Part one of this series ended by noting three elements that were lacking in the Simple Linear Regression class. In this article, the author, Paul Meagher, addresses these shortcomings with PHP-based probability functions; demonstrates how to integrate output methods into the SimpleLinearRegression class; and creates graphical output. He then tackles these issues by building a data-exploration tool, designed to plumb the depths of information contained in small- to medium-sized datasets. (In part one, the author demonstrated how to develop and implement the heart of a simple linear regression algorithm package using PHP as the implementation language.)

While the first article in this series discussed building intelligent Web applications through conditional probability, this Bayesian inference article examines how you can use Bayes methods to solve parameter estimation problems. Relevant concepts are explained in the context of Web survey analysis using PHP and JPGraph.

A missing, but powerful, tool in the PHP arena is a language-based math library. In this two-part series, Paul Meagher hopes to inspire PHP developers to develop and implement a PHP-based math library by providing you with an example of how a library of analytic models might be developed. In this first part, he demonstrates how to develop and implement the heart of a Simple Linear Regression algorithm package using PHP as the implementation language. In Part 2, the author adds features to the package for a useful data-analysis tool for small- to medium-sized datasets.

Conditional probability -- the probability of observing one event as a result of having observed another event -- is a potentially important factor in designing intelligent Web applications. Paul Meagher introduces Bayesian inference by discussing the basic mathematical concepts involved and demonstrating how to implement the underlying conditional probability calculations using PHP. In this article, the author discusses how Bayesian inference can be used to build an online PHP-based wizard that guides a user through the process making a medical diagnosis. This three-part series features interesting applications designed to help you appreciate the power and potential of Bayesian inference concepts.

To help developers learn to fit the benefits of probability modeling into Web application development, Paul Meagher introduces you to basic concepts, techniques, and PHP-based tools that define the area of probability modeling and probability distributions. He demonstrates how to develop univariate probability models in PHP; discusses how to fit empirical data distributions to a theoretical probability distribution; and showcases an important tool for all this -- the Probability Distributions Library (PDL).

Effective, multi-level analysis of Web data is a critical element for the survival of many Web-oriented businesses, and the design (and determination) of data-analysis tests is often the job of systems administrators and in-house application designers who may not have an understanding of statistics beyond tabulating raw counts. In this article, Paul Meagher delivers the skills and concepts Web developers need to be able to apply inferential statistics to their Web data streams.

Effective, multi-level analysis of Web data is a critical element for the survival of many Web-oriented businesses, and the design (and determination) of data-analysis tests is often the job of systems administrators and in-house application designers who may not have an understanding of statistics beyond tabulating raw counts. In this article, Paul Meagher delivers the skills and concepts Web developers need to be able to apply inferential statistics to their Web data streams.