions. This last step is known as encoding. Some of the considerations in eliciting expert knowledge include determining how to work with multiple experts and how to combine multiple judgments, minimizing bias in the elicited information, and verifying the accuracy of expert information. We highlight structured elicitation techniques that, if adopted, will improve the accuracy and information content of expert judgment and ensure uncertainty is captured accurately. We suggest four aspects of an expert elicitation exercise be examined to determine its comprehensiveness and effectiveness: study design and context, elicitation design, elicitation method, and elicitation output. Just as the reliability of empirical data depends on the rigor with which it was acquired so too does that of expert knowledge.

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Summary1. Meta-analysis has become a standard way of summarizing empirical studies in many fields, including ecology and evolution. In ecology and evolution, meta-analyses comparing two groups (usually experimental and control groups) have almost exclusively focused on comparing the means, using standardized metrics such as Cohen's / Hedges' d or the response ratio. 2. However, an experimental treatment may not only affect the mean but also the variance. Investigating differences in the variance between two groups may be informative, especially when a treatment influences the variance in addition to or instead of the mean. 3. In this paper, we propose the effect size statistic lnCVR (the natural logarithm of the ratio between the coefficients of variation, CV, from two groups), which enables us to meta-analytically compare differences between the variability of two groups. We illustrate the use of lnCVR with examples from ecology and evolution. 4. Further, as an alternative approach to the use of lnCVR, we propose the combined use of ln s (the log standard deviation) and ln x (the log mean) in a hierarchical (linear mixed) model. The use of ln s with ln x overcomes potential limitations of lnCVR and it provides a more flexible, albeit more complex, way to examine variation beyond two-group comparisons. Relevantly, we also refer to the potential use of ln s and lnCV (the log CV) in the context of comparative analysis. 5. Our approaches to compare variability could be applied to already published meta-analytic data sets that compare two-group means to uncover potentially overlooked effects on the variance. Additionally, our approaches should be applied to future meta-analyses, especially when one suspects a treatment has an effect not only on the mean, but also on the variance. Notably, the application of the proposed methods extends beyond the fields of ecology and evolution.

We apply recent results in Markov chain theory to Hastings and Metropolis algorithms with either independent or symmetric candidate distributions, and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution .Ž k . In the independence case in ‫ޒ‬ these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded Ž . below by a multiple of ; in the symmetric case in ‫ޒ‬ only we show geometric convergence essentially occurs if and only if has geometric tails. We also evaluate recently developed computable bounds on the rates of convergence in this context: examples show that these theoretical bounds can be inherently extremely conservative, although when the chain is stochastically monotone the bounds may well be effective.

Abstract.In this paper we study the asymptotic behaviour of the posterior distribution in a mixture model when the number of components in the mixture is larger than the true number of components, a situation commonly referred to as overfitted mixture. We prove in particular that quite generally the posterior distribution has a stable and interesting behaviour, since it tends to empty the extra components. This stability is achieved under some restriction on the prior, which can be used as a guideline for choosing the prior. Some simulations are presented to illustrate this behaviour.