Driven by the rising need for model efficiency to enable timely and accurate data analytics, stochastic modelers in the actuarial community have been seeking innovative alternatives to increase model reality, dynamics, capacity, speed, and precision. These challenges have motivated this paper to demonstrate free research software tools for case studies in financial stochastic modeling. Case stu...

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

To address the unknown nature of probability-sampling models, in this paper we use information theoretic concepts and the Cressie-Read (CR) family of information divergence measures to produce a flexible family of probability distributions, likelihood functions, estimators, and inference procedures. The usual case in statistical modeling is that the noisy indirect data are observed and known an...

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-speci c probability density functions which are used to generate sample points for the numerical quadrature. Probability dens...

We consider the problem of estimating hitting probabilities related to a class of interacting particle systems. These systems, in which two types of particles — ‘electrons’ and ‘holes’ — move on a graph, are simplified versions of models describing charge transport in disordered materials. The probability of interest is the probability that an electron reaches a certain region of the graph befo...

It is well-established that some aspects of perception and action can be understood as probabilistic inferences over underlying probability distributions. In some situations, it would be advantageous for the nervous system to sample interpretations from a probability distribution rather than commit to a particular interpretation. In this study, we asked whether visual percepts correspond to sam...

Two studies examined how sampling of base rate information and causal explanation of false positives facilitate intuitive probability judgments. Experiment 1a varied these two manipulations factorially. Each had an additive effect on reducing base rate neglect and increasing choice of the normatively correct solution. Experiment 1b showed that description of relevant distributional information ...

The Horvitz-Thompson estimator is a general estimator for a population total, which can be used for any probability sampling plan. This includes both sampling with and without replacement. • Let π i be the probability that the i th unit of the population is included in the sample (inclusion probability). • On each unit i, we measure a response y i , and typically seek to estimate: τ = N i=1 y i...

Ambiguity is often characterized with unknown probability distributions (for potential outcomes), which people avoid while making decisions. Existing literature shows that ambiguity aversion often persists even when these probability distributions are explicitly described to decision makers. We test the hypothesis that exposure to these probability distributions via sampling experience, rather ...

Case-control sampling is an extremely common design used to generate data to estimate effects of exposures or treatments on a binary outcome of interest when the proportion of cases (i.e., binary outcome equal to 1) in the population of interest is low. Case-control sampling represents a biased sample of a target population of interest by sampling a disproportional number of cases. Case-control...