Probability concepts in real world

Probability can be simply as how likely something is to happen. Whenever we are unsure of the result, we tends toward there is certain chance of this happening. And, the analysis of events governed by probability is called statistics. Here are some real world use cases of probability.

Bayesian Networks in Aircraft Fault Diagnosis

One of the most elegant and powerful real-world uses of probability lies inside modern aircraft — in Bayesian networks that monitor system health and predict failures before they happen.

The Concept:

A Bayesian network is a probabilistic graphical model. Each node represents a variable (like “Fuel Pump Failure” or “Low Hydraulic Pressure”), and edges encode dependencies.

Each time a new signal or sensor reading comes in, the system updates the probability of various hidden faults.

Real Example: Airbus Fault Diagnosis System

Airbus uses Bayesian reasoning to assess whether unusual vibration means:

• A loose flap?

• An engine imbalance?

• Just turbulence?

Each possible cause has:

• A prior based on failure rates

• Likelihoods from sensor patterns

As new evidence arrives, the system refines its belief — just like a trained engineer would.

Why It’s Brilliant?

• Explains its reasoning: “Given symptoms A, B, and C, 70% chance it’s a fuel issue”

• Handles uncertainty gracefully

• Improves with more evidence

• Combines expert knowledge with real-time data

The Takeaway

Probability isn’t just theory — it literally keeps planes in the sky.

The fusion of domain knowledge + probabilistic reasoning leads to interpretable, reliable, life-saving systems. That’s the kind of AI I admire — and strive to build.

Another use case of probability in real world and the one I personally admire.

Diagnosing Disease with Bayesian Models

One probability concept I admire—marginal likelihood—is quietly powering some of the most critical decision systems in the real world. It's a cornerstone of Bayesian model comparison, allowing us to weigh how well different models explain observed data, while accounting for uncertainty in their parameters.

Medical Diagnosis:

Consider a scenario in diagnostic medicine where clinicians must decide between competing models for predicting the presence of a disease based on noisy biomarkers (e.g., MRI intensity, blood pressure, or lab values).

• Model A is simple, with one threshold.

• Model B includes interaction terms between biomarkers.

• Model C is more flexible, possibly overfitting noise.

If we rely on traditional metrics like maximum likelihood or cross-validation, we might favor overly complex models that fit the data well but generalize poorly. That’s where marginal likelihood comes in—it integrates over all possible parameter values, favoring models that not only fit the data but are also parsimonious.

In Bayesian diagnostics:

• Each model is assigned a prior belief.

• The marginal likelihood is computed for each based on observed patient data.

• Models with better balance between fit and complexity receive higher posterior probabilities.

This makes marginal likelihood a powerful guardrail against overfitting in life-critical applications, where interpretability, generalizability, and uncertainty all matter.

Why It Stands Out to Me?

I explored this deeply while comparing MLE vs marginal likelihood in Bayesian linear regression. It revealed a fundamental idea: a good model is not just one that fits data well, but one that admits it could be wrong. That humility baked into Bayesian modeling makes it ideal for high-stakes domains like healthcare and autonomous systems.

Here is the link to my another blog regarding this topic.