Maximize Precision Deep Learning For some binary image classification problems having close to 100% precision is super important and recall is much less important.

What are best practices for maximizing precision? Setting the probability threshold for model.predict() greater than 0.5 seems like a reasonable approach. 

Are there any other recommended methods?
If you are exploring the best hyper-parameter combination that maximizes precision you could try GridsearchCV along with KerasClassifier. You create a wrapper of your model and use it as the estimator of the GridsearchCV method. Also, since you want to maximize precision, you would have to set the scorer parameter to precision. After that you are going to have to set the hyper-parameter space that you would like to explore and finally run the experiment. 

Please bear in mind that this approach is computationally expensive. If your dataset is very large, a space of n > 2 (i.e 2-d), would need a cluster so as to produce results in a timely manner.