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In this paper, we introduce the R package mcmsupply which implements Bayesian hierarchical models for estimating and projecting modern contraceptive market supply shares over time. The package implements four model types. These models vary by the administration level of their outcome estimates (national or subnational estimates) and dataset type utilised in the estimation (multi-country or single-country contraceptive market supply datasets). mcmsupply contains a compilation of national and subnational level contraceptive source datasets, generated by IPUMS and Demographic and Health Survey microdata. We describe the functions that implement the models through practical examples. The annual estimates and projections with uncertainty of the contraceptive market supply, produced by mcmcsupply at a national and subnational level, are the first of their kind. These estimates and projections have diverse applications, including acting as an indicator of family planning market stability over time and being utilised in the calculation of estimates of modern contraceptive use.

Polytomous categorical data are frequent in studies, that can be obtained with an individual or grouped structure. In both structures, the generalized logit model is commonly used to relate the covariates on the response variable. After fitting a model, one of the challenges is the definition of an appropriate residual and choosing diagnostic techniques. Since the polytomous variable is multivariate, raw, Pearson, or deviance residuals are vectors and their asymptotic distribution is generally unknown, which leads to difficulties in graphical visualization and interpretation. Therefore, the definition of appropriate residuals and the choice of the correct analysis in diagnostic tools is important, especially for nominal data, where a restriction of methods is observed. This paper proposes the use of randomized quantile residuals associated with individual and grouped nominal data, as well as Euclidean and Mahalanobis distance measures, as an alternative to reduce the dimension of the residuals. We developed simulation studies with both data structures associated. The half-normal plots with simulation envelopes were used to assess model performance. These studies demonstrated a good performance of the quantile residuals, and the distance measurements allowed a better interpretation of the graphical techniques. We illustrate the proposed procedures with two applications to real data., Comment: 20 pages

We present reslr, an R package to perform Bayesian modelling of relative sea level data. We include a variety of different statistical models previously proposed in the literature, with a unifying framework for loading data, fitting models, and summarising the results. Relative sea-level data often contain measurement error in multiple dimensions and so our package allows for these to be included in the statistical models. When plotting the output sea level curves, the focus is often on comparing rates of change, and so our package allows for computation of the derivative of sea level curves with appropriate consideration of the uncertainty. We provide a large example dataset from the Atlantic coast of North America and show some of the results that might be obtained from our package.

We propose a Bayesian, noisy-input, spatial-temporal generalised additive model to examine regional relative sea-level (RSL) changes over time. The model provides probabilistic estimates of component drivers of regional RSL change via the combination of a univariate spline capturing a common regional signal over time, random slopes and intercepts capturing site-specific (local), long-term linear trends and a spatial-temporal spline capturing residual, non-linear, local variations. Proxy and instrumental records of RSL and corresponding measurement errors inform the model and a noisy-input method accounts for proxy temporal uncertainties. Results focus on the decomposition of RSL over the past 3000 years along the Atlantic coast of North America.

We propose a Bayesian hierarchical model which produces probabilistic reconstructions of hydroclimatic variability in Queensland Australia. The model provides a standardised approach to hydroclimate reconstruction using multiple palaeoclimate proxy records derived from natural archives such as speleothems, ice cores and tree rings. The method combines time-series modelling with inverse prediction to quantify the relationships between a given hydroclimate index and relevant proxies over an instrumental period and subsequently reconstruct the hydroclimate back through time. We present case studies for Brisbane and Fitzroy catchments focusing on two hydroclimate indices, the Rainfall Index (RFI) and the Standardised Precipitation-Evapotranspiration Index (SPEI). The probabilistic nature of the reconstructions allows us to estimate the probability that a hydroclimate index in any reconstruction year was lower (higher) than the minimum (maximum) value observed over the instrumental period. In Brisbane, the RFI is unlikely (probabilities < 20%) to have exhibited extremes beyond the minimum/maximum values observed between 1889 and 2017. However, in Fitzroy there are several years during the reconstruction period where the RFI is likely (> 50% probability) to have exhibited behaviour beyond the minimum/maximum of what has been observed. For SPEI, the probability of observing such extremes since the end of the instrumental period in 1889 doesn't exceed 50% in any reconstruction year in Brisbane or Fitzroy., Comment: 20 pages, 10 figures

Characterizing the spatio-temporal variability of relative sea level (RSL) and estimating local, regional, and global RSL trends requires statistical analysis of RSL data. Formal statistical treatments, needed to account for the spatially and temporally sparse distribution of data and for geochronological and elevational uncertainties, have advanced considerably over the last decade. Time-series models have adopted more flexible and physically-informed specifications with more rigorous quantification of uncertainties. Spatio-temporal models have evolved from simple regional averaging to frameworks that more richly represent the correlation structure of RSL across space and time. More complex statistical approaches enable rigorous quantification of spatial and temporal variability, the combination of geographically disparate data, and the separation of the RSL field into various components associated with different driving processes. We review the range of statistical modeling and analysis choices used in the literature, reformulating them for ease of comparison in a common hierarchical statistical framework. The hierarchical framework separates each model into different levels, clearly partitioning measurement and inferential uncertainty from process variability. Placing models in a hierarchical framework enables us to highlight both the similarities and differences among modeling and analysis choices. We illustrate the implications of some modeling and analysis choices currently used in the literature by comparing the results of their application to common datasets within a hierarchical framework. In light of the complex patterns of spatial and temporal variability exhibited by RSL, we recommend non-parametric approaches for modeling temporal and spatio-temporal RSL., Comment: 30 pages, 7 figures

We present a holistic Bayesian hierarchical model for reconstructing the continuous and dynamic evolution of relative sea-level (RSL) change with fully quantified uncertainty. The reconstruction is produced from biological (foraminifera) and geochemical ({\delta}13C) sea-level indicators preserved in dated cores of salt-marsh sediment. Our model is comprised of three modules: (1) A Bayesian transfer function for the calibration of foraminifera into tidal elevation, which is flexible enough to formally accommodate additional proxies (in this case bulk-sediment {\delta}13C values); (2) A chronology developed from an existing Bchron age-depth model, and (3) An existing errors-in-variables integrated Gaussian process (EIV-IGP) model for estimating rates of sea-level change. We illustrate our approach using a case study of Common Era sea-level variability from New Jersey, U.S.A. We develop a new Bayesian transfer function (B-TF), with and without the {\delta}13C proxy and compare our results to those from a widely-used weighted-averaging transfer function (WA-TF). The formal incorporation of a second proxy into the B-TF model results in smaller vertical uncertainties and improved accuracy for reconstructed RSL. The vertical uncertainty from the multi-proxy B-TF is ~28% smaller on average compared to the WA-TF. When evaluated against historic tide-gauge measurements, the multi-proxy B-TF most accurately reconstructs the RSL changes observed in the instrumental record (MSE = 0.003). The holistic model provides a single, unifying framework for reconstructing and analysing sea level through time. This approach is suitable for reconstructing other paleoenvironmental variables using biological proxies., Comment: 27 pages, 7 figures

We perform Bayesian inference on historical and late Holocene (last 2000 years) rates of sea-level change. The input data to our model are tide-gauge measurements and proxy reconstructions from cores of coastal sediment. These data are complicated by multiple sources of uncertainty, some of which arise as part of the data collection exercise. Notably, the proxy reconstructions include temporal uncertainty from dating of the sediment core using techniques such as radiocarbon. The model we propose places a Gaussian process prior on the rate of sea-level change, which is then integrated and set in an errors-in-variables framework to take account of age uncertainty. The resulting model captures the continuous and dynamic evolution of sea-level change with full consideration of all sources of uncertainty. We demonstrate the performance of our model using two real (and previously published) example data sets. The global tide-gauge data set indicates that sea-level rise increased from a rate with a posterior mean of 1.13 mm$/$yr in 1880 AD (0.89 to 1.28 mm$/$yr 95% credible interval for the posterior mean) to a posterior mean rate of 1.92 mm$/$yr in 2009 AD (1.84 to 2.03 mm$/$yr 95% credible interval for the posterior mean). The proxy reconstruction from North Carolina (USA) after correction for land-level change shows the 2000 AD rate of rise to have a posterior mean of 2.44 mm$/$yr (1.91 to 3.01 mm$/$yr 95% credible interval). This is unprecedented in at least the last 2000 years., Comment: Published at http://dx.doi.org/10.1214/15-AOAS824 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)