Optimal scaling for the pseudo-marginal random walk Metropolis: insensitivity to the noise generating mechanism

We examine the optimal scaling and the efficiency of the pseudo-marginal random walk Metropolis algorithm using a recently-derived result on the limiting efficiency as the dimension, $d\rightarrow \infty$. We prove that the optimal scaling for a given target varies by less than $20\%$ across a wide range of distributions for the noise in the estimate of the target, and that any scaling that is within $20\%$ of the optimal one will be at least $70\%$ efficient. We demonstrate that this phenomenon occurs even outside the range of distributions for which we rigorously prove it. We then conduct a simulation study on an example with $d=10$ where importance sampling is used to estimate the target density; we also examine results available from an existing simulations study with $d=5$ and where a particle filter was used. Our key conclusions are found to hold in these examples also.Comment: New version: simulation study now on a real statistical example (confusing typos corrected

Chiral and stable isotope analysis of synthetic cathinones

In the past decade synthetic cathinones have appeared in drug markets worldwide. Chiral analysis can provide information on relative enantiomeric abundances of synthetic cathinones in their drug products, potentially giving a signature of these products and hence linking the products or excluding them from possible sources. Additionally, due to natural variations of relative stable isotopic abundances of elements, stable isotope analysis of synthetic cathinone drug products provides the stable isotopic signature of the products and hence also has potential to provide additional information for the purpose of drug intelligence. Therefore, both molecular (chirality) and physicochemical (relative stable isotopic abundances) properties are important for forensic chemists to investigate. Chiral and isotope ratio mass spectrometric analysis are becoming increasingly important to forensic chemists and therefore this review will focus on an overview of these techniques applied to the synthetic cathinones

Tracing the Initiation of the Tribeč Mountain Exhumation by Laser-Probe ⁴⁰Ar/³⁹Ar Dating of Seismogenic Pseudotachylytes (Western Carpathians, Slovakia)

The seismogenic pseudotachylytes from the Tribeč Mountains (Western Carpathians, Slovakia) were dated by means of the laser microprobe 40Ar/39Ar method. The Tribeč Mountain crystalline basement was buried to 5–7.5-km depths, where it experienced approximately >110°C and <210°C thermal conditions. The dated pseudotachylytes have spot ages between 58 ± 1 and 46 ± 1 Ma with a weighted mean age of 49.7 ± 1.3 Ma, indicating that seismic activity caused their origin, the propagation of subvertical basement marginal faults, and/or the inception of basement unroofing processes in the southern part of the Central Carpathian Paleogene Basin. The extensional tectonics were responsible for the exhumation of basement highs and the opening of the intramontane depressions on the northwest margin of the Pannonian Basin