Calculating Probability
Moose Gimmick
Listing 2 uses the CPAN Moose module, which saves me from having to code the Distrib
constructor in Perl. However, the code instead needs to use has
(line 3) to declare and initialize the class attributes. This is just a neat gimmick in the present case; for more attributes, however, the code would be much leaner than manually creating classes.
The set()
method expects the name of a hypothesis (e.g., BB
) and its a priori probability and stores this in the object's internal values
array. To multiply a hypothesis value by a constant value, both are passed to mult()
; it finds the previously stored value in values
and multiplies it with the value passed in for $prob
.
The normalize()
method iterates over all values previously inserted into the hash, adds them up in $sum
, and then divides all the values by the sum. Thus, the new sum of all probability values after a multiplication is again 1. Each value can thus be interpreted as a probability between 0 and 1. At the bottom of the module, prob()
finds the value for the searched-for hypothesis by retrieving the hash value using the values()
method. The latter has been automatically generated by Moose and returns the value stored under the key of the desired hypothesis.
More Abstraction
If you perform several such tests for various problems, you will identify a pattern: After establishing the hypotheses, the probabilities of all defined hypotheses are always multiplied by the likelihood of newly incoming data. It makes sense (as shown in Think Bayes [3]) to define a class derived from Distrib
by the name of HypoTest
, much as in Listing 3. The class uses an update()
method to update all the values for all hypotheses, based on the probabilities of incoming data.
Listing 3
HypoTest.pm
HypoTest
also relies on classes derived from it (e.g., CardHypoTest
in Listing 4) to overload the abstract likelihood()
method and return the value for P(D|H) based on the probability of the additionally available data D under the assumption that hypothesis H is true.
Listing 4
hypotest
The HypoTest
framework in Listing 3 calls the likelihood()
method repeatedly to obtain the data probabilities under the assumption of individual hypotheses before storing them in the Distrib
distribution. The framework further provides a print()
method, which is used to output the values of all the updated probabilities for each hypothesis.
Testing Hypotheses
In Listing 4, likelihood()
accepts the letter R from the main program as $data
– to record a drawn card with red front as an additional condition. Then, based on the hypothesis also passed in (RR
, RB
, BB
), it computes how likely it is that the test candidate will look at a red surface: 1 (i.e., 100 percent) for RR
, 0.5 for RB
, and 0 for BB
.
For this calculation, the function uses a regular expression that counts the number of Rs in the hypothesis and divides the result by 2 as a floating-point value, so that Perl does not perform integer division and dump the remainder.
Finally, hypotest
outputs the probabilities for all hypotheses in the distribution using the print()
method from the HypoTest
module and correctly reports that the red-red card will appear in 2/3 of all cases:
$ ./hypotest RC 0.333333333333333 RR: 0.666666666666667 BB 0
In other words, the test candidate, who has just drawn a card with a red front and now turns over this card, will see a red back with probability of 2/3.
« Previous 1 2 3 Next »
Buy this article as PDF
(incl. VAT)
Buy Linux Magazine
Direct Download
Read full article as PDF:
Price $2.95
Subscribe to our Linux Newsletters
Find Linux and Open Source Jobs
Subscribe to our ADMIN Newsletters
Find SysAdmin Jobs
News
-
KDE Plasma 5.27 Beta is Ready for Testing
The latest beta iteration of the KDE Plasma desktop is now available and includes some important additions and fixes.
-
Netrunner OS 23 Is Now Available
The latest version of this Linux distribution is now based on Debian Bullseye and is ready for installation and finally hits the KDE 5.20 branch of the desktop.
-
New Linux Distribution Built for Gamers
With a Gnome desktop that offers different layouts and a custom kernel, PikaOS is a great option for gamers of all types.
-
System76 Beefs Up Popular Pangolin Laptop
The darling of open-source-powered laptops and desktops will soon drop a new AMD Ryzen 7-powered version of their popular Pangolin laptop.
-
Nobara Project Is a Modified Version of Fedora with User-Friendly Fixes
If you're looking for a version of Fedora that includes third-party and proprietary packages, look no further than the Nobara Project.
-
Gnome 44 Now Has a Release Date
Gnome 44 will be officially released on March 22, 2023.
-
Nitrux 2.6 Available with Kernel 6.1 and a Major Change
The developers of Nitrux have officially released version 2.6 of their Linux distribution with plenty of new features to excite users.
-
Vanilla OS Initial Release Is Now Available
A stock GNOME experience with on-demand immutability finally sees its first production release.
-
Critical Linux Vulnerability Found to Impact SMB Servers
A Linux vulnerability with a CVSS score of 10 has been found to affect SMB servers and can lead to remote code execution.
-
Linux Mint 21.1 Now Available with Plenty of Look and Feel Changes
Vera has arrived and although it is still using kernel 5.15, there are plenty of improvements sure to please everyone.