Posts Tagged ‘ books ’

Bernoulli, Montmort and Waldegrave

April 14, 2015
By
Bernoulli, Montmort and Waldegrave

In the last issue of Statistical Science, David Belhouse [author of De Moivre’s biography]  and Nicolas Fillion published an accounting of a discussion between Pierre Rémond de Montmort, Nicolaus Bernoulli—”the” Bernoulli associated with the St. Petersburg paradox—, and Francis Waldegrave, about the card game of Le Her (or Hère, for wretch). Here is the abridged […]

Read more »

failures and uses of Jaynes’ principle of transformation groups

April 13, 2015
By
failures and uses of Jaynes’ principle of transformation groups

This paper by Alon Drory was arXived last week when I was at Columbia. It reassesses Jaynes’ resolution of Bertrand’s paradox, which finds three different probabilities for a given geometric event depending on the underlying σ-algebra (or definition of randomness!). Both Poincaré and Jaynes argued against Bertrand that there was only one acceptable solution under […]

Read more »

a vignette on Metropolis

April 12, 2015
By
a vignette on Metropolis

Over the past week, I wrote a short introduction to the Metropolis-Hastings algorithm, mostly in the style of our Introduction to Monte Carlo with R book, that is, with very little theory and worked-out illustrations on simple examples. (And partly over the Atlantic on my flight to New York and Columbia.) This vignette is intended […]

Read more »

an email exchange about integral representations

April 7, 2015
By
an email exchange about integral representations

I had an interesting email exchange [or rather exchange of emails] with a (German) reader of Introducing Monte Carlo Methods with R in the past days, as he had difficulties with the validation of the accept-reject algorithm via the integral in that it took me several iterations [as shown in the above] to realise the […]

Read more »

scalable Bayesian inference for the inverse temperature of a hidden Potts model

April 6, 2015
By
scalable Bayesian inference for the inverse temperature of a hidden Potts model

Matt Moores, Tony Pettitt, and Kerrie Mengersen arXived a paper yesterday comparing different computational approaches to the processing of hidden Potts models and of the intractable normalising constant in the Potts model. This is a very interesting paper, first because it provides a comprehensive survey of the main methods used in handling this annoying normalising […]

Read more »

Le Monde puzzle [#905]

March 31, 2015
By
Le Monde puzzle [#905]

A recursive programming  Le Monde mathematical puzzle: Given n tokens with 10≤n≤25, Alice and Bob play the following game: the first player draws an integer1≤m≤6 at random. This player can then take 1≤r≤min(2m,n) tokens. The next player is then free to take 1≤s≤min(2r,n-r) tokens. The player taking the last tokens is the winner. There is […]

Read more »

intuition beyond a Beta property

March 29, 2015
By
intuition beyond a Beta property

A self-study question on X validated exposed an interesting property of the Beta distribution: If x is B(n,m) and y is B(n+½,m) then √xy is B(2n,2m) While this can presumably be established by a mere change of variables, I could not carry the derivation till the end and used instead the moment generating function E[(XY)s/2] […]

Read more »

Le Monde puzzle [#904.5]

March 25, 2015
By
Le Monde puzzle [#904.5]

About this #904 arithmetics Le Monde mathematical puzzle: Find all plural integers, namely positive integers such that (a) none of their digits is zero and (b) removing their leftmost digit produces a dividing plural integer (with the convention that one digit integers are all plural). a slight modification in the R code allows for a […]

Read more »

The synoptic problem and statistics [book review]

March 19, 2015
By
The synoptic problem and statistics [book review]

A book that came to me for review in CHANCE and that came completely unannounced is Andris Abakuks’ The Synoptic Problem and Statistics.  “Unannounced” in that I had not heard so far of the synoptic problem. This problem is one of ordering and connecting the gospels in the New Testament, more precisely the “synoptic” gospels […]

Read more »

amazing Gibbs sampler

February 18, 2015
By
amazing Gibbs sampler

When playing with Peter Rossi’s bayesm R package during a visit of Jean-Michel Marin to Paris, last week, we came up with the above Gibbs outcome. The setting is a Gaussian mixture model with three components in dimension 5 and the prior distributions are standard conjugate. In this case, with 500 observations and 5000 Gibbs […]

Read more »


Subscribe

Email:

  Subscribe