The ABNMS BN Repository

From the book Neapolitan, Richard E. (1990) Probabilistic Reasoning in Expert Systems: Theory and Algorithms, John Wiley & Sons, New York, p. 259. Started as problem 5.5.2, p.183, it becomes example 7.5, p. 261 (with diagram on p. 259), and continues numerically on p. 279. Originally based on the Lauritzen & Spiegelhalter 1988 paper.

BN link: <www.norsys.com...>

This Bayes net is for the famous experiments of Mendel, in which he developed the foundations of hereditary genetics. The experiments involved breeding red and white flowered pea plants.

A tutorial, with a complete description, is available at <www.norsys.com...>

Paper link: <www.norsys.com...>

This Bayes net demonstrates learning a latent (or "hidden") variable, which occurs when you have an important node in the net for which no data appears in the case file.

Paper link: <www.norsys.com...>

Demo of the impossible condition check. Refer to the following link for a description and tutorial of the BN: <www.norsys.com...>

Paper link: <www.norsys.com...>

In order to express the belief in a node as a function, it must be expressed as a function of the joint beliefs of its Markov boundary nodes (i.e. the beliefs in the Cartesian product of their values). Thinking in terms of paths can obscure this. Consider the False Barrier BN illustrated:

When there is no evidence, the beliefs of A, B, C, and D are all 1/2. If we get evidence TRUE for A, the beliefs of B and C remain at 1/2, but the belief at D changes to 3/4. Thinking in terms of a constraint network, or "flow of influence along paths," it is hard to see how a change at A can create a change at D without changing the beliefs at B or C. Of course, it is the joint belief in B and C which have changed (BEL (+b+c) changes from 1/4 to 3/8, BEL(+b-c) changes from 1/4 to 1/8, etc). Therefore, we must be careful with the path concept.

Paper link: <www.norsys.com...>

This Bayes net demonstrates how to solve constraint satisfaction problems (CSPs) using Bayes nets. A CSP consists of a number of variables, and some constraints between them. The goal is to find values for the variables that satisfy all the constraints.

Paper link: <www.norsys.com...>

A BN classifier.

An explanation of this BN can be found at <www.norsys.com...>

Paper link: <www.norsys.com...>

This Bayes net is to demonstrate the Central Limit Theorem.

Paper link: <www.norsys.com...>

A simple example belief network for diagnosing why a car won't start, based on spark plugs, headlights, main fuse, etc. This example is small and just calls out to be expanded.

BN link: <www.norsys.com...>

A time delay belief network for the position and velocity of a friction-less 'ball' bouncing between 2 barriers. More information: <www.norsys.com...>

There are two book bags each containing 10 poker chips. In one bag there are 7 red and 3 blue. In the other bag there are 3 red and 7 blue. Five chips are drawn out of one of the bags and shown to the subject (one at a time then returned to the bag). The subject does not know which bag the chips came from. There is an equal chance that the draws are made from either bag. After each draw the subject reports which bag he believes the chips are coming from and provides a probability that the chips are being drawn from that bag.

The problem comes from the early "revision of judgment" work that indicated that people were conservative with respect to Bayes.

A subjective belief network for a particular scenario of neighborhood events, that shows how even distant concepts have some connection. More information: <www.norsys.com...>

The polar bear (Ursus maritimus) was listed as a globally threatened species under the U.S. Endangered Species Act (ESA) in 2008. We updated a Bayesian network model (available at <abnms.org...>) previously used to forecast the future status of polar bears worldwide, using new information on actual and predicted sea ice loss and polar bear responses, to evaluate the relative influence of plausible threats and their mitigation through management actions on the persistence of polar bears in four ecoregions. Overall sea ice conditions, determined by rising global temperatures, were the most influential determinant of population outcomes which worsened over time through the end of the century under both stabilized and unabated greenhouse gas (GHG) emission pathways. Marine prey (seal) availability, linked closely to sea ice trend, had slightly less influence on outcomes than did sea ice availability itself. Reduced mortality from hunting and defense of life and property interactions resulted in modest declines in the probability of a decreased or greatly decreased population outcome. Minimizing other stressors alone such as trans-Arctic shipping, oil and gas exploration, and contaminants had a negligible effect on polar bear outcomes. A case file for the model can be found here: <abnms.org...>.

The Phase I Polar Bear Stressor Model can be found here: <abnms.org...>

This problem is about how to determine the proportion of white and black balls in a bag. In order to do this, you draw a ball or several balls from the bag and replace them. This can be repeated several times.

This network is also available at <www.norsys.com...> See the tutorial <www.norsys.com...> for more details.

A demonstration of Simpson's Paradox (also available at <<www.norsys.com...> An explanation of this BN can be found at: <www.norsys.com...>

With this network (also available from <www.norsys.com...>) you can enter some characteristics of a particular animal, and watch how the probabilities of its other characteristics (and what type of animal it is) change.

This is just a toy example. For a real-world application, it would have to be extended to include many animals (or plants, bacteria, etc.), probably all from the same environment, or the same subclass, etc. Also, the "Animal" node should probably have an "Other" state.

The fun part of this network is to extend it to include more animals and more characteristics. You may need to define other groupings, such as the "Class" node, in order to keep things manageable. If you make a great network, send it to Norsys; we would love to include it in our library (with the proper credits).

These models, trained from laboratory and field data, predict the age of individuals of two species of marten (Martes americana and M. caurina) in North America, from relative length of telomeres (fragmented ends of chromosomes that shorten over time) and other anatomical and environmental factors. It is the first time that age of an organism can be predicted from telomeres (and other factors) in a reliable manner. Two models are presented here: the "live capture" versions, for predicting age in years from captured (or museum specimen) martens; and the "noninvasive" version for predicting age class from non-invasive genetic samples where the actual animal does not need to be captured and handled. A case file for running the live capture model version can be found at <abnms.org...>.

This model illustrates potential food web and species interaction dynamics related to interactions between bull trout (Salvelinus confluentus) and anadromous salmonid fish existing in the same river system. (Explanation of nodes: small bull trout = at least juveniles and possibly resident adults; terrestrial wildlife predators = some amphibians, reptiles, birds, and mammals; juvenile [juv.] anadromous salmonids eaten = average annual percentage of total juvenile anadromous salmonids that are consumed by fish and other predators; juvenile anadromous salmonids = parr to smolt stages, although some bull trout predation on eggs also occurs; popn = population; anadromous reproduction = number of offspring [embryos] produced by spawning adult salmonids; other sources of mortality = poor water quality, passage through reservoirs and past dams, natural disturbances, etc.).

We developed a Bayesian network model to integrate potential effects of changing environmental conditions and anthropogenic stressors on the future status of the Pacific walrus population in the Chukchi and Bering Seas, at four periods through the twenty-first century. The model framework allowed for inclusion of various sources and levels of knowledge, and representation of structural and parameter uncertainties. Walrus outcome probabilities through the century reflected a clear trend of worsening conditions for the subspecies.

In 2007-08, to inform the U.S. Fish and Wildlife Service decision, whether or not to list polar bears as threatened under the Endangered Species Act (ESA), we projected the status of the world’s polar bears (Ursus maritimus) for decades centered on future years 2025, 2050, 2075, and 2095. We defined four ecoregions based on current and projected sea ice conditions: seasonal ice, Canadian Archipelago, polar basin divergent, and polar basin convergent ecoregions. We incorporated general circulation model projections of future sea ice into a Bayesian network (BN) model structured around the factors considered in ESA decisions. This first-generation (Phase I) BN model combined empirical data, interpretations of data, and professional judgments of one polar bear expert into a probabilistic framework that identifies causal links between environmental stressors and polar bear responses. The BN model projected extirpation of polar bears from the seasonal ice and polar basin divergent ecoregions, where ≈2/3 of the world’s polar bears currently occur, by mid century. Decline in ice habitat was the overriding factor driving the model outcomes.

The Polar Bear Stressor Model, Phase II (2016) can be found here: <abnms.org...>