As once in a while reappears the argument that wearing a bike helmet increases one’s chances of a bike accident. In the current case, it is to argue against a French regulation proposal that helmets should be compulsory for all cyclists. Without getting now into the pros and cons of compulsory helmet laws (enforced in Argentina, Australia, and New Zealand, as well as some provinces of Canada), I see little worth in the study cited by Le Monde towards this argument. As the data is poor and poorly analysed. First, there is a significant fraction of cycling accidents when the presence of an helmet is unknown. Second, the fraction of cyclists wearing helmets is based on a yearly survey involving 500 persons in a few major French cities. The conclusion that there are three times more accidents among cyclists wearing helmets than among cyclists not wearing helmets is thus not particularly reliable. Rather than the highly debatable arguments that (a) seeing a cyclist with an helmet would reduce the caution of car or bus drivers, (b) wearing an helmet would reduce the risk aversion of a cyclist, (c) sport-cyclists are mostly wearing helmets but their bikes are not appropriate for cities (!), I would not eliminate [as the authors do] the basic argument that helmeted cyclists are on average traveling longer distances. With a probability of an accident that necessarily increases with the distance traveled. While people renting on-the-go bikes are usually biking short distances and almost never wear helmets. (For the record, I mostly wear a [bright orange] helmet but sometimes do not when going to the nearby bakery or swimming pool… Each time I had a fall, crash or accident with a car, I was wearing an helmet and I once hit my head or rather the helmet on the ground, with no consequence I am aware of!)
Archive for Australia
don’t wear your helmet, you could have a bike accident!
Posted in Kids, Running, Statistics, Travel with tags Argentina, Australia, bicycle, Canada, cycling regulation, France, helmet, New Zealand, rental bike, Senate, survey, Vélib on January 18, 2022 by xi'anlikelihood-free and summary-free?
Posted in Books, Mountains, pictures, Statistics, Travel with tags ABC, arXiv, Australia, Cramèr-von Mises distance, curse of dimensionality, energy, Gaussian mixture, indirect inference, information, kernel density estimator, likelihood-free methods, mean discrepancy, summary statistics, Wasserstein distance on March 30, 2021 by xi'anMy friends and coauthors Chris Drovandi and David Frazier have recently arXived a paper entitled A comparison of likelihood-free methods with and without summary statistics. In which they indeed compare these two perspectives on approximate Bayesian methods like ABC and Bayesian synthetic likelihoods.
“A criticism of summary statistic based approaches is that their choice is often ad hoc and there will generally be an inherent loss of information.”
In ABC methods, the recourse to a summary statistic is often advocated as a “necessary evil” against the greater evil of the curse of dimension, paradoxically providing a faster convergence of the ABC approximation (Fearnhead & Liu, 2018). The authors propose a somewhat generic selection of summary statistics based on [my undergrad mentors!] Gouriéroux’s and Monfort’s indirect inference, using a mixture of Gaussians as their auxiliary model. Summary-free solutions, as in our Wasserstein papers, rely on distances between distributions, hence are functional distances, that can be seen as dimension-free as well (or criticised as infinite dimensional). Chris and David consider energy distances (which sound very much like standard distances, except for averaging over all permutations), maximum mean discrepancy as in Gretton et al. (2012), Cramèr-von Mises distances, and Kullback-Leibler divergences estimated via one-nearest-neighbour formulas, for a univariate sample. I am not aware of any degree of theoretical exploration of these functional approaches towards the precise speed of convergence of the ABC approximation…
“We found that at least one of the full data approaches was competitive with or outperforms ABC with summary statistics across all examples.”
The main part of the paper, besides a survey of the existing solutions, is to compare the performances of these over a few chosen (univariate) examples, with the exact posterior as the golden standard. In the g & k model, the Pima Indian benchmark of ABC studies!, Cramèr does somewhat better. While it does much worse in an M/G/1 example (where Wasserstein does better, and similarly for a stereological extremes example of Bortot et al., 2007). An ordering inversed again for a toad movement model I had not seen before. While the usual provision applies, namely that this is a simulation study on unidimensional data and a small number of parameters, the design of the four comparison experiments is very careful, eliminating versions that are either too costly or too divergence, although this could be potentially criticised for being unrealistic (i.e., when the true posterior is unknown). The computing time is roughly the same across methods, which essentially remove the call to kernel based approximations of the likelihood. Another point of interest is that the distance methods are significantly impacted by transforms on the data, which should not be so for intrinsic distances! Demonstrating the distances are not intrinsic…