On An Applications of Bayes’ Rule in Probability Theory to Electrocatalytic Reaction Engineering
[1]
Nafeesa Rehman, Department of Mathematics, Virtual University of Pakistan, Lahore, Punjab, Pakistan.
[2]
Kishwer Naheed, Department of Mathematics, Virtual University of Pakistan, Lahore, Punjab, Pakistan.
[3]
Kamran Ayub, Department of Mathematics, Riphah International University, Islamabad, Pakistan.
[4]
Qazi Mahmood Ul-Hassan, Department of Mathematics, University of Wah, Wah, Pakistan.
Bayesian methods stem from the rule of linking prior probability and conditional probability (likelihood) to posterior probability by Bayes’ rule. The posterior probability is an improved version of the prior probability of an event, through the likelihood of finding empirical evidence if the underlying assumptions (hypothesis) are valid. In the absence of a frequency distribution for the prior probability, Bayesian methods have been found more satisfactory than distribution-based techniques. The paper describes the utility of Bayes’ rule in the analysis of electrocatalytic reactor performance by means of four numerical examples involving a catalytic oxygen cathode, hydrogen evolution on a synthetic metal, the dependable of a device testing the quality of an electrocatalyst, and the range of Tafel slopes exhibited by an electrocatalyst.
Prior Probability, Posterior Probability, Conditional Probability, Mutually Exclusive Events, Mutually Exhaustive Events
[1]
J. O’M. BockrisandS. U. M. Khan, Surface Electrochemistry, Plenum, New York, NY, USA, 1993.
[2]
R. Porkess, Collins Internet-Linked Dictionary of Statistics, Harper Collins College, Glenview, Ill, USA, 2nd edition, 2005.
[3]
E. B. Manoukian, Modern Concepts and Theorems of Mathematical Statistics, Springer, New York, NY, USA, 1986.
[4]
M. G. Bulmer, Principles of Statistics, Dover, New York, NY, USA, 2nd edition, 1979.
[5]
S. F. Arnold, Mathematical Statistics, Prentice Hall, Englewood Electrochemistry, vol. 7, pp. 119–123, Research Trends, Trivandrum, India, 2000.
[6]
T. Z. Fahidy, “An application of Bayesian risk theory to electrochemical processes,” ElectrochimicaActa, vol.49, no. 9-10, pp. 1397-1401, 2004.
[7]
S. F. Arnold, Mathematical Statistics, Prentice Hall, Englewood Cliffs, NJ, USA, 1990.
[8]
T. Z. Fahidy, “Bayesian updating of electrochemical process parameters via natural conjugate probability distributions,” ElectrochimicaActa, vol. 49, no. 27, pp. 5013–5021, 2004.
[9]
T. Z. Fahidy, “Probabilistic methods in the analysis of certain electro-Chemical systems,” in Recent Research Developments in Electrochemistry S. G. Pan Dalai, Ed., vol. 6, pp. 116–117, Tran’s world Research Network, Trivandrum, India, 2003.
[10]
T. Z. Fahidy, “Electrochemical applications of net-benefit analysis via Bayesian probabilities,” Journal of Applied Electrochemistry, vol. 37, No. 6, pp. 747–752, 2007.
[11]
K. Wisner and D. Ohms, “Electrocatalysis for environmentally orientated electrochemical processes and environmental protection,” in Environmental Oriented Electrochemistry, C. A. C. Sequeira, Ed., p. 694, Elsevier, Amsterdam, The Nether-lands, 1994.
[12]
J. O’M. Bockris and S. U. M. Khan, loc. cit., Section 3.14.3, Fig. 3.23, p. 268.
[13]
J. O’M. Bockris and S. U. M. Khan, loc. cit., Section 3.21.6, Fig. 3.31, p. 293.
[14]
A. OliveiraNeto, J. Perez, W. T. Napporn, E. A. Ticianelli,and E. R. Gonzalez, “Electrocatalytic oxidation of methanol: study with Pt:Mo dispersed catalysts, “Journal of the Brazilian Chemical Society, vol. 11, no. 1, pp. 39–43, 2000.
