Approximation of Bayesian Hawkes process with inlabru

Hawkes process are very popular mathematical tools for modeling phenomena exhibiting a self-exciting or self-correcting behavior. Typical examples are earthquakes occurrence, wild-fires, drought, capture-recapture, crime violence, trade exchange, and social network activity. The widespread use of Hawkes process in different fields calls for fast, reproducible, reliable, easy-to-code techniques to implement such models. We offer a technique to perform approximate Bayesian inference of Hawkes process parameters based on the use of the R-package inlabru . The inlabru R-package, in turn, relies on the INLA methodology to approximate the posterior of the parameters. Our Hawkes process approximation is based on a decomposition of the log-likelihood in three parts, which are linearly approximated separately. The linear approximation is performed with respect to the mode of the parameters\u27 posterior distribution, which is determined with an iterative gradient-based method. The approximation of the posterior parameters is therefore deterministic, ensuring full reproducibility of the results. The proposed technique only requires the user to provide the functions to calculate the different parts of the decomposed likelihood, which are internally linearly approximated by the R-package inlabru . We provide a comparison with the bayesianETAS R-package which is based on an MCMC method. The two techniques provide similar results but our approach requires two to ten times less computational time to converge, depending on the amount of data

Bayesian modelling of the temporal evolution of seismicity using the ETAS.inlabru package

The epidemic type aftershock sequence (ETAS) model is widely used to model seismic sequences and underpins operational earthquake forecasting (OEF). However, it remains challenging to assess the reliability of inverted ETAS parameters for numerous reasons. For example, the most common algorithms just return point estimates with little quantification of uncertainty. At the same time, Bayesian Markov chain Monte Carlo implementations remain slow to run and do not scale well, and few have been extended to include spatial structure. This makes it difficult to explore the effects of stochastic uncertainty. Here, we present a new approach to ETAS modeling using an alternative Bayesian method, the integrated nested Laplace approximation (INLA). We have implemented this model in a new R-Package called ETAS.inlabru, which is built on the R packages R-INLA and inlabru. Our study has included extending these packages, which provided tools for modeling log-Gaussian Cox processes, to include the self-exciting Hawkes process that ETAS is a special case of. While we just present the temporal component here, the model scales to a spatio-temporal model and may include a variety of spatial covariates. This is a fast method that returns joint posteriors on the ETAS background and triggering parameters. Using a series of synthetic case studies, we explore the robustness of ETAS inversions using this method of inversion. We also included runnable notebooks to reproduce the figures in this article as part of the package\u27s GitHub repository. We demonstrate that reliable estimates of the model parameters require that the catalog data contain periods of relative quiescence, as well as triggered sequences. We explore the robustness of the method under stochastic uncertainty in the training data and show that the method is robust to a wide range of starting conditions. We show how the inclusion of historic earthquakes prior to the modeled time window affects the quality of the inversion. Finally, we show that rate-dependent incompleteness of earthquake catalogs after large earthquakes have a significant and detrimental effect on the ETAS posteriors. We believe that the speed of the inlabru inversion, which includes a rigorous estimation of uncertainty, will enable a deeper exploration of how to use ETAS robustly for seismicity modeling and operational earthquake forecasting

Ranking earthquake forecasts using proper scoring rules: binary events in a low probability environment

Operational earthquake forecasting for risk management and communication during seismic sequences depends on our ability to select an optimal forecasting model. To do this, we need to compare the performance of competing models in prospective experiments, and to rank their performance according to the outcome using a fair, reproducible and reliable method, usually in a low-probability environment. The Collaboratory for the Study of Earthquake Predictability conducts prospective earthquake forecasting experiments around the globe. In this framework, it is crucial that the metrics used to rank the competing forecasts are ‘proper’, meaning that, on average, they prefer the data generating model. We prove that the Parimutuel Gambling score, proposed, and in some cases applied, as a metric for comparing probabilistic seismicity forecasts, is in general ‘improper’. In the special case where it is proper, we show it can still be used improperly. We demonstrate the conclusions both analytically and graphically providing a set of simulation based techniques that can be used to assess if a score is proper or not. They only require a data generating model and, at least two forecasts to be compared. We compare the Parimutuel Gambling score’s performance with two commonly used proper scores (the Brier and logarithmic scores) using confidence intervals to account for the uncertainty around the observed score difference. We suggest that using confidence intervals enables a rigorous approach to distinguish between the predictive skills of candidate forecasts, in addition to their rankings. Our analysis shows that the Parimutuel Gambling score is biased, and the direction of the bias depends on the forecasts taking part in the experiment. Our findings suggest the Parimutuel Gambling score should not be used to distinguishing between multiple competing forecasts, and for care to be taken in the case where only two are being compared

Experience-based VAS values for EQ-5D-3L health states in a national general population health survey in China

Purpose: To investigate the feasibility of deriving experience-based visual analogue scale (VAS) values for EQ-5D-3L health states using national general population health survey data in China. Methods: The EQ-5D-3L was included in the National Health Services Survey (n = 120,709, aged 15–103 years) to measure health-related quality of life. The respondents reported their current health status on a VAS and completed the EQ-5D-3L questionnaire, enabling modelling of the association between the experience-based VAS values and self-reported problems on EQ-5D dimensions and severity levels. Results: VAS values were generally negatively associated with problems reported on the EQ-5D dimensions, and the anxiety/depression dimension had the greatest impact on VAS values. A previously obtained value for dead allowed the values for all 243 EQ-5D-3L health states to be transformed to the 0–1 scale (0 = dead, 1 = full health). Conclusions: This study presents the feasibility of deriving an experience-based VAS values for EQ-5D-3L health states in China. The analysis of these VAS data raises more fundamental issues concerning the universal nature of the classification system and the extent to which Chinese respondents utilise the same concepts of health as defined by this classification system

Calf health from birth to weaning. II. Management of diarrhoea in pre-weaned calves

Calfhood diseases have a major impact on the economic viability of cattle operations. The second of this three part review series considers the management of diarrhoeic diseases in pre-weaned calves. In neonatal calf diarrhoea, oral rehydration therapy is the single most important therapeutic measure to be carried out by the farmer and is usually successful if instigated immediately after diarrhoea has developed. Continued feeding of milk or milk replacer to diarrhoeic calves is important, to prevent malnourishment and weight loss in affected calves. Indiscriminative antibiotic treatment of uncomplicated diarrhoea is discouraged, whereas systemically ill calves can benefit from systemic antibiotic treatment for the prevention of septicaemia or concurrent diseases. Ancillary treatments and specific preventive measures are discussed. Eimeriosis has a high economic impact on the farming industries due to direct cost of treatment and calf losses, but especially due to decreased performance of clinically as well as sub-clinically affected animals. Emphasis lies on prophylactic or metaphylactic treatment, since the degree of damage to the intestinal mucosa once diarrhoea has developed, makes therapeutic intervention unrewarding

TNFRSF1B +676 T>G polymorphism predicts survival of non-Small cell lung cancer patients treated with chemoradiotherapy

<p>Abstract</p> <p>Background</p> <p>The dysregulation of gene expression in the TNF-TNFR superfamily has been involved in various human cancers including non-small cell lung cancer (NSCLC). Furthermore, functional polymorphisms in <it>TNF-α </it>and <it>TNFRSF1B </it>genes that alter gene expression are likely to be associated with risk and clinical outcomes of cancers. However, few reported studies have investigated the association between potentially functional SNPs in both <it>TNF-α </it>and <it>TNFRSF1B </it>and prognosis of NSCLC patients treated with chemoradiotherapy.</p> <p>Methods</p> <p>We genotyped five potentially functional polymorphisms of <it>TNF-α </it>and <it>TNFRSF1B </it>genes [<it>TNF-α </it>-308 G>A (rs1800629) and -1031 T>C (rs1799964); <it>TNFRSF1B </it>+676 T>G (rs1061622), -1709A>T(rs652625) and +1663A>G (rs1061624)] in 225 NSCLC patients treated with chemoradiotherapy or radiotherapy alone. Kaplan-Meier survival analysis, log-rank tests and Cox proportional hazard models were used to evaluate associations between these variants and NSCLC overall survival (OS).</p> <p>Results</p> <p>We found that the <it>TNFRSF1B </it>+676 GG genotype was associated with a significantly better OS of NSCLC (GG <it>vs. </it>TT: adjusted HR = 0.38, 95% CI = 0.15-0.94; GG <it>vs. </it>GT/TT: adjusted HR = 0.35, 95% CI = 0.14-0.88). Further stepwise multivariate Cox regression analysis showed that the <it>TNFRSF1B </it>+676 GG was an independent prognosis predictor in this NSCLC cohort (GG <it>vs. </it>GT/TT: HR = 0.35, 95% CI = 0.14-0.85), in the presence of node status (N_2-3<it>vs. </it>N_0-1: HR = 1.60, 95% CI = 1.09-2.35) and tumor stage (T_3-4<it>vs. </it>T_0-2: HR = 1.48, 95% CI = 1.08-2.03).</p> <p>Conclusions</p> <p>Although the exact biological function for this SNP remains to be explored, our findings suggest a possible role of <it>TNFRSF1B </it>+676 T>G (rs1061622) in the prognosis of NSCLC. Further large and functional studies are needed to confirm our findings.</p