Archive for snow
the sky [isn’t] the limit
Posted in Mountains, pictures, Running, Travel with tags Alpine meadows, Chamonix-Mont-Blanc, clouds, French Alps, glacier, Les Bossons, Les Houches, Mont Blanc, snow, winter running on March 21, 2024 by xi'an
snowballs in summer
Posted in Books, Statistics with tags arXiv, convergence, MCMC, nested sampling, posterior sampling, simulation, snow on September 13, 2023 by xi'an
A new arXival on nested sampling, Snowballing Nested Sampling by Johannes Buchner, just appeared. The idea behind this short note is to increase the number of “live” points at each iteration. (How?! Depending on how the different additions are dependent, the effective sample size will vary.) This exacerbates the tendency of the algorithm to concentrate on high density regions.
“Loosely speaking, each dead point from a run with K is split into two dead points from a run with K′ live points. The noise in the nested sampling estimate due to more dead points is also reduced, because the variance is inversely proportional to K.”
The following line is most puzzling (K being the number of live points and M the number of MCMC steps to simulate from the restricted prior):
“Based on this [argument], K → ∞ with fixed M achieves the properties of M → ∞ with fixed K.”
which connects with the ambiguity of running the MCMC move at each nested iteration a certain number M of steps, even though I always thought a single step was theoretically enough. In practice, this single step may further take forever if no trick is available for simulating from the constrained prior. And when K increases, so does the correlation unless iid sampling can be implemented, which does not sound realistic.
kuva Lapista⁻²³ [jatp]
Posted in Mountains, pictures, Running, Travel with tags -23⁰, Arctic Chill, cross-country skiing, Finland, jatp, Kittilä, Lapland, Levi, morning run, pine trees, snow, sunset on March 24, 2023 by xi'an
kuva Lapista³ [jatp]
Posted in Mountains, pictures, Running, Travel with tags Arctic Chill, cross-country skiing, Finland, jatp, Kittilä, Lapland, Levi, morning run, snow on March 17, 2023 by xi'an
snapshot of Les Diablerets³ [jatp]
Posted in Mountains, pictures, Running, Travel with tags downhill skiing, Les Diablerets, ski resorts, snow, Suisse Occidentale, Swiss, Swiss Alps, Valais, Villars, winter light on March 1, 2023 by xi'an
