Mini-Projects and Self-Checks: Reproducible Workflows, Error Bars, and Evidence-Based Conclusions

Why mini-projects and self-checks matter in data-driven astronomy

In astronomy, you rarely get to “rerun the universe” to verify a result. Your credibility comes from showing that (1) your workflow is reproducible, (2) your uncertainties are quantified and propagated, and (3) your conclusions are tied to evidence rather than intuition. Mini-projects are small, complete investigations that force you to practice this end-to-end discipline. Self-checks are built-in tests that catch common failure modes: unit mistakes, selection bias, overfitting, and underestimated error bars.

This chapter focuses on how to structure reproducible workflows, how to attach meaningful error bars to derived quantities, and how to write evidence-based conclusions that remain valid when assumptions are challenged. The goal is not to introduce new measurement techniques already covered elsewhere, but to help you package and validate the techniques you already know into reliable scientific outputs.

Reproducible workflows: making your analysis rerunnable and auditable

What “reproducible” means in practice

A reproducible workflow is one where another person (or future you) can start from the same raw inputs and obtain the same outputs (tables, plots, fitted parameters) with minimal ambiguity. In practice, reproducibility requires that you control four things: inputs, code, environment, and randomness.

• Inputs: the exact data files, query parameters, and any manual selections.
• Code: scripts or notebooks that transform inputs into outputs.
• Environment: library versions, settings, and system assumptions.
• Randomness: seeds for any stochastic step (bootstrap, MCMC, random splits).

A minimal reproducible project structure

Use a consistent folder layout so that every mini-project looks the same. This reduces cognitive load and makes it easier to review your own work.

project_name/  README.md  environment.txt  data/    raw/    processed/  notebooks/  src/  results/    figures/    tables/  logs/

• README.md states the question, dataset provenance, and how to run the analysis.
• environment.txt (or requirements.txt) pins package versions.
• data/raw is read-only; never edit raw files.
• data/processed contains cleaned subsets with documented steps.
• src contains reusable functions (loading, fitting, plotting).
• results stores final artifacts that support claims.
• logs stores run metadata (timestamp, git commit hash, seed).

Step-by-step: turning a notebook into a reproducible pipeline

Notebooks are great for exploration, but they can hide execution order issues. Convert the final analysis into a linear script or a “run-all” notebook that produces outputs from scratch.

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• Step 1: Freeze the question. Write a one-sentence research question and define the primary output (e.g., a parameter estimate with uncertainty, a classification, or a comparison).
• Step 2: Identify inputs. List every file, query, and constant you used. If you downloaded data, store it in data/raw and record the source and retrieval date.
• Step 3: Parameterize choices. Put thresholds (quality cuts, bin sizes, smoothing windows) into a configuration block at the top of the script so they are visible and editable.
• Step 4: Make the run deterministic. Set a random seed once and pass it through any function that uses randomness.
• Step 5: Separate stages. Use functions like load(), clean(), fit(), validate(), report(). Each returns explicit outputs.
• Step 6: Save intermediate products. Save cleaned tables and fitted results with metadata so you can inspect them without rerunning everything.
• Step 7: Record provenance. Save a small JSON or text file with: data filenames, code version, seed, and key parameters.

Self-checks for reproducibility

Build quick checks that run every time and fail loudly when something is off.

• Row counts and missing values: after cleaning, assert expected ranges (e.g., “no negative fluxes after background subtraction” if that should be true).
• Units sanity: assert plausible bounds (e.g., periods must be positive; magnitudes within expected survey limits).
• Idempotence: running the cleaning step twice should not change the processed output.
• Plot regression: save a key diagnostic plot and compare against a reference (even visually) after changes.

Error bars that mean something: uncertainty propagation and model checking

What an error bar should communicate

An error bar is not decoration; it is a quantitative statement about what values are consistent with your data and assumptions. A useful error bar answers: “If I repeated the measurement process under the same conditions, how much would the result vary?” In mini-projects, you should always state what your uncertainty includes (measurement noise, calibration uncertainty, model uncertainty) and what it does not include (unknown systematics, unmodeled astrophysical variability).

Three common ways to estimate uncertainties in derived results

• Analytic propagation: use partial derivatives to propagate uncertainties through a formula. Best for simple transformations and when errors are small and approximately symmetric.
• Monte Carlo propagation: draw many realizations of inputs from their uncertainty distributions, compute the derived quantity each time, and summarize the distribution. Best when formulas are nonlinear or errors are asymmetric.
• Resampling (bootstrap/jackknife): resample data points to estimate how sensitive your result is to the sample. Best for statistics like medians, percentiles, or fits where analytic errors are hard.

Step-by-step: Monte Carlo uncertainty propagation (template)

This pattern is broadly useful: you already have measured values with uncertainties, and you compute a derived quantity. The Monte Carlo approach makes the uncertainty transparent and robust.

• Step 1: Define inputs and their distributions. For each measured input x with uncertainty sigma_x, choose a distribution (often Gaussian) unless you have a better reason.
• Step 2: Draw samples. Generate N samples for each input (e.g., N = 10,000).
• Step 3: Compute derived quantity. For each sample set, compute y = f(x1, x2, ...).
• Step 4: Summarize. Use the median as a robust central value and the 16th–84th percentile range as a 1-sigma equivalent interval.
• Step 5: Visualize. Plot the distribution of y and check for skewness or multimodality (a warning sign that your model or assumptions may be incomplete).

# Pseudocode template (language-agnostic)seed = 123N = 10000x_samples = Normal(mean=x, sd=sigma_x, size=N)z_samples = Normal(mean=z, sd=sigma_z, size=N)y_samples = f(x_samples, z_samples)y_med = median(y_samples)y_lo, y_hi = percentile(y_samples, [16, 84])

When error bars are misleading: systematics and model mismatch

Many “too precise” results come from ignoring systematics or using a model that does not match the data-generating process. Your mini-project should include at least one diagnostic that tests whether the model is plausible.

• Residual checks: after fitting, plot residuals versus time, wavelength, magnitude, or any predictor. Structure in residuals indicates missing physics or incorrect assumptions.
• Outlier sensitivity: recompute the result after removing the top 1–2% most influential points (or using a robust loss). If the answer changes dramatically, your uncertainty should reflect that fragility.
• Alternative reasonable choices: vary a key threshold (quality cut, bin size) within a plausible range and see if the conclusion holds.

Self-check: uncertainty budget table

For each derived quantity, write a small uncertainty budget: list the dominant sources and how you estimated them. This forces you to acknowledge what you are and are not accounting for.

Quantity: Q (units)Central value: ...Statistical uncertainty: ... (method: Monte Carlo / analytic / bootstrap)Calibration uncertainty: ... (assumption: ...)Model uncertainty: ... (comparison: model A vs model B)Notes: dominant term is ...

Evidence-based conclusions: claims that survive scrutiny

Separating results, interpretation, and assumptions

A strong mini-project write-up separates three layers:

• Result: a measured or inferred quantity with uncertainty (what the data support directly).
• Interpretation: what the result suggests physically (requires a model or context).
• Assumptions: conditions under which the interpretation is valid (selection criteria, model form, priors, calibration).

This separation prevents a common failure: presenting an interpretation as if it were a direct measurement. It also makes it easier to revise the interpretation if a later self-check reveals a systematic effect.

Writing claims with “strength labels”

Use language that matches the evidence. A practical approach is to label claims implicitly by what you have tested.

• Measured: “We estimate X = ... ± ... (statistical) with ... systematic.”
• Supported: “The data favor model A over model B by ... (metric).”
• Consistent with: “The result is consistent with ... within uncertainties.”
• Suggestive: “There is a hint of ... but it is sensitive to ... and requires more data.”

Self-check: the “one-plot, one-number” test

For each main claim, require:

• One number: the key estimate with uncertainty (or a difference with uncertainty).
• One plot: a diagnostic that shows the data and the model/summary (with residuals if applicable).

If you cannot attach a number and a plot, the claim is probably too vague or not supported by your analysis.

Mini-project 1: Build a fully reproducible analysis report from a small dataset

Goal

Practice turning an exploratory analysis into a rerunnable pipeline that produces the same outputs every time and records provenance.

Inputs

Use any small astronomical table you already worked with (a few thousand rows is enough). The content is less important than the workflow discipline.

Step-by-step

• Step 1: Define deliverables. Decide on exactly three outputs: (a) a cleaned table, (b) one figure, (c) one results table with at least one derived quantity and uncertainty.
• Step 2: Create the project structure. Use the folder layout shown earlier. Place the raw data in data/raw.
• Step 3: Write a single entry-point script. Example: src/run_all.py that calls each stage in order.
• Step 4: Implement cleaning with explicit rules. Every filter should be documented in code comments and mirrored in the README (e.g., “remove rows with missing parallax” is a rule; “remove suspicious points” is not a rule unless you define “suspicious”).
• Step 5: Add self-check assertions. Include at least five assertions: row count after cleaning, no NaNs in key columns, plausible value ranges, monotonic time ordering if relevant, and a check that output files were written.
• Step 6: Save provenance. Write a small file like logs/run_metadata.json containing timestamp, seed, and key parameters.
• Step 7: Rerun from scratch. Delete data/processed and results, rerun, and verify identical outputs (hashes match or values match within floating-point tolerance).

Self-check rubric

• Can someone else run your project with one command and get the same figures?
• Are all thresholds and constants visible and documented?
• Does the pipeline fail early when inputs are missing or malformed?

Mini-project 2: Error bars on a derived quantity using two independent methods

Goal

Compute uncertainty on a derived result using (1) analytic propagation and (2) Monte Carlo, then compare. The comparison itself is a self-check: if the two disagree strongly, you likely have nonlinearity, asymmetry, or a violated assumption.

Step-by-step

• Step 1: Choose a derived quantity. Pick something that depends on at least two measured inputs (e.g., a ratio, a difference, a log transform, or a quantity computed from a fitted parameter).
• Step 2: Compute the central value. Use the best estimates of inputs.
• Step 3: Analytic uncertainty. Write y = f(x, z) and compute sigma_y using partial derivatives: sigma_y^2 ≈ (∂f/∂x)^2 sigma_x^2 + (∂f/∂z)^2 sigma_z^2 (include covariance if you have it).
• Step 4: Monte Carlo uncertainty. Use the sampling template to generate y_samples and compute percentile intervals.
• Step 5: Compare and explain. If Monte Carlo gives asymmetric intervals, report them. If analytic and Monte Carlo differ, identify why (nonlinearity, bounds, skewed inputs, correlations).
• Step 6: Report an uncertainty budget. Quantify which input dominates the uncertainty by repeating Monte Carlo with one uncertainty set to zero at a time.

# Sensitivity check ideafor each input i:  set sigma_i = 0, keep others unchanged  run Monte Carlo  record resulting width of y interval

Self-check rubric

• Do your reported intervals match the shape of the sampled distribution?
• Did you state whether you assumed independence or included covariance?
• Can you identify the dominant uncertainty source?

Mini-project 3: Robustness checks that protect against overconfident conclusions

Goal

Demonstrate that your main claim is stable under reasonable alternative choices, or else quantify how fragile it is.

Step-by-step

• Step 1: Identify one “knob.” Choose a decision that could plausibly change the result: quality cut threshold, outlier rejection rule, bin size, smoothing parameter, or model order.
• Step 2: Define a reasonable range. Example: vary a threshold across 5–10 values that are all defensible.
• Step 3: Rerun the pipeline for each setting. Automate this with a loop that writes outputs to separate subfolders (e.g., results/knob_sweep/).
• Step 4: Summarize stability. Plot the key result (with error bars) versus the knob value. If the result changes more than the stated uncertainty, your uncertainty is incomplete or your method is sensitive.
• Step 5: Choose a reporting strategy. Either (a) pick a default setting and include a systematic uncertainty term based on the sweep, or (b) report a range of plausible results rather than a single number.

Self-check rubric

• Does your claim hold across the entire reasonable range?
• If not, did you downgrade the claim language (e.g., from “measured” to “suggestive”)?
• Did you record the knob range and rationale in the README?

Mini-project 4: Evidence-based model comparison with transparent diagnostics

Goal

Compare two plausible models for the same dataset and justify which is better supported, using diagnostics rather than preference.

Step-by-step

• Step 1: Define two models. They should be meaningfully different but both plausible (e.g., linear vs quadratic trend; single-component vs two-component; constant vs variable).
• Step 2: Fit both models using the same data and weighting. Ensure consistent handling of uncertainties.
• Step 3: Compute comparison metrics. Use at least two: a goodness-of-fit measure (e.g., reduced chi-square if appropriate) and a predictive check (e.g., cross-validated error or holdout error).
• Step 4: Inspect residuals. A model can have a decent scalar metric but still show structured residuals that indicate mismatch.
• Step 5: Report the decision with uncertainty. If the metrics are close, say so and avoid overstating. If one model clearly reduces structured residuals and improves predictive error, state that as evidence.

# Predictive self-check ideaSplit data into train/test (or use K-fold CV)Fit model on trainPredict on testCompute error distributionRepeat with fixed seed for reproducibility

Self-check rubric

• Did you use the same preprocessing for both models?
• Did you avoid choosing a model solely because it “looks nicer”?
• Did you include a residual plot for each model?

Mini-project 5: A “claim audit” checklist for your final write-up

Goal

Turn your analysis into a short report where every claim is traceable to an output artifact and every artifact is reproducible.

Step-by-step

• Step 1: List claims. Write 3–5 bullet claims you want to make.
• Step 2: Attach evidence. For each claim, link one figure and one number (with uncertainty) from your results folder.
• Step 3: Attach assumptions. For each claim, list the top 2–3 assumptions that could break it (e.g., independence of errors, calibration stability, sample representativeness).
• Step 4: Attach robustness checks. For each claim, list at least one self-check you ran (knob sweep, outlier sensitivity, alternative model).
• Step 5: Rewrite claim language. If a claim depends strongly on an assumption you did not test, soften it to “consistent with” or “suggestive.”

Claim: ...Evidence number: ... ± ...Evidence plot: results/figures/...Assumptions: (1) ... (2) ...Robustness check: ...Status: measured / supported / consistent / suggestive

Common failure modes and how self-checks catch them

Failure mode: hidden data leakage

If you tune parameters using the same data you later use to evaluate performance, you will overestimate how well your method works. Self-check: enforce a strict separation between tuning and evaluation (holdout set or cross-validation), and record the split seed.

Failure mode: underestimated uncertainties from correlated errors

Many astronomical datasets have correlations (time-correlated noise, shared calibration terms). If you treat correlated errors as independent, your error bars can be too small. Self-check: examine residual autocorrelation (for time series) or compare scatter in binned residuals to expectations.

Failure mode: selection effects disguised as “cleaning”

Quality cuts can change the population you are analyzing. Self-check: report how many points were removed and compare distributions before/after cleaning for key variables.

Failure mode: overfitting with flexible models

More parameters can always fit noise better. Self-check: use predictive checks (cross-validation) and residual structure rather than relying only on in-sample fit quality.

Failure mode: irreproducible randomness

Bootstrap intervals or random splits can change each run. Self-check: set and record seeds; rerun twice and confirm identical outputs.