There are diverse kinds of natural processes and only a small finite number of well-described probability distribution models. One can gain intuition about the varieties of different processes and the characteristics of different probability distributions by interactively exploring their properties using the Distributome tools (calculators, simulators and experiments). The Probability Distributome Game Webapp enables this exploration of natural phenomena and models as a game of matching pairs of processes and distributions.

The goal of the Distributome Game is to correctly identify the correspondences between pairs of processes (represented as problems) and probability distributions (as models).

How to play?

• The game board is a Cartesian plane where Rows and Columns represent problems/processes and distribution models, respectively.
• As you move the mouse over the grid, the zoom-function automatically expands the Cartesian space around the mouse location. Matching Problem-Distribution pairs corresponding for the current location are highlighted.
• Try to find which distribution(s) may represent good model(s) for the process described in the problem.
• Use one mouse click on a cell in this 2D Cartesian plane to select and highlight a matching problem-distribution pair. Correct or incorrect matches are indicated by green and red cell background coloring, respectively.
• Clicking on a highlighted cell provides access to appropriate Distributome tools for the selected distribution and optional hints for solving the problem.

Details

The Distributome Game is available at:

1. Source Code SVN: https://distributome.googlecode.com/svn/trunk/web_site/V3
2. Webapp: http://www.distributome.org/V3/DistributomeGame.html

Updates/Expansions to the set of Problems/Processes would be easy (expand in this CSV format):

1. Problem-Distribution Meta-Data SVN
2. Current Meta-Data (CSV)

Future Improvements

1. Always pick the same number of rows – say 20 picked randomly from problem database and add a clock so players try to beat their best time and score.  Score = # of guesses until all correct plus number of hints requested + 10*(#of seconds used).  Low scores are good.
2.  After you make a selection the cell could stay the same color (red or green as the case may be) until the whole round is over (start-over button)?  That way players can know which problems they have completed and how many errors they have made total.
3.  Label the columns with the distribution names and have them alphabetical so players can easily find the one they are looking for (this is related to the search functionality)
4.  Perhaps allow for problems to be picked from the level of distributions appropriate (i.e., top level, middle level, or all).
5.  Introduce three modes of play.
1. Beginner mode = see the distribution descriptions and only have columns for the distributions used in the round of play.
2. Intermediate mode = don’t see the distribution descriptions and only have columns for distributions used in the round of play.
3. Advanced mode = don’t see the distribution descriptions and have columns for all distributions at level under use.
6.  Another possibility may be to allow some way to enter numerical values of parameters when they are given in the problem.  For example, when you get a distribution correct (green rectangle) that has numerical answers to parameter values then a “bonus” box is seen with place(s) to enter parameter(s) and students get 1 bonus point for each correct parameter removed from their score.  This might detract from the flow of the game – but it would be nice to require parameter values where appropriate.

This is an update on the recent developments of the Probability Distributome project:

(1) We have V.3 of the Navigator available online

• This is a test-version will replace the official Navigator version as soon as we finish validating it.
• It uses the new Textbook-based Preference for the hierarchical organization of the levels of distributions.
• In V.3, all tools (sim, calc, exp) are linked with nodes on the graph.
• All references (BiBTeX format) are working for nodes (distributions) and edges (relations).
• We need community help to proofread the Distributome.xml DB and the BiBTeX sources.
• Note about adding additional BiBTex citations/references. Sometimes references come with Cp1252 encoding that needs to be converted to UTF-8 encoding for proper interpretation. This is achieved with this (UNIX) command (iconv -f cp1252 -t utf-8 Distributome.bib > Distributome_conv.bib).
•  The Distributome database validator (for the new V.3) is also available online.

(2) All these changes are pushed to:

• Distributome web-site.
• Distributome GoogleCode SVN.

(3) Documentation is available online:

• Technical Documentation page.
• Distributome Blog.

(4) Further ongoing Distributome Developments:

• The Distributome DB Editor is still being developed and will allow crowd-based contributions in editing, expanding, correcting and updating the Distributome Database.
• Transition from Protovis to D3 JavaScript library.
• Other features, improvements and customizations are also ongoing.
• We are expanding the collection of tools (calc, sim, exp).
• We are drafting additional activities.

The following types of Distributions (nodes) and relations (edges) are currently allowed. These may later be modified or expanded. These types are referred to in the Distributome.xml Database (see the HTML rendering of the XML).

Node (distribution) Types will be (full-Name and abbreviation)

• 0 No Type Given
• 1 Convolution (Conv)
• 2 Memoryless (Mless)
• 3 Inverse (Inv)
• 4 Linear Combination (LinComb)
• 5 Minimum (min)
• 6 Maximum (max)
• 7 Product (Prod)
• 8 Conditional ResIDual (CondRes)
• 9 Scaling (Scale)
• 10 Simulate (Sim)
• 11 Variate Generation(VGen)

Edge Types (directional distribution relations)

• 0 No Type Given
• 1 Special Case (SC)
• 2 Transform (T)
• 3 Limiting (Lim)
• 4 Bayesian (Bayes)

Below is the status of the Probability Distributome Navigator which describes the new textbook based ontological classification of distributions, using a preference XML file, and the  current status of the integration of the Navigator and different Distributome tools (calculators, experiments, and simulators), also see the technical documentation.