Bayesian Model Challenges

By Dax Bradley

Possible disadvantages to Bayesian learning methods can be significant.  For one thing, the information gleaned from the effort could be theoretically infeasible.  The act of specifying a prior datum is challenging.  Generally, it is necessary to specify a real number for every setting in the real-world parameters (Langford, 2005).  One potential solution is to acquire languages that allow more compact specification of priors.  The task of learning a new language may be prohibitive.  Another solution is to simply lie.  In other words, create a specification that is not accurate.  As deceitful as this sounds, it is not meant that way; in fact, it has been shown to be effective (Langford, 2005).

Another known disadvantage to Bayesian modeling lies in the analysis of causality.  There is a great challenge in analyzing the conditional probability links between various nodes.  Even with physical causal models and known variables, the computational burden is great, since the task equates to inverting a finite-element model (Sankararaman, 2015).  This is especially daunting if the analysis revolves around an acyclic model.  The assumption of independence among variables implies no latent cofounding variable in Bayesian modeling; however, often there are acyclic latent cofounding variables which can force the model to be seriously biased (Shimizu & Bollen, 2014).

Prior choice problems present challenges in the Bayesian methodology.  Another scenario in which researchers using the model is in astronomy.  Scientists have attempted to predict the number of extra-solar planets in this way.  Improper priors are generally disallowed here, so other strategies have been suggested, such as Intrinsic Bayes, Fractional Bayes, and Expected posterior factors (Jeffreys, 2006, p. 11).  The potential defeat of using such methods is that data may be inadvertently duplicated, so allowances must be made.

Many forms of industry employ the Bayesian model of statistical probability.  In drug development, the approach is widely regarded for its accuracy and natural interpretation.  It does, however, demand no small degree of planning.  The flexibility of this method creates an environment prone to potential computational errors.  Without proper planning, the various outcomes of intense computation may be unreliable, prompting some teams to opt instead for a frequentist model (Gupta, 2012).

References

Gupta, S. (2012, June). Use of Bayesian statistics in drug development: Advantages and challenges. International Journal of Applied & Basic Medical Research, 2(1), 3-6. http://dx.doi.org/Use of Bayesian statistics in drug development: Advantages and challenges

Jeffreys, W. (2006). Current challenges in Bayesian model choice: Comments [Lecture notes]. Retrieved from Department of Statistics University of Vermont: http://astrostatistics.psu.edu/scma4/Jefferys.pdf

Langford, J. (2005, April 23). Advantages and disadvantages to Bayesian learning [Discussion group comment]. Retrieved from http://hunch.net/?p=65
Sankararaman, S. (2015). What are the limitations of Bayesian Networks? Retrieved January 18, 2017, from https://www.quora.com/What-are-the-limitations-of-Bayesian-Networks

Shimizu, S., & Bollen, K. (2014, August). Bayesian Estimation of Causal Direction in Acyclic Structural Equation models with individual-specific confounder variables and non-Gaussian distributions. Journal of Machine Learning Research, 15(1), 2629-2652. Retrieved from http://jmlr.org/papers/volume15/shimizu14a/shimizu14a.pdf