an insufficient puzzle

Posted in Books, Kids, Statistics with tags , , , on January 12, 2022 by xi'an

A rather peculiar and challenging question on X validated,  concerning the absolute impossibility of a conditional expectation, given a non-sufficient statistic, being still a statistic (i.e., being independent on the parameter θ). Inspired from the following except from Hogg and Craig. Namely, could there exist a specific function φ(·) such that E[φ(Y¹)|Y³] does not depend on the parameter θ? I could not find a satisfactory explanation right away (and the question remains unanswered!)

After posting this entry, I thought anew that cases when the unbiased estimator φ(Y¹) is not a bijective transform of Y¹ would work as a counter-example, since Y³=φ(Y¹) is not sufficient but E[φ(Y¹) |φ(Y¹) ]=φ(Y¹) is not involving θ… And this case does not exhibit a paradox in that the variance does not decrease any further.

vaccination in Cacao

Posted in Kids, pictures, Travel with tags , , , , , , on January 11, 2022 by xi'an

blind monty hall

Posted in R, Statistics with tags , , , , , , , , on January 10, 2022 by xi'an

As I was waiting for my boat on a French Guiana beach last week, I thought back about a recent riddle from The Riddler where an item does a random walk over a sequence of N integers. Behind doors. The player opens a door at the same rate as the item, door that closes immediately after. What is the fastest strategy to catch the item? With a small value of N, it seemed that repeating the same door twice and moving from 1 to N and backward was eventually uncovering the item.

Here is the cRude code I later wrote to check whether or not this was working:

  p=1+t%%N #starting item position
  h=v=s=m=1 #h=door, v=attempt number, s=direction, m=repeat number
    p=ifelse(p==1,2, #no choice
             ifelse(p==N,N-1, #no choice
                    ifelse(p==h-1,p-1, #avoid door
                           ifelse(p==h+1,p+1, #avoid door
                                  p+sample(c(-1,1),1))))) #random

and the outcome for N=100 was a maximum equal to 198. The optimal strategy leads to 196 as repeating the extreme doors is not useful.

ils nous emmerdent…

Posted in Kids, pictures, Travel on January 9, 2022 by xi'an

.While I agree with President Macron that unvaccinated people are putting a most unreasonable pressure on society and in particular on the health system, and while it was obvious from the start that the sanitary pass was primarily intended as a pressure on unvaccinated, I do not see much of a point in stating it in this unclassy way. Imposing vaccination as in some of the other EU countries like Austria and Italy would be much more rational (if acknowledgingly hard to impose). Especially since there already are mandatory vaccines in France, namely for Diphteria, Tetanus and Poliomyelitis.

what’s wrong with this picture [ans.: nothing]

Posted in Kids, pictures, Travel with tags , , , , , , , , , , on January 8, 2022 by xi'an

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