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As one might intuitively expect, P(h ID) increases with P(h) and with P(D1h) according to Bayes theorem It is also reasonable to see that P(hl D ) decreases as P ( D ) increases, because the more probable it is that D will be observed independent of h, the less evidence D provides in support of h In many learning scenarios, the learner considers some set of candidate hypotheses H and is interested in finding the most probable hypothesis h E H given the observed data D (or at least one of the maximally probable if there are several) Any such maximally probable hypothesis is called a maximum a posteriori (MAP) hypothesis We can determine the MAP hypotheses by using Bayes theorem to calculate the posterior probability of each candidate hypothesis More precisely, we will say that MAP is a MAP hypothesis provided

= argmax P(D 1h) P (h)

Affordance means the degree to which a control reveals its purpose to the user. A button control should look like something that can be pressed, and when you press it it should behave like it has been pressed. Scroll bars have defined handles that leave you in no doubt that you can grab and move them, and their behavior when you do should fit the expected action. A well-designed user interface has controls that spell out for the user exactly how they should be used. The other factor to bear in mind in designing controls with good affordance is that they should invite and reward exploration. A slider control should look and behave like one, and give clear feedback about the consequences of changing its setting.

(62)

BA, June 1996, University of Rhode Island, Kingston, RI Major in geology (GPA 34) with primary interest in oceanography Cumulative GPA 33

Notice in the final step above we dropped the term P ( D ) because it is a constant independent of h In some cases, we will assume that every hypothesis in H is equally probable a priori ( P ( h i ) = P(h;) for all hi and h; in H) In this case we can further simplify Equation (62) and need only consider the term P(D1h) to find the most probable hypothesis P(Dlh) is often called the likelihood of the data D given h, and any hypothesis that maximizes P(Dlh) is called a maximum likelihood (ML) hypothesis, hML

Think for a moment about a common real-world object such as a door handle. As you walk up to a door you will often see a handle on one side of the door and a push-plate on the other. That is great affordance. The door tells you which handle you should pull and which you should push. Now, how often have you seen a glass door that has a pull handle on both sides Watch people using that door, and you will often see them pull when they should be pushing. That s bad affordance.

hML= argmax P(Dlh)

In order to make clear the connection to machine learning problems, we introduced Bayes theorem above by referring to the data D as training examples of some target function and referring to H as the space of candidate target functions In fact, Bayes theorem is much more general than suggested by this discussion It can be applied equally well to any set H of mutually exclusive propositions whose probabilities sum to one (eg, "the sky is blue," and "the sky is not blue") In this chapter, we will at times consider cases where H is a hypothesis space containing possible target functions and the data D are training examples At other times we will consider cases where H is some other set of mutually exclusive propositions, and D is some other kind of data

A mental model is the construction that your user builds in his mind to describe and predict how your software works. For example, a word-processing system provides a mental model to the user of a space in which to create nicely formatted text content, perhaps with pictures. A word processor that didn t support a readily identifiable model would be more difficult to learn, since the user would have no familiar frame of reference in which to approach the program. The mental model that you would be trying to support in writing a word processor would be one involving the creation of a new document (a blank sheet of paper in the real world), tools to put text and images down on the page (a pen or even a typewriter, with a pastepot to glue in a picture), tools to construct the document (more pages when you need them), and some mechanism to store it at the end of the process (folders in a filing system).

To illustrate Bayes rule, consider a medical diagnosis problem in which there are two alternative hypotheses: (1) that the patien; has a- articular form of cancer and (2) that the patient does not The avaiiable data is from a particular laboratory