Generalised likelihood profiles for models with intractable likelihoods

Likelihood profiling is an efficient and powerful frequentist approach for parameter estimation, uncertainty quantification and practical identifiablity analysis. Unfortunately, these methods cannot be easily applied for stochastic models without a tractable likelihood function. Such models are typical in many fields of science, rendering these classical approaches impractical in these settings. To address this limitation, we develop a new approach to generalising the methods of likelihood profiling for situations when the likelihood cannot be evaluated but stochastic simulations of the assumed data generating process are possible. Our approach is based upon recasting developments from generalised Bayesian inference into a frequentist setting. We derive a method for constructing generalised likelihood profiles and calibrating these profiles to achieve desired frequentist coverage for a given coverage level. We demonstrate the performance of our method on realistic examples from the literature and highlight the capability of our approach for the purpose of practical identifability analysis for models with intractable likelihoods

Profile likelihood analysis for a stochastic model of diffusion in heterogeneous media

We compute profile likelihoods for a stochastic model of diffusive transport motivated by experimental observations of heat conduction in layered skin tissues. This process is modelled as a random walk in a layered one-dimensional material, where each layer has a distinct particle hopping rate. Particles are released at some location, and the duration of time taken for each particle to reach an absorbing boundary is recorded. To explore whether this data can be used to identify the hopping rates in each layer, we compute various profile likelihoods using two methods: first, an exact likelihood is evaluated using a relatively expensive Markov chain approach; and, second we form an approximate likelihood by assuming the distribution of exit times is given by a Gamma distribution whose first two moments match the expected moments from the continuum limit description of the stochastic model. Using the exact and approximate likelihoods we construct various profile likelihoods for a range of problems. In cases where parameter values are not identifiable, we make progress by re-interpreting those data with a reduced model with a smaller number of layers.Comment: 41 pages, 11 figure

Modelling the effects of calcium waves and oscillations on saliva secretion

An understanding of Ca2+Ca2+ signalling in saliva-secreting acinar cells is important, as Ca2+Ca2+ is the second messenger linking stimulation of cells to production of saliva. Ca2+Ca2+ signals affect secretion via the ion channels located both apically and basolaterally in the cell. By approximating Ca2+Ca2+ waves with periodic functions on the apical and basolateral membranes, we isolate individual wave properties and investigate them for their effect on fluid secretion in a mathematical model of the acinar cell. Mean Ca2+Ca2+ concentration is found to be the most significant property in signalling secretion. Wave speed was found to encode a range of secretion rates. Ca2+Ca2+ oscillation frequency and amplitude had little effect on fluid secretion

What do aquaporin knockout studies tell us about fluid transport in epithelia?

The investigation of near-isosmotic water transport in epithelia goes back over 100 years; however, debates over mechanism and pathway remain. Aquaporin (AQP) knockouts have been used by various research groups to test the hypothesis of an osmotic mechanism as well as to explore the paracellular versus transcellular pathway debate. Nonproportional reductions in the water permeability of a water-transporting epithelial cell (e.g., a reduction of around 80–90 %) compared to the reduction in overall water transport rate in the knockout animal (e.g., a reduction of 50–60 %) are commonly found. This nonproportionality has led to controversy over whether AQP knockout studies support or contradict the osmotic mechanism. Arguments raised for and against an interpretation supporting the osmotic mechanism typically have partially specified, implicit, or incorrect assumptions. We present a simple mathematical model of the osmotic mechanism with clear assumptions and, for models based on this mechanism, establish a baseline prediction of AQP knockout studies. We allow for deviations from isotonic/isosmotic conditions and utilize dimensional analysis to reduce the number of parameters that must be considered independently. This enables a single prediction curve to be used for multiple epithelial systems. We find that a simple, transcellular-only osmotic mechanism sufficiently predicts the results of knockout studies and find criticisms of this mechanism to be overstated. We note, however, that AQP knockout studies do not give sufficient information to definitively rule out an additional paracellular pathway

The Physical Activity Messaging Framework (PAMF) and Checklist (PAMC): International consensus statement and user guide

Effective physical activity messaging plays an important role in the pathway towards changing physical activity behaviour at a population level. The Physical Activity Messaging Framework (PAMF) and Checklist (PAMC) are outputs from a recent modified Delphi study. This sought consensus from an international expert panel on how to aid the creation and evaluation of physical activity messages. In this paper, we (1) present an overview of the various concepts within the PAMF and PAMC, (2) discuss in detail how the PAMF and PAMC can be used to create physical activity messages, plan evaluation of messages, and aid understanding and categorisation of existing messages, and (3) highlight areas for future development and research. If adopted, we propose that the PAMF and PAMC could improve physical activity messaging practice by encouraging evidence-based and target population focused messages with clearly stated aims and consideration of potential working pathways. They could also enhance the physical activity messaging research base by harmonising key messaging terminologies, improving quality of reporting, and aiding collation and synthesis of the evidence

Efficiency of primary saliva secretion: an analysis of parameter dependence in dynamic single-cell and acinus models, with application to aquaporin knockout studies

Secretion from the salivary glands is driven by osmosis following the establishment of osmotic gradients between the lumen, the cell and the interstitium by active ion transport. We consider a dynamic model of osmotically driven primary saliva secretion and use singular perturbation approaches and scaling assumptions to reduce the model. Our analysis shows that isosmotic secretion is the most efficient secretion regime and that this holds for single isolated cells and for multiple cells assembled into an acinus. For typical parameter variations, we rule out any significant synergistic effect on total water secretion of an acinar arrangement of cells about a single shared lumen. Conditions for the attainment of isosmotic secretion are considered, and we derive an expression for how the concentration gradient between the interstitium and the lumen scales with water- and chloride-transport parameters. Aquaporin knockout studies are interpreted in the context of our analysis and further investigated using simulations of transport efficiency with different membrane water permeabilities. We conclude that recent claims that aquaporin knockout studies can be interpreted as evidence against a simple osmotic mechanism are not supported by our work. Many of the results that we obtain are independent of specific transporter details, and our analysis can be easily extended to apply to models that use other proposed ionic mechanisms of saliva secretion