Application of Sequential Quasi-Monte Carlo to Autonomous Positioning

Sequential Monte Carlo algorithms (also known as particle filters) are popular methods to approximate filtering (and related) distributions of state-space models. However, they converge at the slow $1/\sqrt{N}$ rate, which may be an issue in real-time data-intensive scenarios. We give a brief outline of SQMC (Sequential Quasi-Monte Carlo), a variant of SMC based on low-discrepancy point sets proposed by Gerber and Chopin (2015), which converges at a faster rate, and we illustrate the greater performance of SQMC on autonomous positioning problems.Comment: 5 pages, 4 figure

Negative association, ordering and convergence of resampling methods

We study convergence and convergence rates for resampling schemes. Our first main result is a general consistency theorem based on the notion of negative association, which is applied to establish the almost-sure weak convergence of measures output from Kitagawa's (1996) stratified resampling method. Carpenter et al's (1999) systematic resampling method is similar in structure but can fail to converge depending on the order of the input samples. We introduce a new resampling algorithm based on a stochastic rounding technique of Srinivasan (2001), which shares some attractive properties of systematic resampling, but which exhibits negative association and therefore converges irrespective of the order of the input samples. We confirm a conjecture made by Kitagawa (1996) that ordering input samples by their states in $\mathbb{R}$ yields a faster rate of convergence; we establish that when particles are ordered using the Hilbert curve in $\mathbb{R}^d$, the variance of the resampling error is ${\scriptscriptstyle\mathcal{O}}(N^{-(1+1/d)})$ under mild conditions, where $N$ is the number of particles. We use these results to establish asymptotic properties of particle algorithms based on resampling schemes that differ from multinomial resampling.Comment: 54 pages, including 30 pages of supplementary materials (a typo in Algorithm 1 has been corrected

Measuring biodiversity: An axiomatic evaluation of measures based on genetic data

Biodiversity measurement is necessary to evaluate conservation alternatives and understand how to maximize biodiversity returns on conservation budgets. In the economics literature, most studies focus on species level diversity. Existing measures based on species' pairwise genetic differences do not perform optimally. This paper develops two new biodiversity measures within the same genetic framework. An axiomatic diagnosis for this class of measures is proposed and four biodiversity measures are then compared. Though the axiomatic comparison points towards a single 'best' measure, it also indicates that the choice of measure should be dependent on the conservation problem at hand.Biodiversitätsmessung ist notwendig, um alternative Naturschutzstrategien zu bewerten und zu verstehen, auf welche Weise der Beitrag der Biodiversität zum Naturschutz maximiert werden kann. In der Literatur stellen die meisten Berechnungen auf die Ebene der Artendiverstität ab, erbringen aber keine optimalen Ergebnisse. Diese Studie entwickelt zwei neue Biodiversitätsmaße innerhalb des gleichen genetischen Rahmens. Sie schlägt eine axiomatische Charakterisierung für diese Gruppe von Maßen vor und vergleicht dann vier Biodiversitätsmaße. Auch wenn der axiomatische Vergleich auf eine einzige 'beste' Maßeinheit hinweist, deutet er auch darauf hin, dass die Wahl des Maßes von der gegebenen Problematik abhängen sollte

Bioenergy and rural development in developing countries : A review of existing studies

Four broad types of studies on rural development and bioenergy technologies are identified. Within these four types, this discussion paper presents a number of existing studies which are most relevant in the context of developing a research focus on the role, feasibility and issues associated with bioenergy, and in particular biofuels, as engine for rural development in developing countries. The results and recommendations of the referenced studies, reflecting the global trends of the current literature, highlight the importance of bioenergy technologies in the evelopment process of poor rural communities. The surge of biofuels and in particular of their feedstocks on the international agricultural markets has recently commended a lot of attention. However, whilst biofuels hold a huge economic potential as internationally traded commodities, the various issues and challenges facing biofuel production systems could indicate that in the context of developing economies, they are better suited for the domestic energy markets. In any case, the analysis necessary to formulate policy recommendations on how, where and when to implement which bioenergy technology calls for a differentiated – per region and/or technology – and integrated – within and alongside other rural production systems – approach. In this context, this review of existing studies exposes some unanswered questions and research gaps

Measuring biodiversity : an axiomatic evaluation of measures based on genetic data

Biodiversity measurement is necessary to evaluate conservation alternatives and understand how to maximize biodiversity returns on conservation budgets. In the economics literature, most studies focus on species level diversity. Existing measures based on species' pairwise genetic differences do not perform optimally. This paper develops two new biodiversity measures within the same genetic framework. An axiomatic diagnosis for this class of measures is proposed and four biodiversity measures are then compared. Though the axiomatic comparison points towards a single "best" measure, it also indicates that the choice of measure should be dependent on the conservation problem at hand

Determinants of participation in child’s education and alternative activities in Pakistan

Using data from Pakistan, this study analyzed the effect of various individual, household, and community level characteristics on the probability that children engage in different activities. According to the existing trend of their prevalence, we considered five child’s activities, namely: secular schooling; religious education; child labor; a combination of child labor and secular schooling; and inactivity (including leisure). Data was collected through field surveys conducted in over 40 villages in four Pakistani provinces: Balochistan, Khyber Paktunkhwa, Punjab, and Sind. A total of 963 households were interviewed on the activities of 2,496 children. Multinomial Probit model was used for the analyses. Results indicated that parental perception had significant relationship to the probability of engagement in secular school attendance, religious education, and child labor. In addition, we investigated the relationships between participation in the different child activities with location (rural/urban) and children’s gender. We detected a lower probability of attending secular school and a higher probability of engaging in child labor among female children in rural areas. We also found that even parents who openly expressed appreciation of the importance of secular schooling were more likely to send male children to school than female children.Child productivity, Child’s activities, Parental perception, Gender, Community/Rural/Urban Development, Labor and Human Capital, Teaching/Communication/Extension/Profession,

Convergence of sequential quasi-Monte Carlo smoothing algorithms

International audienc

Higher-order stochastic integration through cubic stratification

We propose two novel unbiased estimators of the integral $\int_{[0,1]^{s}}f(u) du$ for a function $f$, which depend on a smoothness parameter $r\in\mathbb{N}$. The first estimator integrates exactly the polynomials of degrees $p<r$ and achieves the optimal error $n^{-1/2-r/s}$ (where $n$ is the number of evaluations of $f$) when $f$ is $r$ times continuously differentiable. The second estimator is computationally cheaper but it is restricted to functions that vanish on the boundary of $[0,1]^s$. The construction of the two estimators relies on a combination of cubic stratification and control ariates based on numerical derivatives. We provide numerical evidence that they show good performance even for moderate values of $n$