A comparative review of dimension reduction methods in approximate Bayesian computation

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vectors of summary statistics, rather than full data sets, a central question is how to derive low-dimensional summary statistics from the observed data with minimal loss of information. In this article we provide a comprehensive review and comparison of the performance of the principal methods of dimension reduction proposed in the ABC literature. The methods are split into three nonmutually exclusive classes consisting of best subset selection methods, projection techniques and regularization. In addition, we introduce two new methods of dimension reduction. The first is a best subset selection method based on Akaike and Bayesian information criteria, and the second uses ridge regression as a regularization procedure. We illustrate the performance of these dimension reduction techniques through the analysis of three challenging models and data sets.

Atmosphere drives recent interannual variability of the Atlantic meridional overturning circulation at 26.5°N

The RAPID-MOCHA array has observed the Atlantic Meridional overturning circulation (AMOC) at 26.5°N since 2004. During 2009/2010, there was a transient 30% weakening of the AMOC driven by anomalies in geostrophic and Ekman transports. Here, we use simulations based on the Met Office Forecast Ocean Assimilation Model (FOAM) to diagnose the relative importance of atmospheric forcings and internal ocean dynamics in driving the anomalous geostrophic circulation of 2009/10. Data assimilating experiments with FOAM accurately reproduce the mean strength and depth of the AMOC at 26.5°N. In addition, agreement between simulated and observed stream functions in the deep ocean is improved when we calculate the AMOC using a method that approximates the RAPID observations. The main features of the geostrophic circulation anomaly are captured by an ensemble of simulations without data-assimilation. These model results suggest that the atmosphere played a dominant role in driving recent interannual variability of the AMOC.

An experimental test of response consistency in contingent valuation

We compare hypothetical and observed (experimental) willingness to pay (WTP) for a gradual improvement in the environmental performance of a marketed good (an office table). First, following usual practices in marketing research, subjects’ stated WTP for the improvement is obtained. Second, the same subjects participate in a real reward experiment designed to replicate the scenario valued in the hypothetical question. Our results show that, independently of the degree of the improvement, there are no significant median differences between stated and experimental data. However, subjects reporting extreme values of WTP (low or high) exhibit a more moderate behavior in the experiment.

A multithickness sea ice model accounting for sliding friction

A multithickness sea ice model explicitly accounting for the ridging and sliding friction contributions to sea ice stress is developed. Both ridging and sliding contributions depend on the deformation type through functions adopted from the Ukita and Moritz kinematic model of floe interaction. In contrast to most previous work, the ice strength of a uniform ice sheet of constant ice thickness is taken to be proportional to the ice thickness raised to the 3/2 power, as is revealed in discrete element simulations by Hopkins. The new multithickness sea ice model for sea ice stress has been implemented into the Los Alamos “CICE” sea ice model code and is shown to improve agreement between model predictions and observed spatial distribution of sea ice thickness in the Arctic.

The Holocene temperature conundrum

A recent temperature reconstruction of global annual temperature shows Early Holocene warmth followed by a cooling trend through the Middle to Late Holocene [Marcott SA, et al., 2013, Science 339(6124):1198–1201]. This global cooling is puzzling because it is opposite from the expected and simulated global warming trend due to the retreating ice sheets and rising atmospheric greenhouse gases. Our critical reexamination of this contradiction between the reconstructed cooling and the simulated warming points to potentially significant biases in both the seasonality of the proxy reconstruction and the climate sensitivity of current climate models.

Automated identification of neural correlates of continuous variables

Background: The electroencephalogram (EEG) may be described by a large number of different feature types and automated feature selection methods are needed in order to reliably identify features which correlate with continuous independent variables. New method: A method is presented for the automated identification of features that differentiate two or more groups inneurologicaldatasets basedupona spectraldecompositionofthe feature set. Furthermore, the method is able to identify features that relate to continuous independent variables. Results: The proposed method is first evaluated on synthetic EEG datasets and observed to reliably identify the correct features. The method is then applied to EEG recorded during a music listening task and is observed to automatically identify neural correlates of music tempo changes similar to neural correlates identified in a previous study. Finally,the method is applied to identify neural correlates of music-induced affective states. The identified neural correlates reside primarily over the frontal cortex and are consistent with widely reported neural correlates of emotions. Comparison with existing methods: The proposed method is compared to the state-of-the-art methods of canonical correlation analysis and common spatial patterns, in order to identify features differentiating synthetic event-related potentials of different amplitudes and is observed to exhibit greater performance as the number of unique groups in the dataset increases. Conclusions: The proposed method is able to identify neural correlates of continuous variables in EEG datasets and is shown to outperform canonical correlation analysis and common spatial patterns.

Simulation of long-term thermal characteristics of three Estonian lakes

A one-dimensional surface energy-balance lake model, coupled to a thermodynamic model of lake ice, is used to simulate variations in the temperature of and evaporation from three Estonian lakes: Karujärv, Viljandi and Kirjaku. The model is driven by daily climate data, derived by cubic-spline interpolation from monthly mean data, and was run for periods of 8 years (Kirjaku) up to 30 years (Viljandi). Simulated surface water temperature is in good agreement with observations: mean differences between simulated and observed temperatures are from −0.8°C to +0.1°C. The simulated duration of snow and ice cover is comparable with observed. However, the model generally underpredicts ice thickness and overpredicts snow depth. Sensitivity analyses suggest that the model results are robust across a wide range (0.1–2.0 m−1) of lake extinction coefficient: surface temperature differs by less than 0.5°C between extreme values of the extinction coefficient. The model results are more sensitive to snow and ice albedos. However, changing the snow (0.2–0.9) and ice (0.15–0.55) albedos within realistic ranges does not improve the simulations of snow depth and ice thickness. The underestimation of ice thickness is correlated with the overestimation of snow cover, since a thick snow layer insulates the ice and limits ice formation. The overestimation of snow cover results from the assumption that all the simulated winter precipitation occurs as snow, a direct consequence of using daily climate data derived by interpolation from mean monthly data.

abctools: an R package for tuning approximate Bayesian computation analyses

Approximate Bayesian computation (ABC) is a popular family of algorithms which perform approximate parameter inference when numerical evaluation of the likelihood function is not possible but data can be simulated from the model. They return a sample of parameter values which produce simulations close to the observed dataset. A standard approach is to reduce the simulated and observed datasets to vectors of summary statistics and accept when the difference between these is below a specified threshold. ABC can also be adapted to perform model choice. In this article, we present a new software package for R, abctools which provides methods for tuning ABC algorithms. This includes recent dimension reduction algorithms to tune the choice of summary statistics, and coverage methods to tune the choice of threshold. We provide several illustrations of these routines on applications taken from the ABC literature.

A regionally informed abundance index for supporting integrative analyses across butterfly monitoring schemes

1. The rapid expansion of systematic monitoring schemes necessitates robust methods to reliably assess species' status and trends. Insect monitoring poses a challenge where there are strong seasonal patterns, requiring repeated counts to reliably assess abundance. Butterfly monitoring schemes (BMSs) operate in an increasing number of countries with broadly the same methodology, yet they differ in their observation frequency and in the methods used to compute annual abundance indices. 2. Using simulated and observed data, we performed an extensive comparison of two approaches used to derive abundance indices from count data collected via BMS, under a range of sampling frequencies. Linear interpolation is most commonly used to estimate abundance indices from seasonal count series. A second method, hereafter the regional generalized additive model (GAM), fits a GAM to repeated counts within sites across a climatic region. For the two methods, we estimated bias in abundance indices and the statistical power for detecting trends, given different proportions of missing counts. We also compared the accuracy of trend estimates using systematically degraded observed counts of the Gatekeeper Pyronia tithonus (Linnaeus 1767). 3. The regional GAM method generally outperforms the linear interpolation method. When the proportion of missing counts increased beyond 50%, indices derived via the linear interpolation method showed substantially higher estimation error as well as clear biases, in comparison to the regional GAM method. The regional GAM method also showed higher power to detect trends when the proportion of missing counts was substantial. 4. Synthesis and applications. Monitoring offers invaluable data to support conservation policy and management, but requires robust analysis approaches and guidance for new and expanding schemes. Based on our findings, we recommend the regional generalized additive model approach when conducting integrative analyses across schemes, or when analysing scheme data with reduced sampling efforts. This method enables existing schemes to be expanded or new schemes to be developed with reduced within-year sampling frequency, as well as affording options to adapt protocols to more efficiently assess species status and trends across large geographical scales.

A solar storm observed from the Sun to Venus using the STEREO, Venus Express, and MESSENGER spacecraft

The suite of SECCHI optical imaging instruments on the STEREO-A spacecraft is used to track a solar storm, consisting of several coronal mass ejections (CMEs) and other coronal loops, as it propagates from the Sun into the heliosphere during May 2007. The 3-D propagation path of the largest interplanetary CME (ICME) is determined from the observations made by the SECCHI Heliospheric Imager (HI) on STEREO-A (HI-1/2A). Two parts of the CME are tracked through the SECCHI images, a bright loop and a V-shaped feature located at the rear of the event. We show that these two structures could be the result of line-of-sight integration of the light scattered by electrons located on a single flux rope. In addition to being imaged by HI, the CME is observed simultaneously by the plasma and magnetic field experiments on the Venus Express and MESSENGER spacecraft. The imaged loop and V-shaped structure bound, as expected, the flux rope observed in situ. The SECCHI images reveal that the leading loop-like structure propagated faster than the V-shaped structure, and a decrease in in situ CME speed occurred during the passage of the flux rope.We interpret this as the result of the continuous radial expansion of the flux rope as it progressed outward through the interplanetary medium. An expansion speed in the radial direction of ~30 km s-1 is obtained directly from the SECCHI-HI images and is in agreement with the difference in speed of the two structures observed in situ. This paper shows that the flux rope location can be determined from white light images, which could have important space weather applications.

Observed and simulated precipitation responses in wet and dry regions 1850–2100

Global warming is expected to enhance fluxes of fresh water between the surface and atmosphere, causing wet regions to become wetter and dry regions drier, with serious implications for water resource management. Defining the wet and dry regions as the upper 30% and lower 70% of the precipitation totals across the tropics (30° S–30° N) each month we combine observations and climate model simulations to understand changes in the wet and dry regions over the period 1850–2100. Observed decreases in precipitation over dry tropical land (1950–2010) are also simulated by coupled atmosphere–ocean climate models (−0.3%/decade) with trends projected to continue into the 21st century. Discrepancies between observations and simulations over wet land regions since 1950 exist, relating to decadal fluctuations in El Niño southern oscillation, the timing of which is not represented by the coupled simulations. When atmosphere-only simulations are instead driven by observed sea surface temperature they are able to adequately represent this variability over land. Global distributions of precipitation trends are dominated by spatial changes in atmospheric circulation. However, the tendency for already wet regions to become wetter (precipitation increases with warming by 3% K−1 over wet tropical oceans) and the driest regions drier (precipitation decreases of −2% K−1 over dry tropical land regions) emerges over the 21st century in response to the substantial surface warming.

Turbulent structure and scaling of the inertial subrange in a stratocumulus-topped boundary layer observed by a Doppler lidar

The turbulent structure of a stratocumulus-topped marine boundary layer over a 2-day period is observed with a Doppler lidar at Mace Head in Ireland. Using profiles of vertical velocity statistics, the bulk of the mixing is identified as cloud driven. This is supported by the pertinent feature of negative vertical velocity skewness in the sub-cloud layer which extends, on occasion, almost to the surface. Both coupled and decoupled turbulence characteristics are observed. The length and timescales related to the cloud-driven mixing are investigated and shown to provide additional information about the structure and the source of the mixing inside the boundary layer. They are also shown to place constraints on the length of the sampling periods used to derive products, such as the turbulent dissipation rate, from lidar measurements. For this, the maximum wavelengths that belong to the inertial subrange are studied through spectral analysis of the vertical velocity. The maximum wavelength of the inertial subrange in the cloud-driven layer scales relatively well with the corresponding layer depth during pronounced decoupled structure identified from the vertical velocity skewness. However, on many occasions, combining the analysis of the inertial subrange and vertical velocity statistics suggests higher decoupling height than expected from the skewness profiles. Our results show that investigation of the length scales related to the inertial subrange significantly complements the analysis of the vertical velocity statistics and enables a more confident interpretation of complex boundary layer structures using measurements from a Doppler lidar.