Approximate Bayesian Computation with composite score functions

Both Approximate Bayesian Computation (ABC) and composite likelihood methods are useful for Bayesian and frequentist inference, respectively, when the likelihood function is intractable. We propose to use composite likelihood score functions as summary statistics in ABC in order to obtain accurate approximations to the posterior distribution. This is motivated by the use of the score function of the full likelihood, and extended to general unbiased estimating functions in complex models. Moreover, we show that if the composite score is suitably standardised, the resulting ABC procedure is invariant to reparameterisations and automatically adjusts the curvature of the composite likelihood, and of the corresponding posterior distribution. The method is illustrated through examples with simulated data, and an application to modelling of spatial extreme rainfall data is discussed.Comment: Statistics and Computing (final version

A note on marginal posterior simulation via higher-order tail area approximations

We explore the use of higher-order tail area approximations for Bayesian simulation. These approximations give rise to an alternative simulation scheme to MCMC for Bayesian computation of marginal posterior distributions for a scalar parameter of interest, in the presence of nuisance parameters. Its advantage over MCMC methods is that samples are drawn independently with lower computational time and the implementation requires only standard maximum likelihood routines. The method is illustrated by a genetic linkage model, a normal regression with censored data and a logistic regression model

Robust approximate Bayesian inference

We discuss an approach for deriving robust posterior distributions from $M$-estimating functions using Approximate Bayesian Computation (ABC) methods. In particular, we use $M$-estimating functions to construct suitable summary statistics in ABC algorithms. The theoretical properties of the robust posterior distributions are discussed. Special attention is given to the application of the method to linear mixed models. Simulation results and an application to a clinical study demonstrate the usefulness of the method. An R implementation is also provided in the robustBLME package.Comment: This is a revised and personal manuscript version of the article that has been accepted for publication by Journal of Statistical Planning and Inferenc

The Social Life of Sardex and Liberex: Kin or Acquaintances? A Comparison Between Two Mutual Credit Circuits in Italy

We offer the first informed comparison of two regional mutual credit systems – Sardex and Liberex – aimed at sustaining the local economy. Building on previous research on Sardex, we develop an equivalent qualitative research investigating both organizers and members of the local circuit in Emilia Romagna. Within a theoretical framework that considers money as a social institution, socially and politically constructed, we first give an overview of the plurality of existing money pointing out a heated debate over the nature of money itself. Then, we move to evaluate whether the same monetary architecture – adopted by the two mutual credit systems – concretely comes with a similar social life. We confirm how social life of money is strictly intertwined with its monetary architecture by design, and discover how deeply it is also rooted in the institutional and relational contexts where it concretely operates. Money differs not only by nature and design, but also by context

From complementary currency to institution: a micro-macro study of the Sardex mutual credit system

The remarkable growth of Sardex as a local currency throughout the island of Sardinia over the past 5 years motivated an in-depth look at its starting assumptions, design and operational principles, and local context. The paper looks at Sardex as a social innovation start-up, a complementary currency, a mutual credit system, and a socio-economic «circuit». The analysis relies on interviews of circuit members and its founders. The main findings are that trust was and continues to be fundamentally important for the creation and operation of the mutual credit system, and that Sardex encompasses both economic and social value(s) in a process of re-embedding of the economy. Sardex configured itself as a crucial mediator of economic exchanges and became a valuable actor acting as an institution at the regional level. These properties make it an ideal space for experimentation in socio-economic innovation that can be characterized as a «laboratory for multi-level governance»

In Search for (the Lost) Smartness in the Evolution of the Smart Cities: Consumers or Citizens?

The paper develops a systematic reflection about the future of smart cites at the time of Covid-19, starting from an original periodization about the evolution of the concept of smartness, declined through a four fold analytical tool (technological, human-social, institutional and spatial-environmental dimensions). Focusing on the role of smart citizens and on the “right to the city” concept, we list and critically appraise the emerging trends made visible by the worldwide sanitary crisis

Self-funded social impact investment: an interdisciplinary analysis of the Sardex mutual credit system

Sardex is an electronic B2B mutual credit system that has been operating on the island of Sardinia since 2009 as a complementary currency. In contrast to other funding mechanisms, it allows private funding driving social and environmental impact to be endogenously generated within a given geographically limited socio-economic context, rather than injected from exogenous sources. By drawing on different strands of monetary theory, sociology and anthropology, we argue that mutual credit is central to a form of social finance and social impact investment that we identify with sustainable development, i.e. stable and constructive integration of market activity with democratic institutions and socio-cultural values and structures. The empirical basis of the paper consists of approximately thirty semi-structured in-depth interviews of Sardex circuit members and founders over 4 years. We conclude that Sardex as a collective social enterprise is best understood through an interdisciplinary perspective that demonstrates its sustainability through the different levels of its workings and its strengths as a hybrid multilayered system

Objective Bayesian higher-order asymptotics in models with nuisance parameters

We discuss higher-order approximations to the marginal posterior distribution for a scalar parameter of interest in the presence of nuisance parameters. These higher-order approximations are obtained using a suitable matching prior. The proposed procedure has several advantages since it does not require the elicitation on the nuisance parameter, neither numerical integration or MCMC simulation, and it enables us to perform accurate Bayesian inference even for very small sample sizes. Numerical illustrations are given for models of practical interest, such as linear non-normal models and logistic regression. We also illustrate how the proposed accurate approximation can routinely be applied in practice using results from likelihood asymptotics and the R package bundle ho

Improved Laplace approximation for marginal likelihoods

Statistical applications often involve the calculation of intractable multidimensional integrals. The Laplace formula is widely used to approximate such integrals. However, in high-dimensional or small sample size problems, the shape of the integrand function may be far from that of the Gaussian density, and thus the standard Laplace approximation can be inaccurate. We propose an improved Laplace approximation that reduces the asymptotic error of the standard Laplace formula by one order of magnitude, thus leading to third-order accuracy. We also show, by means of practical examples of various complexity, that the proposed method is extremely accurate, even in high dimensions, improving over the standard Laplace formula. Such examples also demonstrate that the accuracy of the proposed method is comparable with that of other existing methods, which are computationally more demanding. An R implementation of the improved Laplace approximation is also provided through the R package iLaplace available on CRAN.Comment: 24 page

From an idea to a scalable working model: merging economic benefits with social values in Sardex

The remarkable growth of Sardex as a local currency throughout the island of Sardinia over the past 4 years motivated an in-depth look at its starting assumptions, its design and operational principles, and its socio- economic context. The paper looks at Sardex as a social innovation start-up, as a medium of exchange and unit of account, as an online and offline mutual credit system, and as a closed economic community or ‘circuit’. The analysis relies on interviews of circuit members conducted in the Summer of 2014 and benefits from the reflexive point of view of one of its founders. The main findings are that trust was and continues to be fundamentally important for the creation and operation of the local Sardex currency and of the circuit, and that Sardex mediates both economic and social value(s). These properties make it an ideal space for experimentation in socio-economic innovation that can be characterized as a ‘laboratory of institutional learning.