Chapter 9

Probability and Likelihood

9.1

The Notion of Probability

In everyday speech, statements such as “probably the train will be late” or “probably

it will be foggy tomorrow” have the character of judgements. Formally, however

(i.e., in the sense used throughout this book), probabilities do not refer to judgments,

but to possible results (outcomes) of an experiment. These outcomes constitute the

“sample space”. ¹ For example, attributing a probability of 0.6 to an event means that

the event is expected to occur 60 times out of 100. This is the “frequentist” concept

of probability, based on random choices from a defined population.

The frequentist concept is sometimes called the “objective” school of thought:

The probability of an event is regarded as an objective property of the event (which

has occurred), measurable via the frequency ratios in an actual experiment. Histor-

ically, it has been opposed by the “subjective” school, ² which regards probabilities

as expressions of human ignorance; the probability of an event merely formalizes

the feeling that an event will occur, based on whatever information is available. ³ The

purpose of theory is then merely to help in reaching a plausible conclusion when

there is not enough information to enable a certain conclusion to be reached. A pil-

lar of this school is Laplace’s Principle of Insufficient Reason: Two events are to

be assigned equal probabilities if there is no reason to think otherwise. Under such

circumstances, if information were really lacking, the objectivist would refrain from

attempting to assign a probability.

These differing schools have a bearing on the whole concept of causality, and

it may be useful to recall here some remarks of Max Planck. ⁴ One starts with the

1 Called Merkmalraum (“label space”) in von Mises’ (1931) treatise Wahrscheinlichkeitsrechnung.

2 Its protagonists include Laplace, Keynes, and Jeffreys.

3 According to J. M. Keynes, probability is to be regarded as “the degree of our rational belief in a

proposition”.

4 Made during the 17th Guthrie Lecture to the Physical Society in London (Planck 1932).

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J. Ramsden, Bioinformatics, Computational Biology,

https://doi.org/10.1007/978-3-030-45607-8_9

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