贝叶斯网络导论（An Introduction to Bayesian Networks）

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An Introduction to Bayesian Networks and their

Contemporary Applications

Daryle Niedermayer, I.S.P., PMP, B.Sc., B.A., M.Div.

relevance and applicability of Bayesian Network theory for issues of advanced computability forms the

core of the current discussion. A number of current applications using Bayesian networks is examined.

The paper concludes with a brief discussion of the appropriateness and limitations of Bayesian Networks

for human-computer interaction and automated learning.

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Introduction

Inferential statistics is a branch of statistics that attempts to make valid predictions based on only a sample

of all possible observations[1]

. For example, imagine a bag of 10,000 marbles. Some are black and some

white, but of which the exact proportion of these colours is unknown. It is unnecessary to count all the

This is assumption is not necessarily correct. As the sample size becomes smaller, the potential for error

grows. For this reason, inferential statistics has developed numerous techniques for stating the level of

confidence that can be placed on these inferences.

If we took ten samples of 100 marbles each, we might find the following results:

Table 1: Relative proportions of 10 samples from a

population of 10,000

Sample Number

Number of White

Marbles

where x

(eq. 2)

and n is the number of samples. In our example, the mean number of White marbles is

.

We might be tempted to say that about 40% of the marbles are white, but we are unable to argue that point

with any degree of certainty. Using equation 2 above, we determine that the Standard Deviation is 11.15.

We must then determine the "Sample Error of the Mean" (where s=[sigma]):

An Introduction to Bayesian Networks and their Contemporary Applic... http://www.niedermayer.ca/papers/bayesian

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(eq. 4)

The confidence we can put on our hypothesis that u=40 of the marbles are white is found using a standard

38.4. Since the distribution is two-sided or "two-tailed" (i.e. the sample average could also be greater than

the population average), we would also expect

to greater than ((u- )+u=) 41.6 in another 32% of cases.

In summary, if we expect 40% of all marbles in the bag to be white, then a series of ten samples with only

38.4% of marbles being white would be expected in (100-64%=) 36% of the time. Clearly, the confidence

we can place in our conclusion is not as good as it was on first glance. This lack of confidence is due to

the high variability among the samples. If we took more samples or larger samples, our confidence in our

conclusion might increase.

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An Introduction to Bayesian Inference

the enterprise to be profitable. Using some of her investment funds, she hires a polling company to

conduct a randomized survey. The results conclude that from a random sample of 20 consumers, 25% of

the population would indeed be prepared to purchase her services. Is this sufficient evidence to proceed

with the investment?

If this is all the investor has to go on, she could find herself on her break-even point and could just as

easily turn a loss instead of a profit. She may not have enough confidence in this survey or her plan to

proceed.

Fortunately, the franchising company has a wealth of experience in exploiting new markets. Their results

show that in 20% of cases, new franchises only achieve a 25% market saturation, while in 40% of cases,

new franchises achieve a 30% market saturation. The entire table of their findings appears below: