Gaussian processes:iterative sparse approximations

In recent years there has been an increased interest in applying non-parametric methods to real-world problems. Significant research has been devoted to Gaussian processes (GPs) due to their increased flexibility when compared with parametric models. These methods use Bayesian learning, which generally leads to analytically intractable posteriors. This thesis proposes a two-step solution to construct a probabilistic approximation to the posterior. In the first step we adapt the Bayesian online learning to GPs: the final approximation to the posterior is the result of propagating the first and second moments of intermediate posteriors obtained by combining a new example with the previous approximation. The propagation of em functional forms is solved by showing the existence of a parametrisation to posterior moments that uses combinations of the kernel function at the training points, transforming the Bayesian online learning of functions into a parametric formulation. The drawback is the prohibitive quadratic scaling of the number of parameters with the size of the data, making the method inapplicable to large datasets. The second step solves the problem of the exploding parameter size and makes GPs applicable to arbitrarily large datasets. The approximation is based on a measure of distance between two GPs, the KL-divergence between GPs. This second approximation is with a constrained GP in which only a small subset of the whole training dataset is used to represent the GP. This subset is called the em Basis Vector, or BV set and the resulting GP is a sparse approximation to the true posterior. As this sparsity is based on the KL-minimisation, it is probabilistic and independent of the way the posterior approximation from the first step is obtained. We combine the sparse approximation with an extension to the Bayesian online algorithm that allows multiple iterations for each input and thus approximating a batch solution. The resulting sparse learning algorithm is a generic one: for different problems we only change the likelihood. The algorithm is applied to a variety of problems and we examine its performance both on more classical regression and classification tasks and to the data-assimilation and a simple density estimation problems.

A performance assessment method for hospitals:the case of municipal hospitals in Angola

Over 60% of the recurrent budget of the Ministry of Health (MoH) in Angola is spent on the operations of the fixed health care facilities (health centres plus hospitals). However, to date, no study has been attempted to investigate how efficiently those resources are used to produce health services. Therefore the objectives of this study were to assess the technical efficiency of public municipal hospitals in Angola; assess changes in productivity over time with a view to analyzing changes in efficiency and technology; and demonstrate how the results can be used in the pursuit of the public health objective of promoting efficiency in the use of health resources. The analysis was based on a 3-year panel data from all the 28 public municipal hospitals in Angola. Data Envelopment Analysis (DEA), a non-parametric linear programming approach, was employed to assess the technical and scale efficiency and productivity change over time using Malmquist index.The results show that on average, productivity of municipal hospitals in Angola increased by 4.5% over the period 2000-2002; that growth was due to improvements in efficiency rather than innovation. © 2008 Springer Science+Business Media, LLC.

Technical efficiency:efficiency, change, technical progress and productivity growth in the national health systems of continental African countries

In May 2006, the Ministers of Health of all the countries on the African continent, at a special session of the African Union, undertook to institutionalise efficiency monitoring within their respective national health information management systems. The specific objectives of this study were: (i) to assess the technical efficiency of National Health Systems (NHSs) of African countries for measuring male and female life expectancies, and (ii) to assess changes in health productivity over time with a view to analysing changes in efficiency and changes in technology. The analysis was based on a five-year panel data (1999-2003) from all the 53 countries of continental Africa. Data Envelopment Analysis (DEA) - a non-parametric linear programming approach - was employed to assess the technical efficiency. Malmquist Total Factor Productivity (MTFP) was used to analyse efficiency and productivity change over time among the 53 countries' national health systems. The data consisted of two outputs (male and female life expectancies) and two inputs (per capital total health expenditure and adult literacy). The DEA revealed that 49 (92.5%) countries' NHSs were run inefficiently in 1999 and 2000; 50 (94.3%), 48 (90.6%) and 47 (88.7%) operated inefficiently in 2001, 2002, and 2003 respectively. All the 53 countries' national health systems registered improvements in total factor productivity attributable mainly to technical progress. Fifty-two countries did not experience any change in scale efficiency, while thirty (56.6%) countries' national health systems had a Pure Efficiency Change (PEFFCH) index of less than one, signifying that those countries' NHSs pure efficiency contributed negatively to productivity change. All the 53 countries' national health systems registered improvements in total factor productivity, attributable mainly to technical progress. Over half of the countries' national health systems had a pure efficiency index of less than one, signifying that those countries' NHSs pure efficiency contributed negatively to productivity change. African countries may need to critically evaluate the utility of institutionalising Malmquist TFP type of analyses to monitor changes in health systems economic efficiency and productivity over time. African national health systems, per capita total health expenditure, technical efficiency, scale efficiency, Malmquist indices of productivity change, DEA

Measurement efficiency and productivity in SAS/OR

This paper explores the use of the optimisation procedures in SAS/OR software with application to the measurement of efficiency and productivity of decision-making units (DMUs) using data envelopment analysis (DEA) techniques. DEA was originally introduced by Charnes et al. [J. Oper. Res. 2 (1978) 429] is a linear programming method for assessing the efficiency and productivity of DMUs. Over the last two decades, DEA has gained considerable attention as a managerial tool for measuring performance of organisations and it has widely been used for assessing the efficiency of public and private sectors such as banks, airlines, hospitals, universities and manufactures. As a result, new applications with more variables and more complicated models are being introduced. Further to successive development of DEA a non-parametric productivity measure, Malmquist index, has been introduced by Fare et al. [J. Prod. Anal. 3 (1992) 85]. Employing Malmquist index, productivity growth can be decomposed into technical change and efficiency change. On the other hand, the SAS is a powerful software and it is capable of running various optimisation problems such as linear programming with all types of constraints. To facilitate the use of DEA and Malmquist index by SAS users, a SAS/MALM code was implemented in the SAS programming language. The SAS macro developed in this paper selects the chosen variables from a SAS data file and constructs sets of linear-programming models based on the selected DEA. An example is given to illustrate how one could use the code to measure the efficiency and productivity of organisations.

The comparative impact of privatisation and regulation on productivity growth in the English and Welsh water and sewerage industry, 1985-99

After the 10 regional water authorities of England and Wales were privatized in November 1989, the successor WASCs (water and sewerage companies) faced a new regulatory regime that was designed to promote productivity growth while simultaneously improving drinking water and environmental quality. As legally mandated quality improvements necessitated a costly capital investment programme, the industry's economic regulator – the Office of Water Services – implemented a RPI + K pricing system, designed to compensate the WASCs for their capital investment programme while also encouraging faster rates of productivity growth. This paper considers the relative effects of privatization and regulation on productivity growth in the industry using both non-parametric and parametric methods to provide a crosscheck on the robustness of the results. While there is evidence that labour productivity improved after privatization, there is no evidence that privatization led to a growth in TFP (total factor productivity). However, there is some evidence of a small increase in the rate of TFP growth in the aftermath of a substantial tightening of the regulatory regime that took place in 1995. These results, therefore, are consistent with evidence from other research that privatization, in the absence of effective competition and/or regulation, is not necessarily associated with improved economic performance.

Is there a trade-off between quality and productivity? The case of diagnostic technologies in Portugal

The purpose of this paper is twofold: first, we compute quality-adjusted measures of productivity change for the three most important diagnostic technologies (i.e., the Computerised Tomography Scan, Electrocardiogram and Echocardiogram) in the major Portuguese hospitals. We use the Malmquist–Luenberger index, which allows to measure productivity growth while controlling for the quality of the production. Second, using non-parametric tests, we analyse whether the implementation of the Prospective Payment System may have had a positive impact on the movements of productivity over time. The results show that the PPS has helped hospitals to use these tools more efficiently and to improve their effectiveness.

Patterns of corporate governance and technical efficiency in Italian manufacturing

The purpose of this paper is to analyse the relationship between the corporate governance system and technical efficiency in Italian manufacturing. We use a non-parametric frontier technique (DEA) to derive technical efficiency measures for a sample of Italian firms taken from nine manufacturing industries. These measures are then related to the characteristics of the corporate governance system. Two of these characteristics turn out to have a positive impact on technical efficiency: the percentage of the company shares owned by the largest shareholder and the fact that a firm belongs to a pyramidal group. Interestingly, a trade-off emerges between these influences, in the sense that one is stronger in industries where the other is weaker. Copyright © 2007 John Wiley & Sons, Ltd.

Public capital and total factor productivity:new evidence from the Italian regions, 1970-98

This paper analyses the relationship between industrial total factor productivity and public capital across the 20 Italian administrative regions. It adds upon the existing literature in a number of ways: it analyses a longer period (1970-98); it allows for the role of human capital accumulation; it tests for the existence of a long-run relationship between total factor productivity and public capital (through previously suggested panel techniques) and for weak exogeneity of public capital; and it assesses the significance of public capital within a non-parametric set-up based on the Free Disposal Hull. The results confirm that public capital has a significant impact on the evolution of total factor productivity, particularly in the Southern regions. This impact is mainly ascribed to the core infrastructures (road and airports, harbours, railroads, water and electricity, telecommunications). Also, core infrastructures are weakly exogenous. © 2005 Regional Studies Association.

A cautionary note on methods of comparing programmatic efficiency between two or more groups of DMUs in data envelopment analysis

In some applications of data envelopment analysis (DEA) there may be doubt as to whether all the DMUs form a single group with a common efficiency distribution. The Mann-Whitney rank statistic has been used to evaluate if two groups of DMUs come from a common efficiency distribution under the assumption of them sharing a common frontier and to test if the two groups have a common frontier. These procedures have subsequently been extended using the Kruskal-Wallis rank statistic to consider more than two groups. This technical note identifies problems with the second of these applications of both the Mann-Whitney and Kruskal-Wallis rank statistics. It also considers possible alternative methods of testing if groups have a common frontier, and the difficulties of disaggregating managerial and programmatic efficiency within a non-parametric framework. © 2007 Springer Science+Business Media, LLC.

Programmatic efficiency comparisons between unequally sized groups of DMUs in DEA

Data envelopment analysis (DEA) is a popular non-parametric technique for determining the efficiency of a homogeneous set of decision-making units (DMUs). In many practical cases, there is some doubt if the all the DMUs form a single group with a common efficiency distribution. The Mann-Whitney rank statistic has been used in DEA both to test if two groups of DMUs come from a common efficiency distribution and also to test if the two groups have a common frontier, each of which are likely to have important but different policy implications for the management of the groups. In this paper it is demonstrated that where the Mann-Whitney rank statistic is used for the second of these it is likely to overestimate programmatic inefficiency, particularly of the smaller group. A new non-parametric statistic is proposed for the case of comparing the efficient frontiers of two groups, which overcomes the problems we identify in the use of the Mann-Whitney rank statistic for this purpose. © 2005 Operational Research Society Ltd. All rights reserved.

On the existence of visual technical patterns in the UK stock market

The aim in this paper is to replicate and extend the analysis of visual technical patterns by Lo et al. (2000) using data on the UK market. A non-parametric smoother is used to model a nonlinear trend in stock price series. Technical patterns, such as the 'head-and-shoulders' pattern, that are characterised by a sequence of turning points are identified in the smoothed data. Statistical tests are used to determine whether returns conditioned on the technical patterns are different from random returns and, in an extension to the analysis of Lo et al. (2000), whether they can outperform a market benchmark return. For the stocks in the FTSE 100 and FTSE 250 indices over the period 1986 to 2001, we find that technical patterns occur with different frequencies to each other and in different relativities to the frequencies found in the US market. Our extended statistical testing indicates that UK stock returns are less influenced by technical patterns than was the case for US stock returns.

Measurement of productivity index with dynamic DEA

Fare, Grosskopf, Norris and Zhang developed a non-parametric productivity index, Malmquist index, using data envelopment analysis (DEA). The Malmquist index is a measure of productivity progress (regress) and it can be decomposed to different components such as 'efficiency catch-up' and 'technology change'. However, Malmquist index and its components are based on two period of time which can capture only a part of the impact of investment in long-lived assets. The effects of lags in the investment process on the capital stock have been ignored in the current model of Malmquist index. This paper extends the recent dynamic DEA model introduced by Emrouznejad and Thanassoulis and Emrouznejad for dynamic Malmquist index. This paper shows that the dynamic productivity results for Organisation for Economic Cooperation and Development countries should reflect reality better than those based on conventional model.

Profitability of a sample of Portuguese bank branches and its decomposition into technical and allocative components

The efficiency literature, both using parametric and non-parametric methods, has been focusing mainly on cost efficiency analysis rather than on profit efficiency. In for-profit organisations, however, the measurement of profit efficiency and its decomposition into technical and allocative efficiency is particularly relevant. In this paper a newly developed method is used to measure profit efficiency and to identify the sources of any shortfall in profitability (technical and/or allocative inefficiency). The method is applied to a set of Portuguese bank branches first assuming long run and then a short run profit maximisation objective. In the long run most of the scope for profit improvement of bank branches is by becoming more allocatively efficient. In the short run most of profit gain can be realised through higher technical efficiency. © 2003 Elsevier B.V. All rights reserved.

Exchanging uncertainty: interoperable geostatistics?

Traditionally, geostatistical algorithms are contained within specialist GIS and spatial statistics software. Such packages are often expensive, with relatively complex user interfaces and steep learning curves, and cannot be easily integrated into more complex process chains. In contrast, Service Oriented Architectures (SOAs) promote interoperability and loose coupling within distributed systems, typically using XML (eXtensible Markup Language) and Web services. Web services provide a mechanism for a user to discover and consume a particular process, often as part of a larger process chain, with minimal knowledge of how it works. Wrapping current geostatistical algorithms with a Web service layer would thus increase their accessibility, but raises several complex issues. This paper discusses a solution to providing interoperable, automatic geostatistical processing through the use of Web services, developed in the INTAMAP project (INTeroperability and Automated MAPping). The project builds upon Open Geospatial Consortium standards for describing observations, typically used within sensor webs, and employs Geography Markup Language (GML) to describe the spatial aspect of the problem domain. Thus the interpolation service is extremely flexible, being able to support a range of observation types, and can cope with issues such as change of support and differing error characteristics of sensors (by utilising descriptions of the observation process provided by SensorML). XML is accepted as the de facto standard for describing Web services, due to its expressive capabilities which allow automatic discovery and consumption by ‘naive’ users. Any XML schema employed must therefore be capable of describing every aspect of a service and its processes. However, no schema currently exists that can define the complex uncertainties and modelling choices that are often present within geostatistical analysis. We show a solution to this problem, developing a family of XML schemata to enable the description of a full range of uncertainty types. These types will range from simple statistics, such as the kriging mean and variances, through to a range of probability distributions and non-parametric models, such as realisations from a conditional simulation. By employing these schemata within a Web Processing Service (WPS) we show a prototype moving towards a truly interoperable geostatistical software architecture.

A cost Malmquist productivity index

This paper develops a productivity index applicable when producers are cost minimisers and input prices are known. The index is inspired by the Malmquist index as extended to productivity measurement. The index developed here is defined in terms of input cost rather than input quantity distance functions. Hence, productivity change is decomposed into overall efficiency and cost technical change. Furthermore, overall efficiency change is decomposed into technical and allocative efficiency change and cost technical change into a part capturing shifts of input quantities and shifts of relative input prices. These decompositions provide a clearer picture of the root sources of productivity change. They are illustrated here in a sample of hospitals; results are computed using non-parametric mathematical programming. © 2003 Elsevier B.V. All rights reserved.