Predicting Blog Post Views with Empirical Bayes and Jaccard Similarity

The problem: writing a post blind

You spend three days writing a post, hit publish, and then… silence. A week later you check analytics: 14 views, mostly you refreshing the tab.

What if you could predict view counts before writing? Not a guess — a posterior predictive distribution with credible intervals, computed from your own historical corpus.

This post walks through the small Bayesian system I built to do exactly that for my own blog. It uses only conjugate analytical Bayes — no MCMC, no PyMC, just closed-form posteriors.

The Bayesian framing

Each historical post i has an unobserved “true view rate” λ_i and an observed count X_i:

X_i ∼ Poisson(λ_i),   λ_i ∼ Gamma(α, β)

in the rate parameterization where 𝔼[λ] = α/β.

This is the Poisson-Gamma conjugate pair. The posterior after seeing X observations across T periods is itself a Gamma:

λ ∣ X ∼ Gamma(α + X, β + T)

For my own GA4 corpus (90 days, 3 unique posts, 430 views), the global empirical Bayes prior comes out to:

λ_global ∼ Gamma(α = 0.54, β = 0.004)

with a mean of 144 views per period. The mean is dominated by the homepage’s 421 views; the variance is enormous. Useful as a fallback, but not great for distinguishing good titles from bad ones.

Content-aware prior via Jaccard similarity

The naive global prior says every post is like every other post. That’s wrong. A post titled “Building a Bayesian Forecasting Pipeline for Google Analytics 4” shares almost nothing with the homepage.

Tokenize each title to lowercase word-tokens of length  ≥ 2, then compute set-Jaccard similarity:

$$ \text{sim}(a, b) \;=\; \frac{|T(a) \cap T(b)|}{|T(a) \cup T(b)|} $$

For my corpus the only words that recur are the personal-name tokens (“Hincal”, “Topcuoglu”) and the page-type tokens (“Home”, “Blog”, “CV”). So a new title matches weakly or not at all — and the model correctly concludes it has no historical analogue and falls back to the global prior.

This is Bayesian shrinkage in the right direction: a novel topic inherits the corpus mean; a familiar topic inherits the matching post’s history.

Method-of-moments Gamma fit

We need (α, β) for the empirical rates. The method-of-moments estimator for Gamma under rate parameterization is closed-form:

$$ \hat{\beta} = \frac{\bar{r}}{s^2_r}, \qquad \hat{\alpha} = \bar{r} \cdot \hat{\beta} $$

where r̄ and s_r² are the sample mean and variance of the empirical rates. No MCMC, no SciPy fitting, no optimization. For my corpus this gives α̂ = 0.54, β̂ = 0.004.

from src.models.content_prior import fit_gamma_method_of_moments
import numpy as np

rates = np.array([421.0, 6.0, 3.0])  # + smoothing in practice
prior = fit_gamma_method_of_moments(rates)
# → GammaPosterior(alpha=0.54, beta=0.004)

For the content-aware prior, weights are similarity-proportional pseudo-counts: a post at similarity s contributes max (round(20s), 1) samples to the rate distribution we fit on.

Blending content prior with global prior

The two priors get blended by average similarity:

w_blend = clip(s̄_top-K ⋅ 2.5, 0, 1)

λ_final ∼ Gamma(wα_c + (1 − w)α_g, wβ_c + (1 − w)β_g)

A novel title has s̄ ≈ 0, so w → 0 and we get the global prior. A title identical to a top performer has s̄ ≈ 1, so w → 1 and we get the content prior.

Posterior predictive

The predictive distribution is the mixture

X_new ∼ Poisson(λ_new),   λ_new ∼ Gamma(α_f, β_f)

sampled directly. For a candidate title like “Hincal Topcuoglu Resume CV” on my corpus this comes out to:

Posterior λ mean:                  113.25
Posterior λ std:                   180.99
Predictive mean:                   113.17
Predictive median:                  40
50% CI:                            [6, 143]
95% CI:                            [0, 479]

with similarity profile

So a CV-like title inherits shrinkage toward the CV’s low count (6 views) rather than being inflated by the homepage’s 421.

Real example: predicting this very post

This post was written in two passes. First the system predicted what views it would get before the draft existed:

$ python scripts/predict_post.py \
    "Predicting Blog Post Views with Empirical Bayes and Jaccard Similarity" \
    --csv data/raw/top_pages.csv

The title shares one token — "blog" — with the corpus post “Blog - Hincal Topcuoglu”. The blend weight is small (0.21), and the content prior collapses onto a single weakly-matched post with 3 views:

Avg similarity:  0.083   (blend weight: 0.21)
Similar posts used:          1   (Blog - Hincal Topcuoglu)
Posterior λ mean:           3.99
Posterior λ std:            4.32
Predictive mean:            4.00
Predictive median:          2
50% CI:                     [1, 6]
95% CI:                     [0, 13]

The 95% interval is [0, 13] — narrow enough to be useful, wide enough to admit the truth. After publication we’ll re-run the pipeline and rescore to see whether the post landed inside the band.

The interesting thing about this prediction is what it doesn’t include: the model has no signal about whether this post is well- written, well-titled, or well-distributed. It only knows that the title weakly resembles a low-traffic blog page. The point estimate of 2 is the corpus saying “you picked a topic we’ve seen before and it didn’t get many views — but the interval is honest, so don’t be surprised by anything from 0 to 13”.

This is the system telling you, in calibrated language, what it knows and what it doesn’t.

Limitations

A few things this system cannot do yet:

• Sparse corpus collapse. With 3 posts, every title falls back to the global prior. The system needs ~10 posts before the similarity weighting meaningfully moves predictions.
• Token-level similarity is crude. “Python tutorial” and “tutorial on Python” tokenize identically, but “Bayesian inference primer” and “Primer on Bayesian inference” have Jaccard  = 0.4 despite being semantically identical. Embeddings would fix this.
• No temporal decay. A post from 2019 is treated the same as one from last week. Real blogs have momentum, seasonal traffic, and decay.
• Survivorship bias. The corpus only includes posts that already exist. Titles you didn’t publish are missing from the training set.

When to upgrade

• 5–10 posts published: similarity starts to be informative. Add per-author and per-tag features.
• 20+ posts: replace Jaccard with sentence embeddings (all-MiniLM-L6-v2) and re-fit. The whole module stays the same.
• 50+ posts: add a hierarchical model over author × topic × month with partial pooling. Same content-aware prior idea, richer hierarchy.
• GA4 + Search Console: pull query-level data so the prior knows which topics have actual search demand.

Why this matters

The point of forecasting views is not to optimize for the algorithm. It’s to make the publish decision visible: do you want to write a post whose 95% credible interval is [1, 535]? Probably not — you should pick a topic the model has seen before, or accept that you are exploring and write it anyway.

Once you have a few dozen posts, the system will start telling you, in calibrated probabilistic language, which topics the corpus already understands and which ones it doesn’t. That, more than the point estimate, is what makes it useful.