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rom Biology to Data Science: How ABC Changes the Game of Statistical Inferenc
With the rapid advancement of data science, traditional statistical methods face more and more challenges. All this has changed thanks to a method called Approximate Bayesian Computation (ABC). ABC provides a new mode of thinking that not only enables complex models to perform statistical inferences, but also improves the flexibility and accuracy of research.
Approximate Bayesian computing is a computational method built on Bayesian statistics that aims to estimate the posterior distribution of model parameters.
In traditional model inference, the likelihood function is of utmost importance because it directly expresses the probability of observing data under a specific statistical model. However, for some complex models, it is often very difficult to obtain an analytical expression for the likelihood function. Therefore, traditional methods fall into the dilemma of "too high computational cost". The ABC method does not require explicit evaluation of the likelihood function, which enables it to expand the scope of applicability of statistical inference and focus on modeling flexibility.
The roots of the ABC method can be traced back to the 1980s. At that time, scholar Donald Rubin first introduced the concept that this conceived sampling mechanism could derive samples from the posterior distribution. Although the early idea was little more than a conceptual thought experiment, it paved the way for the later ABC approach. With the in-depth development of the ABC method, more and more scholars have begun to apply it to the analysis of multiple complex problems in biological sciences, especially in the fields of population genetics, ecology and epidemiology.
The so-called approximate Bayesian calculation can actually be understood as a Bayesian version of indirect inference.
In the ABC method, researchers use simulation instead of calculating the likelihood function. This process involves drawing parameter points from the prior distribution and then generating data under the specified model. If the generated data differs too much from the observed data, the parameter point is discarded. This approach subverts the process of traditional inference and provides new possibilities for many complex models.
A typical ABC algorithm is the ABC rejection algorithm, whose core idea is to accept or reject sample parameters based on the distance between simulated data and observed data. This algorithm is particularly suitable for high-dimensional data scenarios, because directly calculating the likelihood function of high-dimensional data is often computationally expensive. ABC alleviates this challenge to some extent by introducing summary statistics, making the inference process more efficient.
Informative but potentially inadequate summary statistics are often used in the application of the ABC method.
For example, in biology, Hidden Markov Models (HMMs) are widely used to describe the dynamic behaviors in biological systems. For example, when studying the role of the Sonic hedgehog (Shh) transcription factor in Drosophila, the ABC method can accurately estimate the parameters that affect state transitions. This not only improves the accuracy of research, but also expands our understanding of how biological systems work.
In general, the importance of approximate Bayesian computing as a statistical inference tool cannot be ignored. With the rapid development of data science, we should think: Will future data analysis rely more on these innovative methods to solve current and future complex problems?
