## 2005-05-30

### binomial uncertainties

Blanton asked for error bars on yesterday's plot, so I calculated the uncertainties for binomial estimation, by taking two derivatives of the log likelihood for the "success" probability p given a sample of N trials in which there are M successes. (I used a flat prior on p.)

As expected (from the first derivative) I get that the maximum likelihood estimate of p is M/N, and (from the second derivative) I get that the (linearized) uncertainty on this is sqrt(pq/N), where q=1−p.

The clustocentric result of yesterday appears marginally significant.

#### 1 comment:

1. We work like a horse.
We eat like a pig.
We like to play chicken.
You can get someone's goat.
We can be as slippery as a snake.
We get dog tired.
We can be as quiet as a mouse.
We can be as quick as a cat.
Some of us are as strong as an ox.
People try to buffalo others.
Some are as ugly as a toad.
We can be as gentle as a lamb.
Sometimes we are as happy as a lark.
Some of us drink like a fish.
We can be as proud as a peacock.
A few of us are as hairy as a gorilla.
You can get a frog in your throat.
We can be a lone wolf.
But I'm having a whale of a time!

You have a riveting web log
and undoubtedly must have
atypical & quiescent potential
May I suggest that you do
Designer/Architect as well

restrict anyone's opportunities
for ascertaining uninterrupted
existence for their quintessence.

There is a time for everything,
a season for every activity
under heaven. A time to be
born and a time to die. A
time to plant and a time to
harvest. A time to kill and
a time to heal. A time to
tear down and a time to
rebuild. A time to cry and
a time to laugh. A time to
grieve and a time to dance.
A time to scatter stones
and a time to gather stones.
A time to embrace and a
time to turn away. A time to
search and a time to lose. A
time to keep and a time to
throw away. A time to tear
and a time to mend. A time
to be quiet and a time to
speak up. A time to love
and a time to hate. A time
for war and a time for peace.

Best wishes for continued ascendancy,
Howdy
Editor

P.S. One thing of which I am sure is
that the common culture of my youth
is gone for good. It was hollowed out
by the rise of ethnic "identity politics,"
then splintered beyond hope of repair
by the emergence of the web-based
technologies that so maximized and
facilitated cultural choice as to make
the broad-based offerings of the old
mass media look bland and unchallenging
by comparison."

'Thought & Humor'
Cyber-Humor & Cyber-Thought
http://ilovehowdy.blogspot.com/
Harvard Humor Club
http://groups.yahoo.com/group/Harvard_Humor_Club/