Band 26, Heft 2

Evaluation of teaching performance of faculty members, on the basis of students’ feedback, is routinely performed by almost all tertiary education institutions. Objective assessment of faculty members requires a comprehensive index of teaching performance. A composite indicator is proposed to assess teaching performance of faculty members. It is based on the combination of several items evaluated by students such as punctuality, communication ability and subject coverage. Robustness of the indicator is assessed applying uncertainty analysis. An application to a data set from an Indian institution is presented. It is shown that the proposed index can be used to rank faculty members from the least to the worst performer according to students’ feedback.

In this paper, we derive a Markov chain Monte Carlo (MCMC) algorithm supported by a neural network. In particular, we use the neural network to substitute derivative calculations made during a Metropolis adjusted Langevin algorithm (MALA) step with inexpensive neural network evaluations. Using a complex, high-dimensional blood coagulation model and a set of measurements, we define a likelihood function on which we evaluate the new MCMC algorithm. The blood coagulation model is a dynamic model, where derivative calculations are expensive and hence limit the efficiency of derivative-based MCMC algorithms. The MALA adaptation greatly reduces the time per iteration, while only slightly affecting the sample quality. We also test the new algorithm on a 2-dimensional example with a non-convex shape, a case where the MALA algorithm has a clear advantage over other state of the art MCMC algorithms. To assess the impact of the new algorithm, we compare the results to previously generated results of the MALA and the random walk Metropolis Hastings (RWMH).

In the following article, we consider the non-linear filtering problem in continuous time and in particular the solution to Zakai’s equation or the normalizing constant. We develop a methodology to produce finite variance, almost surely unbiased estimators of the solution to Zakai’s equation. That is, given access to only a first-order discretization of solution to the Zakai equation, we present a method which can remove this discretization bias. The approach, under assumptions, is proved to have finite variance and is numerically compared to using a particular multilevel Monte Carlo method.

The multilevel Monte Carlo (MLMC) method developed by M. B. Giles [Multilevel Monte Carlo path simulation, Oper. Res. 56 2008, 3, 607–617] has a natural application to the evaluation of nested expectations 𝔼[g(𝔼[f(X,Y)|X])]{\mathbb{E}[g(\mathbb{E}[f(X,Y)|X])]}, where f,g{f,g} are functions and (X,Y){(X,Y)} a couple of independent random variables. Apart from the pricing of American-type derivatives, such computations arise in a large variety of risk valuations (VaR or CVaR of a portfolio, CVA), and in the assessment of margin costs for centrally cleared portfolios. In this work, we focus on the computation of initial margin. We analyze the properties of corresponding MLMC estimators, for which we provide results of asymptotic optimality; at the technical level, we have to deal with limited regularity of the outer function g (which might fail to be everywhere differentiable). Parallel to this, we investigate upper and lower bounds for nested expectations as above, in the spirit of primal-dual algorithms for stochastic control problems.

This paper is devoted to random-bit simulation of probability densities, supported on [0,1]{[0,1]}. The term “random-bit” means that the source of randomness for simulation is a sequence of symmetrical Bernoulli trials. In contrast to the pioneer paper [D. E. Knuth and A. C. Yao, The complexity of nonuniform random number generation, Algorithms and Complexity, Academic Press, New York 1976, 357–428], the proposed method demands the knowledge of the probability density under simulation, and not the values of the corresponding distribution function. The method is based on the so-called binary decomposition of the density and comes down to simulation of a special discrete distribution to get several principal bits of output, while further bits of output are produced by “flipping a coin”. The complexity of the method is studied and several examples are presented.