Articles by xi'an

a null hypothesis with a 99% probability to be true…

March 27, 2018 | xi'an

When checking the Python t distribution random generator, np.random.standard_t(), I came upon this manual page, which actually does not explain how the random generator works but spends instead the whole page to recall Gosset’t test, illustrating its use on an energy intake of 11 women, but ending ...
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spacings on a torus

March 21, 2018 | xi'an

While in Brussels last week I noticed an interesting question on X validated that I considered in the train back home and then more over the weekend. This is a question about spacings, namely how long on average does it take to cover an interval of length L when drawing ... [Read more...]

uniform on the sphere [or not]

March 7, 2018 | xi'an

While looking at X validated questions, I came upon this comment that simulating a uniform distribution on a d-dimensional unit sphere does not proceed from generating angles at random on (0,2π) and computing spherical coordinates… Which I must confess would have been my initial suggestion! This is obvious, nonetheless, when computing ...
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StanCon in Helsinki [29-31 Aug 2018]

March 7, 2018 | xi'an

As emailed to me by Aki Vehtari, the next StanCon will take place this summer in the wonderful city of Helsinki, at the end of August. On Aalto University Töölö Campus precisely. The list of speakers and tutorial teachers is available on the webpage. (The only “negative point” is ...
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a one-chance meeting [puzzle]

March 5, 2018 | xi'an

This afternoon, I took a quick look at the current Riddler puzzle, which sums up as, given three points A, B, C, arbitrarily moving on a plane with a one-shot view of their respective locations, find a moving rule to bring the three together at the same point at the ...
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weakly informative reparameterisations

February 13, 2018 | xi'an

Our paper, weakly informative reparameterisations of location-scale mixtures, with Kaniav Kamary and Kate Lee, got accepted by JCGS! Great news, which comes in perfect timing for Kaniav as she is currently applying for positions. The paper proposes a unidimensional mixture Bayesian modelling based on the first and second moment constraints, ...
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València summer school

January 31, 2018 | xi'an

In another continuation of the summer of Bayesian conferences in Europe, the Universidat de Valencià is organising a summer school on Bayesian statistics, from 16 July till 20 July, 2018. Which thus comes right after our summer school on computational statistics at Warwick. With a basic course on Bayesian learning (2 days). And a ...
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Le Monde puzzle [#1037]

January 23, 2018 | xi'an

A purely geometric Le Monde mathematical puzzle this (or two independent ones, rather): Find whether or not there are inscribed and circumscribed circles to a convex polygon with 2018 sides of lengths ranging 1,2,…,2018. In the first (or rather second) case, the circle of radius R that is tangential to the polygon ...
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Le Monde puzzle [#1036]

January 3, 2018 | xi'an

An arithmetic Le Monde mathematical puzzle to conclude 2017: Find (a¹,…,a¹³), a permutation of (1,…,13) such that a¹/a²+a³=a²+a³/a³+a⁴+a⁵=b¹
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correlation for maximal coupling

January 2, 2018 | xi'an

An interesting (if vaguely formulated) question on X validated: given two Gaussian variates that are maximally coupled, what is the correlation between these variates? The answer depends on the parameters of both Gaussian, with a correlation of one when both Gaussians are identical. Answering the question by simulation (as I ...
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cyclic riddle [not in NYC!]

December 28, 2017 | xi'an

In the riddle of this week on fivethirtyeight, the question is to find the average number of rounds when playing the following game: P=6 players sitting in a circle each have B=3 coins and with probability 3⁻¹ they give one coin to their right or left side neighbour, or dump the ...
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random wake

December 26, 2017 | xi'an

Just too often on X validated, one sees questions displaying a complete ignorance of the basics that makes one purposelessly wonder what is the point of trying to implement advanced methods when missing the necessary background. And just as often, I reacted to the question by wondering out loud about ... [Read more...]

Le Monde puzzle [#1033]

December 18, 2017 | xi'an

A simple Le Monde mathematical puzzle after two geometric ones I did not consider: Bob gets a 2×3 card with three integer entries on the first row and two integer entries on the second row such that (i) entry (1,1) is 1, (ii) summing up subsets of adjacent entries produces all integers from 1 ...
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sliced Wasserstein estimation of mixtures

November 27, 2017 | xi'an

A paper by Soheil Kolouri and co-authors was arXived last week about using Wasserstein distance for inference on multivariate Gaussian mixtures. The basic concept is that the parameter is estimated by minimising the p-Wasserstein distance to the empirical distribution, smoothed by a Normal kernel. As the general Wasserstein distance is ...
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Le Monde puzzle [#1029]

November 21, 2017 | xi'an

A convoluted counting Le Monde mathematical puzzle: A film theatre has a waiting room and several projection rooms. With four films on display. A first set of 600 spectators enters the waiting room and vote for their favourite film. The most popular film is projected to the spectators who voted for ...
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normal variates in Metropolis step

November 13, 2017 | xi'an

A definitely puzzled participant on X validated, confusing the Normal variate or variable used in the random walk Metropolis-Hastings step with its Normal density… It took some cumulated efforts to point out the distinction. Especially as the originator of the question had a rather strong a priori about his or ...
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bridgesampling [R package]

November 8, 2017 | xi'an

Quentin F. Gronau, Henrik Singmann and Eric-Jan Wagenmakers have arXived a detailed documentation about their bridgesampling R package. (No wonder that researchers from Amsterdam favour bridge sampling!) [The package relates to a [52 pages] tutorial on bridge sampling by Gronau et al. that I will hopefully comment soon.] The bridge sampling ...
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Le Monde [last] puzzle [#1026]

November 1, 2017 | xi'an

The last and final Le Monde puzzle is a bit of a disappointment, to wit: A 4×4 table is filled with positive and different integers. A 3×3 table is then deduced by adding four adjacent [i.e. sharing a common corner] entries of the original table. Similarly with a 2×2 table, summing up ...
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splitting a field by annealing

October 17, 2017 | xi'an

A recent riddle [from The Riddle] that I pondered about during a [long!] drive to Luxembourg last weekend was about splitting a square field into three lots of identical surface for a minimal length of separating wire… While this led me to conclude that the best solution was a T ...
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