Comparación de resultados de resistencia a la compresión:

One fundamental difference between the frequentist and Bayesian paradigms is the explicit inclusion of prior knowledge within the calculation of the posterior distribution. The frequentist would claim this prior information acts as a bias to the experiment since

researchers can influence the results by imposing a strong prior distribution on the model. In fact, different results may be obtained from the same data if different researchers choose to apply differing prior distributions (Little, 2006). Efron (2005, p. 1) exemplifies this when observing physicists stating “there’s only one way of doing physics, but there seems to be at least two ways to do statistics, and they don’t always give the same answers”. Another example is risk assessment work by Viscusi (1985) which demonstrates a person’s prior knowledge can be systematically biased and, although not criticizing Bayesian philosophy per se, points out the challenges by citing work by Lichtenstein (1978) showing the over assessing of small risks and under assessing of larger risks.

The Bayesian practitioner, however, views this prior knowledge as an important element to the calculation since it matches how a person learns in everyday life (Bernado, 1999). A human mind operates by observing new data and compares this to what (s)he already knows (O’ Hagan, 1998). How these pieces “fit together in the light of changing evidence” is

fundamentally how the human mind learns (Bernado and Smith, 2000, p. 4). The Bayesian acknowledges the frequentist concern of differing prior distributions leading to differing model estimates though claims this is an issue for the quality of the researchers’ knowledge rather than the methods employed to inform the inference (Dunson, 2001). The Bayesian claims frequentist methods themselves are subject to the prior view(s) of researchers being imposed on the model, through the construction of biased questionnaires or leading questions. Leamer (1992) also argues that, in practice, the frequentist researcher must have some prior incline as to the nature of parameters and would reject any absurd model outputs, hence the Bayesian principle is being used in hindsight. Rossi and Allenby (2003) say the fact Bayesian methods require a prior specification is an advantage, since assumptions are explicit and model assumptions in themselves are a form of prior information usually implicit under frequentist based models. Gelman (2010) agrees, quoting Don Rubin when he says scientists interpret uncertainty in a Bayesian manner without realising it, despite working with

frequentist methods. (Aspinall, 2010) claims uncertainty should be embraced and quantified, not ignored from the decision making process. O’Hagan (1998, p. 21) agrees saying it is better to embrace and quantify additional information around an experiment and the

construction of realistic prior information is better than “relying on ignorance”. Researchers are not passive observers and experiments are designed to fit analytic models whether be it within a frequentist or Bayesian framework and the inclusion of the prior is an extension of this build (Efron, 2005).

Dunson (2001) argues the prior distribution can be obtained in a practical manner, deduced from previous studies (hence need not be over complicated) or may be as simple as

controlling for absurd results. Practical considerations for both sides of the argument are demonstrated by Efron (2005) in the following example. A drug company performing research may wish to incorporate information from prior studies that can lead to early

adoption/rejection of drug development, which they would claim is a better risk for the public and the test subjects of the new drug. However, the FDA would suggest this prior knowledge is of no interest and demand the industry frequentist standards. (Though Efron (2005) notes these standards will have been developed under the dominant frequentist paradigm at the time.)

Gelman, (2010) says the Bayesian paradigm is often discarded as too radical from that of the frequentist, however argues it is the Bayesian that is the more conservative paradigm as it

implies the current thinking is preserved unless the data is strong enough to lead to reconsideration. In fact, Gelman (2010, p. 163) strongly criticises frequentist methods

claiming “unbiased estimates and other unregularized classical procedures are noisy and get

jerked around by whatever data happen to come by”.

Prior distributions which contain “minimal information” have been used for some time within Bayesian models (Lunn et al, 2012). These are described by Gelman as

“Prior distributions that are uniform, or nearly so, and basically allow the information from the likelihood to be interpreted probabilistically. These are non-informative priors, or maybe, in some cases, weakly informative” (Gelman, 2007). However, Lunn et al (2012) disregard the term non-informative as every prior distribution contains some information and the terms, vague, objective or reference are more suited. The use of these vague priors yield parameter estimates similar to those from maximum likelihood techniques, particularly as the sample size increases and the observed data will have more of a bearing than the prior (Dunson, 2001). Samaniego and Reneau (1994) prefer non-informative prior distribution be used as they mimic a more frequentist approach. Also, Hansen et al (2004) utilize vague priors in their studies.

From a frequentist perspective, it may be argued whether the increased complexity in model computation is necessary for models yielding results similar to frequentist methods. Though from a Bayesian perspective, for such experiments that have no anticipated result, the vague prior is a tool that can reflect this absence of knowledge. This vague prior can be updated for future models of the same form, in light of new information gained from the outputs of the vague prior model and hence laying a baseline for future work (Lunn et al., 2012).