Analysis: cc17h

Understanding Orthogonal Statistics

Orthodox statistics, a diverse collection of independent ad hoc devices, is often criticized for its lack of coherence in providing a unified theory. This deficiency stems from multiple complexities, including the application of Bayes' Law, which may shift responsibility to the statistician or the individual employing the results.

The Paradoxes of Bayesian Methods

Bayesian methods have been misrepresented in orthodox literature throughout history. In Chapter 15, we noted that orthodox objections to Bayesian methods were always philosophical or ideological in nature, never addressing numerical results that differ from those given by orthodoxians.

A Comparison of Orthodoxy and Bayes

When an orthodox method yields a satisfactory result in some problem, it is acknowledged and not criticized merely on ideological grounds. Conversely, when a common procedure leads to a result that appears simplistic or flawed, concerns are raised about the methodology.

Information Loss and Its Consequences

Orthodox statistics often relies on sampling distributions, which assume normal distribution around the true parameter value. However, information loss can occur due to small sample sizes or non-normal data. In one instance, a study found that the unbiased estimator M2 was more accurate than the Bayesian estimator β in estimating the variance of a sampling distribution with K = 3.

A Real-World Example

Consider a portfolio consisting of stocks from different industries, such as BAC (Bank of America), EEM (iShares ETF Global X US Energy ETF), MS (Morgan Stanley Alpha Index Fund), C (Vanguard FTSE Developed All Cap ex USA Index Fund), and AGG (Vanguard Total Stock Market Index Fund). The estimated variance using Bayesian methods was found to be K = 3. However, if M2 is used as the estimator for the variance, it is more accurate than Bayesian estimation in estimating the variance of a sampling distribution with K = 3.

Why Most Investors Fail to Recognize This Pattern

Most investors overlook the significance of information loss when using orthodox statistics. They often rely on assumptions about data and do not consider the potential consequences of using these methods.