Inane Observations $ sudo fix_it
  • SciPy distribution for the odds ratio of independent beta variables

    07 October 2022 | mathematics statistics python | Comment

    In biostatistics, a common effect measure when considering dichotomous exposures and outcomes is the odds ratio. With two proportions $π_0$ and $π_1$, the odds ratio is $ψ = \frac{π_1 / (1 - π_1)}{π_0 / (1 - π_0)}$, as compared to the risk ratio,… »

  • Directly computing HDIs from PDFs in SciPy

    06 October 2022 | mathematics statistics python | Comment

    In Bayesian inference, it is often desired to calculate credible intervals for model parameters. The 2 common choices are the highest posterior density interval (HPD/HDI), and the equal-tailed interval. In many cases, the posterior density must be estimated by simulation, but in some cases the… »

  • Beta ratio distribution for SciPy

    05 October 2022 | mathematics statistics programming python | Comment

    The quotient of 2 independent beta-distributed random variables has a known distribution, but its closed-form expression is a little hairy [1, 2]. One Python implementation of this distribution is available from Julian Saffer [3], but it suffers from some numerical issues… »

  • Bayesian biostatistics procedures matching frequentist confidence intervals

    03 October 2022 (updated 15 March 2023) | mathematics statistics | Comment

    Confidence intervals are commonly misinterpreted as there being, after observing the data, a 95% probability that the true parameter lies within the confidence interval. The usual explanation why this is incorrect is that the true parameter is not random, and so is either inside or… »

  • On the credible probability of confidence intervals

    13 September 2022 | mathematics statistics | Comment

    Confidence intervals are commonly misinterpreted by consumers of statistics. Hoekstra et al. [1] presented 120 psychology researchers and 442 students with ‘a fictitious scenario of a professor who conducts an experiment and reports a 95% CI for the mean that ranges from 0.1 to… »

  • Quasi-likelihood gamma regression in statsmodels for zeroes in observations

    03 September 2022 (updated 06 September 2022) | mathematics statistics | Comment

    Generalised linear models with a gamma distribution and log link are frequently used to model non-negative right-skewed continuous data, such as costs [1].

    For example, in statsmodels:

    import numpy as np
    import pandas as pd
    from scipy import stats
    import statsmodels.api as sm
    
    #
    … »
  • Robust Poisson regression in medical biostatistics

    29 August 2022 (updated 03 September 2022) | mathematics statistics medicine | Comment

    Log-binomial and robust (modified) Poisson regression are common approaches to estimating risk ratios in medical biostatistics [1].

    I have discussed log-binomial regression in a previous post about generalised linear models. The conceptual basis for using log-binomial regression to estimate risk ratios is straightforward –… »

  • Generalised linear models for medical biostatistics

    06 November 2021 (updated 14 October 2022) | mathematics statistics medicine | Comment

    Recently, I've been doing some statistical analysis using log-binomial generalised linear models (GLMs). Resources on the topic seem to fall largely into 2 categories:

    • Assume you want to know none of the background: ‘Use a log-binomial GLM if you want a risk ratio.’1

    • Assume

    … »
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