Skip to content
Curriculum / Phase 1 · Common Quantitative Core

Probability, Statistics and Financial Data

Connect probability, statistical inference and regression to the analysis of financial data.

Why study Probability, Statistics and Financial Data?

A strong historical result may reflect a useful effect, sampling noise or a badly chosen test. Probability and statistics give you the language to separate what a dataset shows from what you can reasonably infer.

Who this is for

For future researchers, traders and risk analysts who can handle basic algebra and want to reason carefully about evidence.

What you should be able to do

  • Work with distributions, dependence and conditional expectation.
  • Use estimation, confidence intervals and hypothesis tests.
  • Analyse financial data with regression, simulation and resampling.

An example of the work this prepares you for

A short analysis of return data with an estimate, an uncertainty interval, a diagnostic and a clearly stated limitation.

Prerequisites and suggested preparation

You should be comfortable with the background covered in these programmes. Equivalent knowledge from university study or independent learning is also suitable.

A preview of the learning journey

The lessons build towards these kinds of reasoning and practical work.

Describe uncertainty

Choose a sensible model for variability and dependence.

Evaluate evidence

Interpret estimates and tests without treating significance as certainty.

Check a data result

Use simulation and diagnostics to investigate a statistical claim.

Members work through the detailed lessons, derivations, worked examples and solutions inside the learning dashboard.

Explore lesson previews by topic

Open a topic preview to see its introduction, learning objectives and prerequisites. Previous and next links let you explore the lessons in study order. Full lessons are available in the member dashboard; selected samples are free to read in full.

Topic previewProbability foundations4 lessonsTopic previewStatistical inference3 lessonsTopic previewFinancial-data methods3 lessonsTopic previewProbability Foundations5 lessonsTopic previewDiscrete Random Variables6 lessonsTopic previewContinuous Random Variables7 lessonsTopic previewMultivariate and Derived Distributions6 lessonsTopic previewLimit Theorems5 lessonsTopic previewSampling Distributions and the Normal Family6 lessonsTopic previewStatistical Models and Data Reduction6 lessonsTopic previewPoint Estimation: MOM, MLE, and Optimality Theory9 lessonsTopic previewBayesian Estimation and Posterior Inference5 lessonsTopic previewConfidence Intervals and Interval Estimation4 lessonsTopic previewNeyman-Pearson Theory and Uniformly Most Powerful Tests6 lessonsTopic previewLikelihood Ratio Tests, Wilks' Theorem, and Goodness of Fit5 lessonsTopic previewLinear Regression and Analysis of Variance7 lessons

Free resources to start learning

Use these alongside the programme or to prepare independently. Start with the introductory material, work through an example, then return to the research papers when the underlying ideas are familiar.

  1. Textbook · Free

    OpenIntro Statistics

    OpenIntro

    Start with sampling, inference and regression; the PDF can be obtained for free.

  2. Video lectures · Free

    Statistics 110: Probability on YouTube

    Harvard · Joe Blitzstein

    Watch conditional probability, expectation and limit-theorem lectures.

  3. University course · Free

    Topics in Mathematics with Applications in Finance

    MIT OpenCourseWare · 18.S096

    Connect probability and regression to financial examples.

  4. Research paper · Free

    The Probability of Backtest Overfitting

    David H. Bailey, Jonathan M. Borwein, Marcos López de Prado and Qiji Jim Zhu

    Read after inference basics to see how repeated research trials can distort evidence.

Links reviewed 14 October 2026. Free refers to the linked reading, notes or videos; printed books and certificates may cost extra.

Find more papers and learning materials in the SelfMadeQuant Directory.

Ready to study Probability, Statistics and Financial Data? Explore membership for access to the complete lessons.

Explore membership
Phase 1Financial Instruments, Markets and ConventionsStudy financial instruments, pricing conventions, funding and liquidity through a structured quant finance course.Phase 1Linear Algebra, Optimisation and Numerical MethodsStudy matrix methods, optimisation and numerical techniques for quantitative finance models and calibration.Phase 1Python for Quantitative FinanceDevelop scientific Python and financial-data skills for building, testing and delivering quantitative models.Phase 1Econometrics and Financial Time SeriesStudy regression diagnostics, financial time series, volatility and forecast evaluation with applied econometrics.