In the study of natural and artificial complex systems, responses that are not completely determined by considered decision variables commonly modelled probabilistically, resulting in response distributions varying across space. We consider cases where spatial variation these does only concern their mean and/or variance but also other features including for instance shape or uni-modality versus...

Belief updating in Bayes nets, a well known computationally hard problem, has recently been approximated by several deterministic algorithms, and by various randomized approximation algorithlns. Deterministic algorithms usually provide probability bounds, but have an exponential runtime. Some randomized schemes haw~, a polynomial runtime, but provide only probability estimates. We present rando...

The effectiveness and accuracy of detection using environmental DNA (eDNA) is dependent on understanding the influence laboratory methods such as DNA extraction and PCR strategies have on detection probability. Ideally choice of sampling and extraction method will maximize eDNA yield and detection probability. Determining the survey effort required to reach a satisfactory detection probability ...

Assessing the accuracy of land cover maps is often prohibitively expensive because of the difficulty of collecting a statistically valid probability sample from the classified map. Even when post-classification sampling is undertaken, cost and accessibility constraints may result in imprecise estimates of map accuracy. If the map is constructed via supervised classification, then the training s...

I would like to congratulate Professor Graham Kalton for his significant and inspiring article entitled as "Probability vs. Nonprobability Sampling: From the Birth of Survey Sampling Present Day". The provides an elegant overview history survey sampling, covering purposive approaches that dominated sampling field in early days but from 1940s, at least official statistics, were gradually replace...

Let me first thank Dr. Kalton for his amazing historical review of the development survey sampling from its origin, contrasting purposive sampling, until now, where some elements in terms web or big data seem to supersede well-elaborated theory statistics. Shall message be that we do not need any courses at universities anymore, official statistics should turn modelling using with unknown gener...

In a distribution ray tracer, the crucial part of the direct lighting calculation is the sampling strategy for shadow ray testing. Monte Carlo integration with importance sampling is used to carry out this calculation. Importance sampling involves the design of integrand-specic probability density functions which are used to generate sample points for the numerical quadrature. Probability densi...

We consider the problem of random sampling for band-limited functions. When can a band-limited function f be recovered from randomly chosen samples f(xj), j ∈ N? We estimate the probability that a sampling inequality of the form A‖f‖ 2 ≤ ∑ j∈N |f(xj)| ≤ B‖f‖2 hold uniformly all functions f ∈ L(R) with supp f̂ ⊆ [−1/2, 1/2] or some subset of band-limited functions. In contrast to discrete models,...