Why transformed probabilities need a Jacobian adjustment
Square a random variable and the probability density stretches with it. Here is why naive substitution integrates to 2.0 instead of 1, and how the Jacobian factor puts it back.
Author: Ahmad Wael
I'm a WordPress and WooCommerce developer with 15+ years of experience building custom e-commerce solutions and plugins. I specialize in PHP development, following WordPress coding standards to deliver clean, maintainable code. Currently, I'm exploring AI and e-commerce by building multi-agent systems and SaaS products that integrate technologies like Google Gemini API with WordPress platforms, approaching every project with a commitment to performance, security, and exceptional user experience.
You can pivot your tech career without starting over
Feeling stale in your role? A tech career pivot usually means reusing what you already know rather than deleting it. Four common moves, plus what three people who made the switch had to say about it.
RFM analysis for WooCommerce customer segmentation
Reporting plugins bloat the database and still guess at who your best customers are. Here is how I build RFM scores from WooCommerce order data in Pandas, and what the segments are actually good for.
Why WordPress Core may drop the PHP filter extension
The latest dev chat turned into an argument over whether WordPress Core should require PHP’s filter extension. PHPMailer uses it today. Here is what that costs you on hosts that compiled PHP without it.
CSS container queries after size: scroll-state and style
Container queries began as a way to check a parent’s width. They now read scroll state, custom property values and anchor flips, which removes a lot of the JavaScript that used to handle sticky headers and tooltips.
Learning WordPress without burning out
The WordPress ecosystem ships faster than anyone can absorb it. After 14 years I scan most of it and go deep on very little. Here is how I set stopping points so that keeping up does not turn into burnout.
Why I use GliNER2 for structured data extraction
A client had ten thousand messy biographical records that needed to become a clean knowledge graph. GPT-4o would have done it and cost a fortune, so I used GliNER2 instead: schema-driven extraction that runs on a CPU.
How I handle covariance shift with IPW
A WooCommerce recommendation engine scored 0.85 AUC in staging and fell apart on launch day because the live audience did not match the training data. Inverse probability weighting is how I got an honest read on what the model was really doing.
Cyclical feature encoding and the midnight paradox
A client’s hourly sales model lost its accuracy every night at midnight because it read 23:00 and 00:00 as far apart. Sine and cosine encoding puts the hours back on a circle, which is where they belong.
Distributed computing with Ray, from one core to 64
A client bought a 64-core Threadripper and their script still ran on one core for an hour. Ray brought it down to about two minutes, with less code than the multiprocessing version I tried first.