Bayesian Adaptive Smoothing Splines Using Stochastic Differential Equations

Yu, Yue; Simpson, Daniel; Lindgren, Finn; Rue, Håvard

doi:10.1214/13-ba866

Cited by 33 publications

(34 citation statements)

References 49 publications

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“…July 1962 to June 1963). Time was also treated as a random effect and its effect on catch was modelled with an order two random walk, which is equivalent to a cubic spline 63 . Gear (net, drumlines) was included in the model as a fixed effect, to account for differences in catchability between gear types.…”

Section: Methodsmentioning

confidence: 99%

Decline of coastal apex shark populations over the past half century

et al. 2018

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Overexploitation of large apex marine predators is widespread in the world’s oceans, yet the timing and extent of declines are poorly understood. Here we reconstruct a unique fisheries-independent dataset from a shark control programme spanning 1760 km of the Australian coastline over the past 55 years. We report substantial declines (74–92%) of catch per unit effort of hammerhead (Sphyrnidae), whaler (Carcharhinidae), tiger shark (Galeocerdo cuvier) and white sharks (Carcharodon carcharias). Following onset of the program in the 1960s, catch rates in new installations in subsequent decades occurred at a substantially lower rate, indicating regional depletion of shark populations over the past half a century. Concurrent declines in body size and the probability of encountering mature individuals suggests that apex shark populations are more vulnerable to exploitation than previously thought. Ongoing declines and lack of recovery of vulnerable and protected shark species are a cause for concern.

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Section: Methodsmentioning

confidence: 99%

Decline of coastal apex shark populations over the past half century

et al. 2018

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“…The state-specific function f c (�) is a second-order random walk (RW2) model as a continuous time process [18] on the log-scaled TFR F c,t . The function is flexible to incorporate the non-linear fertility transition given the reverse of fertility at very low level [19].…”

Section: Plos Onementioning

confidence: 99%

Probabilistic projection of the sex ratio at birth and missing female births by State and Union Territory in India

Chao

Guilmoto

et al. 2020

PLoS ONE

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The sex ratio at birth (SRB) in India has been reported to be imbalanced since the 1970s. Previous studies have shown there is a great variation in the SRB between geographic locations across India till 2016. Considering the enormous population and regional heterogeneity of India, producing probabilistic SRB projections at the state level is crucial for policy planning and population projection. In this paper, we implement a Bayesian hierarchical time series model to project the SRB across India by state. We generate SRB probabilistic projections from 2017 to 2030 for 29 States and Union Territories (UTs) in India, and present results for 21 States/UTs with data available from the Sample Registration System. Our analysis takes into account two state-specific factors that contribute to sex-selective abortion in India, resulting in sex imbalances at birth: the intensity of son preference and fertility squeeze. We project that the highest deficits in female births will occur in Uttar Pradesh, with a cumulative number of missing female births of 2.0 (95% credible interval [1.9; 2.2]) million from 2017 to 2030. The total female birth deficits during 2017-2030 for the whole of India is projected to be 6.8 [6.6; 7.0] million.

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“…Without giving any concrete details, Lindgren et al (2011) suggested that this SPDE can be used in connection with their Gaussian Markov random-field method. See also Simpson et al (2012) and Yue et al (2012). Cameletti et al (2013) modelled particulate matter concentration in space and time with a separable covariance structure and an SPDE-based spatial Gaussian Markov random field for the innovation term.…”

Section: A Continuous Space-time Model: the Advection-diffusion Stochmentioning

confidence: 99%

Stochastic Partial Differential Equation Based Modelling of Large Space–Time Data Sets

Sigrist

Künsch

Stahel

2014

Journal of the Royal Statistical Society Series B: Statistical Methodology

106

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Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advectiondiffusion partial differential equation provides a flexible model class for spatio-temporal processes which is computationally feasible also for large data sets. The Gaussian process defined through the stochastic partial differential equation has in general a nonseparable covariance structure. Furthermore, its parameters can be physically interpreted as explicitly modeling phenomena such as transport and diffusion that occur in many natural processes in diverse fields ranging from environmental sciences to ecology. In order to obtain computationally efficient statistical algorithms we use spectral methods to solve the stochastic partial differential equation. This has the advantage that approximation errors do not accumulate over time, and that in the spectral space the computational cost grows linearly with the dimension, the total computational costs of Bayesian or frequentist inference being dominated by the fast Fourier transform. The proposed model is applied to postprocessing of precipitation forecasts from a numerical weather prediction model for northern Switzerland. In contrast to the raw forecasts from the numerical model, the postprocessed forecasts are calibrated and quantify prediction uncertainty. Moreover, they outperform the raw forecasts, in the sense that they have a lower mean absolute error.

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Bayesian Adaptive Smoothing Splines Using Stochastic Differential Equations

Cited by 33 publications

References 49 publications

Decline of coastal apex shark populations over the past half century

Decline of coastal apex shark populations over the past half century

Probabilistic projection of the sex ratio at birth and missing female births by State and Union Territory in India

Stochastic Partial Differential Equation Based Modelling of Large Space–Time Data Sets

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