Category Archives: Statistics

5th Artificial Intelligence in Chemistry Symposium

The lineup for the Royal Society of Chemistry’s 5th “Artificial Intelligence in Chemistry” Symposium (Thursday-Friday, 1st-2nd September 2022) is now complete for both oral and poster presentations. It really is a fantastic selection of topics and speakers and it is clear this event is now a highlight of the scientific calendar. Our very own Prof. Charlotte M. Deane, MBE will be giving a keynote.

5th RSC-BMCS/RSC-CICAG Airtificial Intelligence in Chemistry Symposium, 1st-2nd September, Churchill College, Cambridge + Zoom broadcast.

It marks a return to in-person meetings: it will be held at Churchill College, Cambridge, with a conference dinner at Trinity Hall.

More details are here: https://www.rscbmcs.org/events/aichem22/.

Registration for in person attendance is open until Monday 29th August 17:00 (BST).

It is also possible to register for virtual attendance; the meeting will be broadcast on Zoom.

Benford’s law and OAS

Benford’s law is an observation that in numerical data (produced by many kinds of process), the leading digit tends to be small. Wikipedia tells you that it in datasets obeying Benford’s law, the number 1 appears as the leading digit about 30% of the time while 9 appears less than 5% of the time (p(n) = log10(1+1/n) where n is the leading digit). Wikipedia further lists multiple kinds of data where this tends to be true such as electricity bills, population numbers and physical and mathematical constants, and particularly where data can be described by a power law.

Power laws and antibodies have been co-discussed in reference to network descriptions of antigen-experienced BCR repertoires [1], which are often described as scale-free to use the network terminology (following a power law). This means a few highly-connected nodes in the network and lots of nodes with few or no connections. This is an obvious candidate for Benford’s law.

This is of no practical relevance, but I wondered if I could see Benford’s law in other kinds of data besides clone counts in the Observed Antibody Space (OAS). For example, I looked at the leading digit in the number of sequences in all of the data units in OAS. It looks like a good fit for Benford’s law (though with more density at the smaller leading digits) and has a chi-squared value of 0.007 (Figure 1A).

Continue reading

Why can a man not lift himself by pulling up on his bootstrap hypothesis test?

This blogpost highlights a typical mistake when performing the bootstrap hypothesis test. Bootstrapping is a method of resampling data to estimate measures of variability, such as confidence intervals or variance. 

In the simplest form of the bootstrap, assume you have a set of values 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. You want to estimate the mean and variability of the mean using these data. The recipe is as follows:

Continue reading

Non-linear Dependence? Mutual Information to the Rescue!

We are all familiar with the idea of a correlation. In the broadest sense of the word, a correlation can refer to any kind of dependence between two variables. There are three widely used tests for correlation:

  • Spearman’s r: Used to measure a linear relationship between two variables. Requires linear dependence and each marginal distribution to be normal.
  • Pearson’s ρ: Used to measure rank correlations. Requires the dependence structure to be described by a monotonic relationship
  • Kendall’s 𝛕: Used to measure ordinal association between variables.

While these three measures give us plenty of options to work with, they do not work in all cases. Take for example the following variables, Y1 and Y2. These might be two variables that vary in a concerted manner.

Perhaps we suspect that a state change in Y1 leads to a state change in Y2 or vice versa and we want to measure the association between these variables. Using the three measures of correlation, we get the following results:

Continue reading

Monty Python

Every now and then I decide to overthink a problem I thought I understood and get confused – last week, it was the Monty Hall problem. 

For those unfamiliar with the thought experiment, the basic premise is that you are on a game show and are presented with three doors. Behind one of the doors is a car, while behind the other two are goats. 

With zero initial information, you make a guess as to which door you think the car is behind (we assume you have enough goats already). Before looking behind your chosen door, the host opens one of the remaining two doors and reveals a goat. The host then asks you if you would like to change your guess. What should you do? 

Continue reading

Multiple Testing: What is it, why is it bad and how can we avoid it?

P-values play a central role in the analysis of many scientific experiments. But, in 2015, the editors of the Journal of Basic and Applied Social Psychology prohibited the usage of p-values in their journal. The primary reason for the ban was the proliferation of results obtained by so-called ‘p-hacking’, where a researcher tests a range of different hypotheses and publishes the ones which attain statistical significance while discarding the others. In this blog post, we’ll show how this can lead to spurious results and discuss a few things you can do to avoid engaging in this nefarious practice.

The Basics: What IS a p-value?

Under a Hypothesis Testing framework, a p-value associated with a dataset is defined as the probability of observing a result that is at least as extreme as the observed one, assuming that the null hypothesis is true. If the probability of observing such an event is extremely small, we conclude that it is unlikely the null hypothesis is true and reject it.

But therein lies the problem. Just because the probability of something is small, that doesn’t make it impossible. Using the standard significance test threshold of 0.05, even if the null hypothesis is true, there is a 5% chance of obtaining a p-value below the significance threshold and therefore rejecting it. Such false positives are an inescapable part of research; there’s always a possibility that the subset you were working with isn’t representative of the global data and sometimes we take the wrong decision even though we analysed the data in a perfectly rigorous fashion.

Continue reading

Former OPIGlets – where are they now?

Since OPIG began in 2003, 53 students* have managed to escape. But where are these glorious people now? I decided to find out, using my best detective skills (aka LinkedIn, Google and Twitter).

* I’m only including full members who have left the group, as per the former members list on the OPIG website

Where are they?

Firstly, the countries. OPIGlets are mostly still residing in the UK, primarily in the ‘golden triangle’ of London, Oxford and Cambridge. The US comes in second, followed closely by Germany (Note: one former OPIGlet is in Malta, which is too small to be recognised in Geopandas so just imagine it is shown on the world map below)

Continue reading

2021 likely to be a bumper year for therapeutic antibodies entering clinical trials; massive increase in new targets

Earlier this month the World Health Organisation (WHO) released Proposed International Nonproprietary Name List 125 (PL125), comprising the therapeutics entering clinical trials during the first half of 2021. We have just added this data to our Therapeutic Structural Antibody Database (Thera-SAbDab), bringing the total number of therapeutic antibodies recognised by the WHO to 711.

This is up from 651 at the end of 2020, a year which saw 89 new therapeutic antibodies introduced to the clinic. This rise of 60 in just the first half of 2021 bodes well for a record-breaking year of therapeutics entering trials.

Continue reading

How do I do regression when my predictors have multicollinearity?

A quick summary of the key idea of principal components regression (PCR), its advantages and extensions.

Sometimes we find ourselves in a dire situation. We have measured some response y and a set of predictors W. Unfortunately, W is a wide but short matrix, say 10×100 or worse 10×100000. We’ve made only 10 observations. Standard regression is simply not going to work, because W is singular. Some would say p is bigger than n.

So what can we do? Many of us would jump to LASSO or ridge regression. However, there is another way that is often overlooked.

Continue reading