Conditional fiducial models

The fiducial is not unique in general, but we prove that in a restricted class of models it is uniquely determined by the sampling distribution of the data. It depends in particular not on the choice of a data generating model. The arguments lead to a generalization of the classical formula found by Fisher (1930). The restricted class includes cases with discrete distributions, the case of the shape parameter in the Gamma distribution, and also the case of the correlation coefficient in a bivariate Gaussian model. One of the examples can also be used in a pedagogical context to demonstrate possible difficulties with likelihood-, Bayesian-, and bootstrap-inference. Examples that demonstrate non-uniqueness are also presented. It is explained that they can be seen as cases with restrictions on the parameter space. Motivated by this the concept of a conditional fiducial model is introduced. This class of models includes the common case of iid samples from a one-parameter model investigated by Hannig (2013), the structural group models investigated by Fraser (1968), and also certain models discussed by Fisher (1973) in his final writing on the subject

On the proper treatment of improper distributions

The axiomatic foundation of probability theory presented by Kolmogorov has been the basis of modern theory for probability and statistics. In certain applications it is, however, necessary or convenient to allow improper (unbounded) distributions, which is often done without a theoretical foundation. The paper reviews a recent theory which includes improper distributions, and which is related to Renyi's theory of conditional probability spaces. It is in particular demonstrated how the theory leads to simple explanations of apparent paradoxes known from the Bayesian literature. Several examples from statistical practice with improper distributions are discussed in light of the given theoretical results, which also include a recent theory of convergence of proper distributions to improper ones.Comment: Journal of Statistical Planning and Inference, 201

Casimir experiments showing saturation effects

We address several different Casimir experiments where theory and experiment disagree. First out is the classical Casimir force measurement between two metal half spaces; here both in the form of the torsion pendulum experiment by Lamoreaux and in the form of the Casimir pressure measurement between a gold sphere and a gold plate as performed by Decca et al.; theory predicts a large negative thermal correction, absent in the high precision experiments. The third experiment is the measurement of the Casimir force between a metal plate and a laser irradiated semiconductor membrane as performed by Chen et al.; the change in force with laser intensity is larger than predicted by theory. The fourth experiment is the measurement of the Casimir force between an atom and a wall in the form of the measurement by Obrecht et al. of the change in oscillation frequency of a 87 Rb Bose-Einstein condensate trapped to a fused silica wall; the change is smaller than predicted by theory. We show that saturation effects can explain the discrepancies between theory and experiment observed in all these cases.Comment: 10 pages, 11 figure

Do firms wait to invest? : an empirical investigation

The paper tests a standard real options model of investment using a data set of listed Dutch manufacturing firms over the period of 1984-1997. The threshold value that triggers investment is based on the historical distribution of the profit process and the risk-adjusted discount rate of the firm. The system Generalized Method of Moments (GMM) estimates show that Dutch firms are on average concerned with the option values of investment opportunities. We explore the arguments why firms would be confronted with higher investment hurdles.

D-particle Dynamics and Bound States

We study the low energy effective theory describing the dynamics of D-particles. This corresponds to the quantum mechanical system obtained by dimensional reduction of $9+1$ dimensional supersymmetric Yang-Mills theory to $0+1$ dimensions and can be interpreted as the non relativistic limit of the Born-Infeld action. We study the system of two like-charged D-particles and find evidence for the existence of non-BPS states whose mass grows like $\lambda^{1/3}$ over the BPS mass. We give a string interpretation of this phenomenon in terms of a linear potential generated by strings stretching from the two D-particles. Some comments on the possible relations to black hole entropy and eleven dimensional supergravity are also given.Comment: 16 pages, Latex. References and footnote adde

Band-steaming reduces laborious hand-weeding in vegetables

Band-steaming is a new method that may reduce the need for hand-weeding in demanding row crops like carrot and drilled onion. Band-steaming only affects a soil volume equal to the intra-row area of the subsequent crop, and effectively kills the weed seeds in this soil volume. Side-effects on beneficial soil organisms are minimized as compared to current steaming technology, but still need to be assessed