Fitting a spatial-temporal rainfall model using Approximate Bayesian Computation

We fit a stochastic spatial-temporal model to high-resolution rainfall radar data for a single rainfall event. Approximate Bayesian Computation (ABC) is used to fit a model of Cox, Isham and Northrop, previously fitted using the Generalised Method of Moments (GMM). We then show that ABC readily adapts to more general, and thus more realistic, variants of the model. The Simulated Method of Moments (SMM) is used to initialise the ABC fit

Spatial-temporal rainfall models based on Poisson cluster processes

We fit stochastic spatial-temporal models to high-resolution rainfall radar data using Approximate Bayesian Computation (ABC). We consider models constructed from cluster point-processes, starting with the model of Cox, Isham and Northrop, which is the current state of the art. We then generalise this model to allow for more realistic rainfall intensity gradients and for a richer covariance structure that can capture negative correlation between the intensity and size of localised rain cells. The use of ABC is of central importance, as it is not possible to fit models of this complexity using previous approaches. We also introduce the use of Simulated Method of Moments (SMM) to initialise the ABC fit

Fitting the Bartlett-Lewis rainfall model using approximate Bayesian computation

The Bartlett–Lewis (BL) rainfall model is a stochastic model for the rainfall at a single point in space, constructed using a cluster point process. The cluster process is constructed by taking a primary/parent process, called the storm arrival process in our context, and then attaching to each storm point a finite secondary/daughter point process, called a cell arrival process. To each cell arrival point we then attach a rain cell, with an associated rainfall duration and intensity. The total rainfall at time is then the sum of the intensities from all active cells at that time. Because it has an intractable likelihood function, in the past the BL model has been fitted using the Generalised Method of Moments (GMM). The purpose of this paper is to show that Approximate Bayesian Computation (ABC) can also be used to fit this model, and moreover that it gives a better fit than GMM. GMM fitting matches theoretical and observed moments of the process, and thus is restricted to moments for which you have an analytic expression. ABC fitting compares the observed process to simulations, and thus places no restrictions on the statistics used to compare them. The penalty we pay for this increased flexibility is an increase in computational time

Fitting a spatial-temporal rainfall model using Approximate Bayesian Computation

We fit a stochastic spatial-temporal model to high-resolution rainfall radar data for a single rainfall event. Approximate Bayesian Computation (ABC) is used to fit a model of Cox, Isham and Northrop, previously fitted using the Generalised Method of Moments (GMM). We then show that ABC readily adapts to more general, and thus more realistic, variants of the model. The Simulated Method of Moments (SMM) is used to initialise the ABC fit

Global, regional, and national under-5 mortality, adult mortality, age-specific mortality, and life expectancy, 1970–2016: a systematic analysis for the Global Burden of Disease Study 2016

BACKGROUND: Detailed assessments of mortality patterns, particularly age-specific mortality, represent a crucial input that enables health systems to target interventions to specific populations. Understanding how all-cause mortality has changed with respect to development status can identify exemplars for best practice. To accomplish this, the Global Burden of Diseases, Injuries, and Risk Factors Study 2016 (GBD 2016) estimated age-specific and sex-specific all-cause mortality between 1970 and 2016 for 195 countries and territories and at the subnational level for the five countries with a population greater than 200 million in 2016. METHODS: We have evaluated how well civil registration systems captured deaths using a set of demographic methods called death distribution methods for adults and from consideration of survey and census data for children younger than 5 years. We generated an overall assessment of completeness of registration of deaths by dividing registered deaths in each location-year by our estimate of all-age deaths generated from our overall estimation process. For 163 locations, including subnational units in countries with a population greater than 200 million with complete vital registration (VR) systems, our estimates were largely driven by the observed data, with corrections for small fluctuations in numbers and estimation for recent years where there were lags in data reporting (lags were variable by location, generally between 1 year and 6 years). For other locations, we took advantage of different data sources available to measure under-5 mortality rates (U5MR) using complete birth histories, summary birth histories, and incomplete VR with adjustments; we measured adult mortality rate (the probability of death in individuals aged 15-60 years) using adjusted incomplete VR, sibling histories, and household death recall. We used the U5MR and adult mortality rate, together with crude death rate due to HIV in the GBD model life table system, to estimate age-specific and sex-specific death rates for each location-year. Using various international databases, we identified fatal discontinuities, which we defined as increases in the death rate of more than one death per million, resulting from conflict and terrorism, natural disasters, major transport or technological accidents, and a subset of epidemic infectious diseases; these were added to estimates in the relevant years. In 47 countries with an identified peak adult prevalence for HIV/AIDS of more than 0·5% and where VR systems were less than 65% complete, we informed our estimates of age-sex-specific mortality using the Estimation and Projection Package (EPP)-Spectrum model fitted to national HIV/AIDS prevalence surveys and antenatal clinic serosurveillance systems. We estimated stillbirths, early neonatal, late neonatal, and childhood mortality using both survey and VR data in spatiotemporal Gaussian process regression models. We estimated abridged life tables for all location-years using age-specific death rates. We grouped locations into development quintiles based on the Socio-demographic Index (SDI) and analysed mortality trends by quintile. Using spline regression, we estimated the expected mortality rate for each age-sex group as a function of SDI. We identified countries with higher life expectancy than expected by comparing observed life expectancy to anticipated life expectancy on the basis of development status alone. FINDINGS: Completeness in the registration of deaths increased from 28% in 1970 to a peak of 45% in 2013; completeness was lower after 2013 because of lags in reporting. Total deaths in children younger than 5 years decreased from 1970 to 2016, and slower decreases occurred at ages 5-24 years. By contrast, numbers of adult deaths increased in each 5-year age bracket above the age of 25 years. The distribution of annualised rates of change in age-specific mortality rate differed over the period 2000 to 2016 compared with earlier decades: increasing annualised rates of change were less frequent, although rising annualised rates of change still occurred in some locations, particularly for adolescent and younger adult age groups. Rates of stillbirths and under-5 mortality both decreased globally from 1970. Evidence for global convergence of death rates was mixed; although the absolute difference between age-standardised death rates narrowed between countries at the lowest and highest levels of SDI, the ratio of these death rates-a measure of relative inequality-increased slightly. There was a strong shift between 1970 and 2016 toward higher life expectancy, most noticeably at higher levels of SDI. Among countries with populations greater than 1 million in 2016, life expectancy at birth was highest for women in Japan, at 86·9 years (95% UI 86·7-87·2), and for men in Singapore, at 81·3 years (78·8-83·7) in 2016. Male life expectancy was generally lower than female life expectancy between 1970 and 2016, an

Stochastic spatial-temporal models for rainfall processes

© 2018 Dr. Nanda Ram AryalCurrently clustered rainfall models have been fitted using Generalized Method of Moments (GMM), because typically they have intractable likelihood func- tions. GMM fitting matches theoretical and observed moments of the process and thus is restricted to models for which analytic expressions are available for the moments. We show that Approximate Bayesian Computation (ABC) can also be used to fit clustered rainfall models. We also validate that ABC readily adapts to more general, and thus more realistic, variants of spatial- temporal rainfall models. ABC fitting compares the observed process with simulations and hence places no restrictions on the statistics used for the comparison. This opens up the possibility of fitting much more realistic stochastic rainfall models. The penalty we pay for this increased flexibility is an increase in computational time. Simulated Method of Moments (SMM) is used to initialize the ABC. This can also be used to estimate the weights of the distance measure in the ABC-MCMC setting. We found that our method requires much smaller computation time in comparison with what previous authors have suggested using a separate ABC step to estimate initialisation. A spatial-temporal rainfall model based on a cluster process is constructed by taking a primary process, called the storm arrival process, and attaching to each storm centre a finite secondary process, called a cell process. The total intensity at a point in R2 × [0, ∞) is the sum of the intensities of all cells active at that point. Typically, the model parameters are interde- pendent.This dependency produces complexity in model fitting procedures, and has also restricted further extension of the model, particularly finding theoretical expressions for the moments. Fortunately, ABC can be applied without having analytical expressions for the moments. We reparameterized the models and the parameters were log transformed to reduce dependence and skewness, also simplifies the chain proposal in MCMC steps. We also present two new stochastic spatial-temporal rainfall models that yield with better representation of observed rainfall processes, and also cap- ture the dependence between size and intensity for rain cells