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Use of Bayesian Methods to Improve Prediction of Panicle and Shoot Blight Severity of Pistachio in California

Panicle and shoot blight, caused by a Fusicoccum sp., is one of the major aboveground diseases of pistachio in California. The effects of temperature, number of continuous rainy days in April and May, irrigation system, and incidence of latent infection of the Fusicoccum sp. on severity of panicle and shoot blight of pistachio leaves and fruit have been quantified previously, using data collected from 1999 through 2001. A predictive model for leaves and another model for fruit with good explanatory power were generated. In 2003 and 2004, newly collected data were used to evaluate the two models with non-Bayesian and Bayesian methods. The 95% credible (i.e., confidence) intervals of initial (before modification with non-Bayesian and Bayesian methods) and updated parameter estimates were used to investigate their prognostic validity. In 2003, the non-Bayesian analysis resulted in all parameter estimates, with the exception of cumulative daily mean temperature from 1 June until harvest, having different 95% confidence intervals than the parameter estimates of the original models. In addition, the parameter estimates for drip irrigation for the leaf infection and the parameter estimates for drip irrigation and number of continuous rainy days in April and May for fruit infection were not statistically significant. With Bayesian methods, the reestimated model parameters had overlapping 95% credible intervals with the initial estimated parameters, except for the number of continuous rainy days in April and May. When the two sets of modified parameter estimates were used to predict disease severity, statistically significant (α = 0.05) differences between observed and predicted disease severities were found with non-Bayesian analysis for leaf infection in three locations and with Bayesian analysis for fruit infection in one orchard. The parameter estimates were modified again at the end of the 2004 season and were all statistically significant with both non-Bayesian and Bayesian methods. Both sets of parameter estimates gave predictions that were not significantly different from observed disease severity on leaves and fruit in all monitored orchards in 2004. In summary, Bayesian methods gave more consistent results when used to update parameter estimates with new information and yielded predictions not statistically different from observed disease severity in more cases than the non-Bayesian analysis.