Skip to main content

one bridge further

[This article was first published on R – Xi'an's Og, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

Jackie Wong, Jon Forster (Warwick) and Peter Smith have just published a paper in Statistics & Computing on bridge sampling bias and improvement by splitting.

“… known to be asymptotically unbiased, bridge sampling technique produces biased estimates in practical usage for small to moderate sample sizes (…) the estimator yields positive bias that worsens with increasing distance between the two distributions. The second type of bias arises when the approximation density is determined from the posterior samples using the method of moments, resulting in a systematic underestimation of the normalizing constant.”

Recall that bridge sampling is based on a double trick with two samples x and y from two (unnormalised) densities f and g that are interverted in a ratio

m \sum_{i=1}^n g(x_i)\omega(x_i) \Big/ n \sum_{i=1}^m f(y_i)\omega(y_i)

of unbiased estimators of the inverse normalising constants. Hence biased. The more the less similar these two densities are. Special cases for ω include importance sampling [unbiased] and reciprocal importance sampling. Since the optimal version of the bridge weight ω is the inverse of the mixture of f and g, it makes me wonder at the performance of using both samples top and bottom, since as an aggregated sample, they also come from the mixture, as in Owen & Zhou (2000) multiple importance sampler. However, a quick try with a positive Normal versus an Exponential with rate 2 does not show an improvement in using both samples top and bottom (even when using the perfectly normalised versions)

morc=(sum(f(y)/(nx*dnorm(y)+ny*dexp(y,2)))+
            sum(f(x)/(nx*dnorm(x)+ny*dexp(x,2))))/(
  sum(g(x)/(nx*dnorm(x)+ny*dexp(x,2)))+
         sum(g(y)/(nx*dnorm(y)+ny*dexp(y,2))))

at least in terms of bias… Surprisingly (!) the bias almost vanishes for very different samples sizes either in favour of f or in favour of g. This may be a form of genuine defensive sampling, who knows?! At the very least, this ensures a finite variance for all weights. (The splitting approach introduced in the paper is a natural solution to create independence between the first sample and the second density. This reminded me of our two parallel chains in AMIS.)

To leave a comment for the author, please follow the link and comment on their blog: R – Xi'an's Og.
R-bloggers.com offers daily e-mail updates about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.


from R-bloggers https://ift.tt/2YKFCbM
via IFTTT
Labels:

Comments

Post a Comment

Popular posts from this blog

Controlling legend appearance in ggplot2 with override.aes

[This article was first published on Very statisticious on Very statisticious , and kindly contributed to R-bloggers ]. (You can report issue about the content on this page here ) Want to share your content on R-bloggers? click here if you have a blog, or here if you don't. In ggplot2 , aesthetics and their scale_*() functions change both the plot appearance and the plot legend appearance simultaneously. The override.aes argument in guide_legend() allows the user to change only the legend appearance without affecting the rest of the plot. This is useful for making the legend more readable or for creating certain types of combined legends. In this post I’ll first introduce override.aes with a basic example and then go through three additional plotting scenarios to how other instances where override.aes comes in handy. Table of Contents R packages Introducing override.aes Adding a guides() layer Using the guide argument in scale_*() Changing multiple aesthetic par...
Post a Comment
Read more

Zooming in on maps with sf and ggplot2

(This article was first published on r-bloggers – WZB Data Science Blog , and kindly contributed to R-bloggers) When working with geo-spatial data in R, I usually use the sf package for manipulating spatial data as Simple Features objects and ggplot2 with geom_sf for visualizing these data. One thing that comes up regularly is “zooming in” on a certain region of interest, i.e. displaying a certain map detail. There are several ways to do so. Three common options are: selecting only certain areas of interest from the spatial dataset (e.g. only certain countries / continent(s) / etc.) cropping the geometries in the spatial dataset using sf_crop() restricting the display window via coord_sf() I will show the advantages and disadvantages of these options and especially focus on how to zoom in on a certain point of interest at a specific “zoom level”. We will see how to calculate the coordinates of the display window or “bounding box” around this zoom point. Loading t...
Post a Comment
Read more