Life satisfaction is both a desirable 'end' for sustainable development, and a means to understand the priorities, and behaviour of people towards local ecosystems. Ecosystem-services research on life satisfaction has focused on cultural services in wealthy, Western contexts, although ecosystem services are essential for poor people's livelihoods in the Global South. We examined reported life satisfaction from a survey of over 2000 people in rural and urban settings of coastal Kenya and Mozambique. We coded respondents' open-ended reasons for their reported satisfaction, and used multiple correspondence analysis to explore the characteristics of people who mentioned different reasons. We tested associations between satisfaction and the meeting of basic needs and income, with binary logistic regression, accounting for site and gender. Life satisfaction was lower in Kenya, for men, and in the most urbanised site. Respondents explained high, and low, satisfaction in terms of social relationships, basic needs, money and employment. They rarely mentioned the ecosystem services and related livelihoods that underpin those, suggesting an instrumental relation to nature. Meeting basic needs, including economic security better predicted satisfaction than household income. Life satisfaction reflected material differences in people's lives but also different evaluative criteria and national cultures. For example, family reasons more commonly explained women's satisfaction, while money was more important for urban-dwelling men. We propose that the holistic perspective offered by life-satisfaction research can inform environmental management alongside more focused ecosystem-service research. For example, our results suggest that a) interventions should recognise immediate needs and social relationships, b) the role of ecosystem services for subjective wellbeing varies by local culture and individual identities and c) secure and fair access to ecosystem services may support life satisfaction better than high incomes that are insecure or ineq-uitably distributed.

We consider the problem of deciding on sampling strategy, in particular sampling design. We propose a risk measure, whose minimizing value guides the choice. The method makes use of a superpopulation model and takes into account uncertainty about its parameters through a prior distribution. The method is illustrated with a real dataset, yielding satisfactory results. As a baseline, we use the strategy that couples probability proportional-to-size sampling with the difference estimator, as it is known to be optimal when the superpopulation model is fully known. We show that, even under moderate misspecifications of the model, this strategy is not robust and can be outperformed by some alternatives.

Sampling is a core stage in every survey. A sampling design carefully elaborated may imply not only a more accurate estimation of the parameters of interest, but also a reduction in the required sample size in a study. In this thesis we consider two particular but connected subjects. On the one hand, the selection of samples with probabilities proportional to some prescribed values. The first two papers are devoted to this topic. On the other hand, the choice of sampling design to implement in a given survey, which is a topic to which the last two papers are devoted.

Probability proportional to size sampling designs, often referred to as πps designs, are of practical interest due to their potential efficiency. In the literature we can find many of these designs, all having different characteristics. In the first paper we describe and compare ten πps designs with respect to several desired properties. The results suggest that the so called order sampling methods, as well as those proposed by Sunter and Chromy may be considered as good options from a practitioner's point of view.

In the second paper we introduce an algorithm for approximating a target distribution by a mixture distribution. Being a mixture, most of its properties are easy to calculate. We illustrate the use of the algorithm with several examples, both univariate and multivariate. The results indicate that the algorithm succeeds in approximating the target distribution.

The strategy that couples πps designs with the generalized regression estimator is optimal under a given superpopulation model. However, this optimality assumes that the model is correct and some of its parameters are known, which are assumptions that are hardly satisfied in practice. In the third paper we introduce a method that allows for incorporating uncertainty about the model parameters into the choice of the sampling design and then quantifying this uncertainty with a risk measure. The method is illustrated with a real dataset. The results show that the method allowed us to correctly choose the sampling design. The risk measure -as well as other functions that are useful at the planning stage of a survey- is implemented in the package optimStrat developed for R. The fourth paper in this thesis describes the functions in this package.

The sampling strategy that couples probability proportional-to-size sampling with the GREG estimator has sometimes been called "optimal", as it minimizes the anticipated variance. This optimality, however, relies on the assumption that the finite population of interest can be seen as a realization of a superpopulation model that is known to the statistician. Making use of the same model, the strategy that couples model-based stratification with the GREG estimator is an alternative that, although theoretically less efficient, has shown to be sometimes more efficient than the so-called optimal from an empirical point of view. We compare the two strategies from both analytical and simulation standpoints and show that optimality is not robust towards misspecications of the model. In fact gross errors may be observed when a misspecified model is used.

A large number of probability proportional to size designs have been suggested in the literature. Practitioners will ask themselves if the choice of design matters and, if so, to what extent. We discuss what the desirable properties of a probability proportional to size designs are. We argue the main desirable property is reliability. Other desirable properties include simplicity and, in some contexts, if the sampling design admits sample coordination. We explore the numerical properties of ten probability proportional to size designs in a simulation study. Chromy’s and Sunter’s methods are strong contenders if there is no need of sample coordination. Sunter’s method does not render a strict probability proportional to size design as small units will be drawn with simple random sampling. Should one want to at least keep the possibility of future sample coordination open, order sampling, including sequential Poisson and Pareto sampling, is the best choice.

We consider the problem of deciding on sampling strategy, in particular sampling design. We propose a risk measure, whose minimizing value guides the choice. The method makes use of a superpopulation model and takes into account uncertainty about its parameters through a prior distribution. The method is illustrated with a real dataset, yielding satisfactory results. As a baseline, we use the strategy that couples probability proportional-to-size sampling with the difference estimator, as it is known to be optimal when the superpopulation model is fully known. We show that, even under moderate misspecifications of the model, this strategy is not robust and can be outperformed by some alternatives.

Nowadays, highly efficient algorithms for selecting samples from the most popular distributions are available. Nevertheless, the problem of sampling from any prescribed distribution is yet to be fully resolved, especially when sampling from multidimensional distributions. A large number of methods to sample from prescribed distributions -either exactly or approximately- are available (e.g. the inverse-transform method, the acceptance-rejection method, Gibbs sampling or Metropolis-Hastings sampling), but there is no "optimal" method for all applications. We introduce an algorithm that allows for approximating a density by a mixture of easy-to-sample distributions. The resulting approximation allows for easily obtaining the desired properties of the prescribed distribution under study, e.g. the mean, variance, cumulative distribution, marginal distributions, sample selection, etc. The only requirement is the density to be approximated. This flexibility makes the algorithm a good alternative compared to well known methods that need additional knowledge before implementation. Diagnostics for measuring convergence are also proposed. The algorithm is illustrated with several examples, both univariate and multivariate. Results show that, given the stopping criteria imposed by the user, the algorithm approximates the desired distribution satisfactorily.

At the planning stage of a survey, statisticians have to choose the sampling strategy to implement. If auxiliary information is available, the statistician might, for example, consider using sampling with probabilities proportional to size, or, stratified sampling. With this context in mind, optimStrat, an R package, has been developed. The package assists the choice through two superpopulation models. The first one, called working model, reflects the knowledge or beliefs the statistician has about the relation between the auxiliary variables and the variable of interest. This model, however, might be misspecified. This possibility is reflected on the second model, called true model. In this way, the package allows for determining which sampling strategy is more efficient if a given working model is used when in reality the population is generated by a different model. The package includes an interactive web app that allows users not familiar with R to perform the comparisons for five sampling strategies, namely, STSI--HT, STSI--pos, STSI-reg, πps--pos and πps--reg. Additional functions allow the user to simulate study variables, stratify a given population or calculate the variance of the GREG estimator, among others.