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.

Do smart grids offer a new incentive for SME carbon reduction?

Collectively small and medium sized enterprises (SMEs) are significant energy users although many are unregulated by existing policies due to their low carbon emissions. Carbon reduction is often not a priority but smart grids may create a new opportunity. A smart grid will give electricity suppliers a picture of real-time energy flows and the opportunity for consumers to receive financial incentives for engaging in demand side management. As well as creating incentives for local carbon reduction, engaging SMEs with smart grids has potential for contributing to wider grid decarbonisation. Modelling of buildings, business activities and technology solutions is needed to identify opportunities for carbon reduction. The diversity of the SME sector complicates strategy development. SMEs are active in almost every business area and occupy the full range of property types. This paper reviews previous modelling work, exposing valuable data on floor space and energy consumption associated with different business activities. Limitations are seen with the age of this data and an inability to distinguish SME energy use. By modelling SME energy use, electrical loads are identified which could be shifted on demand, in a smart network. Initial analysis of consumption, not constrained by existing policies, identifies heating and cooling in retail and commercial offices as having potential for demand response. Hot water in hotel and catering and retail sectors may also be significant because of the energy storage potential. Areas to consider for energy efficiency schemes are also indicated.

J-measure based hybrid pruning for complexity reduction in classification rules

Prism is a modular classification rule generation method based on the ‘separate and conquer’ approach that is alternative to the rule induction approach using decision trees also known as ‘divide and conquer’. Prism often achieves a similar level of classification accuracy compared with decision trees, but tends to produce a more compact noise tolerant set of classification rules. As with other classification rule generation methods, a principle problem arising with Prism is that of overfitting due to over-specialised rules. In addition, over-specialised rules increase the associated computational complexity. These problems can be solved by pruning methods. For the Prism method, two pruning algorithms have been introduced recently for reducing overfitting of classification rules - J-pruning and Jmax-pruning. Both algorithms are based on the J-measure, an information theoretic means for quantifying the theoretical information content of a rule. Jmax-pruning attempts to exploit the J-measure to its full potential because J-pruning does not actually achieve this and may even lead to underfitting. A series of experiments have proved that Jmax-pruning may outperform J-pruning in reducing overfitting. However, Jmax-pruning is computationally relatively expensive and may also lead to underfitting. This paper reviews the Prism method and the two existing pruning algorithms above. It also proposes a novel pruning algorithm called Jmid-pruning. The latter is based on the J-measure and it reduces overfitting to a similar level as the other two algorithms but is better in avoiding underfitting and unnecessary computational effort. The authors conduct an experimental study on the performance of the Jmid-pruning algorithm in terms of classification accuracy and computational efficiency. The algorithm is also evaluated comparatively with the J-pruning and Jmax-pruning algorithms.

Temperature-dependent reduction pathways of complexes fac-[Re(CO)3(N-R-imidazole)(1,10-phenanthroline)]+ (R = H, CH3)

Peculiar reduction pathways of the complexes fac-[Re(imH)(CO)3(phen)]+ and fac-[Re(imCH3)(CO)3(phen)]+ (imH = imidazole, imCH3 = N-methylimidazole and phen = 1,10-phenanthroline) have been unravelled by performing combined cyclic voltammetric and in situ IR spectroelectrochemical experiments. In the temperature range of 293–233 K, the initial reduction of the phen ligand in [Re(imH)(CO)3(phen)]+ results in irreversible conversion of the imidazole ligand to 3-imidazolate by a rapid phen•−→ imH intramolecular electron transfer coupled with N H bond cleavage. This process is followed by second phen-localized 1e− reduction producing [ReI(3-im−)(CO)3(phen•−)]−, similar to the analogous 2,2'-bipyridine complex. In contrast to the bpy analogue, the stability of the phen•−-containing complexes is significantly affected by lowering the temperature. At 233 K, a secondary reaction occurs in both [Re(3-im−)(CO)3(phen•−)]− and [Re(imCH3)(CO)3(phen•−)]. The resulting products exhibit v(CO) wavenumbers indistinguishable from those of the parent phen•− complexes; however, their oxidation occurs at a considerably more positive electrode potential. It is proposed that these species are produced by a new C C bond formation between the C(2) site of 3-im− or imCH3 and the C(2) site of the phen•−ligand.

Investigating the value dairy farmers place on a reduction of lameness in their herds using a willingness to pay approach

A survey was conducted to elicit dairy farmers’ willingness to pay (WTP) to reduce the prevalence of lameness in their herds. A choice experiment questionnaire was administered using face-to-face interviews of 163 farmers in England and Wales. Whole herd lameness assessments by trained researchers recorded a mean lameness prevalence of nearly 24% which was substantially higher than that estimated by farmers. Farmers’ responses to a series of attitudinal questions showed that they strongly agreed that cows can suffer a lot of pain from lameness and believed that they could reduce lameness in their herds. Farmers’ mean WTP to avoid lameness amounted to UK£411 per lame cow but with considerable variation across the sample. Median WTP of UK£249 per lame cow was considered a better measure of central tendency for the sample. In addition, the survey found that farmers had a substantial WTP to avoid the inconvenience associated with lameness control (a median value of UK£97 per lame cow) but that they were generally prepared to incur greater inconvenience if it reduced lameness. The study findings suggest that farmers need a better understanding of the scale and costs of lameness in their herds and the benefits of control. To encourage action, farmers need to be convinced that lameness control measures perceived as inconvenient will be cost effective.

Solvent-Dependent Formation of Os(0) Complexes by Electrochemical Reduction of [Os(CO)(2,2′-bipyridine)(L)Cl2]; L = Cl−,PrCN

Cyclic voltammetry and ultraviolet−visible/infrared (UV−vis/IR) spectroelectrochemistry were used to study the cathodic electrochemical behavior of the osmium complexes mer-[OsIII(CO) (bpy)Cl3] (bpy = 2,2′-bipyridine) and trans(Cl)-[OsII(CO) (PrCN)(bpy)Cl2] at variable temperature in different solvents (tetrahydrofuran (THF), butyronitrile (PrCN), acetonitrile (MeCN)) and electrolytes (Bu4NPF6, Bu4NCl). The precursors can be reduced to mer-[OsII(CO) (bpy•−)Cl3]2− and trans(Cl)-[OsII(CO)(PrCN) (bpy•−)Cl2]−, respectively, which react rapidly at room temperature, losing the chloride ligands and forming Os(0) species. mer-[OsIII(CO) (bpy)Cl3] is reduced in THF to give ultimately an Os−Os-bonded polymer, probably [Os0(CO) (THF)-(bpy)]n, whereas in PrCN the well-soluble, probably mononuclear [Os0(CO) (PrCN)(bpy)], species is formed. The same products were observed for the 2 electron reduction of trans(Cl)-[OsII(CO)(PrCN) (bpy)Cl2] in both solvents. In MeCN, similar to THF, the[Os0(CO) (MeCN)(bpy)]n polymer is produced. It is noteworthy that the bpy ligand in mononuclear [Os0(CO) (PrCN)(bpy)] is reduced to the corresponding radical anion at a significantly less negative potential than it is in polymeric [Os0(CO) (THF)(bpy)]n: ΔE1/2 = 0.67 V. Major differences also exist in the IR spectra of the Os(0) species: the polymer shows a broad ν(CO) band at much smaller wavenumbers compared to the soluble Os(0) monomer that exhibits a characteristic ν(Pr-CN) band below 2200 cm−1 in addition to the intense and narrow ν(CO) absorption band. For the first time, in this work the M0-bpy(M = Ru, Os) mono- and dicarbonyl species soluble in PrCN have been formulated as a mononuclear complex. Density functional theory (DFT) and time-dependent-DFT calculations confirm the Os(0) oxidation state and suggest that [Os0(CO)(PrCN)(bpy)] is a square planar moiety. The reversible bpy-based reduction of [Os0(CO) (PrCN)(bpy)] triggers catalytic reduction of CO2 to CO and HCOO−.

An analysis of UK policies for domestic energy reduction using an agent based tool

This paper introduces a new agent-based model, which incorporates the actions of individual homeowners in a long-term domestic stock model, and details how it was applied in energy policy analysis. The results indicate that current policies are likely to fall significantly short of the 80% target and suggest that current subsidy levels need re-examining. In the model, current subsidy levels appear to offer too much support to some technologies, which in turn leads to the suppression of other technologies that have a greater energy saving potential. The model can be used by policy makers to develop further scenarios to find alternative, more effective, sets of policy measures. The model is currently limited to the owner-occupied stock in England, although it can be expanded, subject to the availability of data.