bayesian_inference_posts.txt

# Social Media Posts: Bayesian Inference
# Generated for: bayesian_inference.ipynb

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TWITTER/X (< 280 chars)
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Bayesian inference in action: Watch how your beliefs update as data arrives.

P(θ|D) = P(D|θ)·P(θ)/P(D)

100 coin flips later, all three priors converge to the truth!

#Python #Bayesian #DataScience #Statistics #Math

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BLUESKY (< 300 chars)
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Exploring Bayesian inference with the Beta-Binomial model.

Key insight: Your prior beliefs matter less as data accumulates. With 100 observations, uniform, weak, and strong priors all converge toward the true parameter θ = 0.7.

Credible intervals give direct probability statements about parameters.

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THREADS (< 500 chars)
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Just built a Bayesian inference demo and the results are fascinating!

Started with 3 different priors:
- Uniform (no assumptions)
- Weakly informative (centered at 0.5)
- Strong prior (biased toward 0.75)

After seeing 100 coin flips from a coin with true probability 0.7...

All three posteriors converged to nearly identical distributions centered around the truth!

This is why Bayesian methods are powerful: with enough data, the evidence overwhelms your prior beliefs.

The math: P(θ|D) ∝ P(D|θ)·P(θ)

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MASTODON (< 500 chars)
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Implemented Bayesian inference with Beta-Binomial conjugacy in Python.

The posterior update is elegant:
Prior: Beta(α, β)
Data: k successes in n trials
Posterior: Beta(α+k, β+n-k)

Tested with three priors and 100 Bernoulli trials (true θ=0.7). All posteriors converged, demonstrating how data overwhelms prior beliefs.

Also computed:
- 95% credible intervals
- Bayes factors for model comparison
- Posterior predictive via Beta-Binomial PMF
- Grid approximation for non-conjugate priors

#Bayesian #Statistics #Python #DataScience

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REDDIT (r/learnpython or r/datascience)
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Title: Bayesian Inference in Python: How Your Beliefs Update with Data

---

**What is Bayesian Inference?**

Unlike frequentist statistics which gives you point estimates, Bayesian inference treats parameters as random variables with probability distributions. You start with a prior belief, observe data, and update to get a posterior.

**The Core Equation (ELI5 version)**

P(θ|D) = P(D|θ) × P(θ) / P(D)

In plain English: Your updated belief equals (how likely you'd see this data if θ were true) times (your prior belief), normalized.

**What I Built**

I simulated 100 coin flips from a biased coin (true probability = 0.7) and tested three different priors:

1. **Uniform** - "I have no idea, could be anything from 0 to 1"
2. **Weakly informative** - "Probably around 0.5"
3. **Strong prior** - "I'm pretty sure it's around 0.75"

**The Cool Result**

All three posteriors converged to approximately the same answer! The uniform prior gave a posterior mean of 0.687, the weak prior gave 0.673, and even the strong prior updated to 0.684.

**Key Takeaways**

- Credible intervals are intuitive: "There's a 95% probability θ lies in [0.58, 0.79]"
- Conjugate priors (Beta-Binomial) give closed-form solutions
- Bayes factors let you formally compare models
- Grid approximation works when conjugacy isn't available

**View the full notebook:** https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/notebooks/published/bayesian_inference.ipynb

Libraries used: NumPy, SciPy, Matplotlib

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FACEBOOK (< 500 chars)
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Ever wondered how scientists update their beliefs when new evidence arrives?

I built a simulation showing Bayesian inference in action. Starting with three very different assumptions about a coin's bias, I flipped it 100 times and watched all three converge to the same answer.

The beauty of Bayesian methods: your initial assumptions matter less as evidence accumulates. The data speaks for itself.

See the full interactive notebook: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/notebooks/published/bayesian_inference.ipynb

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LINKEDIN (< 1000 chars)
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Bayesian Inference: A Computational Demonstration

I recently implemented a comprehensive Bayesian inference pipeline demonstrating key concepts in probabilistic reasoning.

**Technical Approach:**
- Implemented Beta-Binomial conjugate model for parameter estimation
- Compared prior sensitivity across uniform, weakly informative, and strong priors
- Computed 95% credible intervals with direct probabilistic interpretation
- Calculated Bayes factors for formal model comparison
- Extended to non-conjugate models via grid approximation

**Key Findings:**
With sufficient data (n=100), all three priors converged to posteriors centered near the true parameter (θ=0.7). The posterior standard deviation decreased from the prior's spread to approximately 0.04, demonstrating how Bayesian methods naturally quantify uncertainty reduction.

**Skills Demonstrated:**
- Statistical modeling (scipy.stats)
- Numerical integration
- Scientific visualization
- Mathematical derivation and implementation

The complete methodology with code is available in the interactive notebook:
https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/notebooks/published/bayesian_inference.ipynb

#DataScience #Statistics #Python #MachineLearning #Bayesian

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INSTAGRAM (< 500 chars)
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Bayesian inference visualized

Start with different beliefs.
Observe the same data.
End up at the same truth.

This plot shows how three different priors (uniform, weak, strong) all converge after seeing 100 coin flips.

The posterior distribution tells you exactly how certain you should be about the parameter.

That's the power of Bayesian thinking: evidence speaks louder than assumptions.

Swipe to see the credible intervals and sequential updating!

#DataScience #Statistics #Python #Bayesian #Math #Visualization #SciComm #CodingLife