## Bayesian Statistical Approach vs. Previous Models

How does the Bayesian statistical approach differ from previous predictive models? According to Professor Raftery, the process “…*is fairly technical. The key point is that previously the UN has taken a deterministic approach (i.e. one that yields a single number) driven by assumptions about future fertility, while our new method incorporates uncertainty and error based on past data, yielding a full range of possible outcomes, with their likelihoods.*”

## What is Bayesian Statistical Analysis?

A Bayesian approach to statistical analysis begins with a “prior distribution”, a probability distribution representing the uncertainty in a model *prior to* examining the most recently acquired data. In general, skill and expertise are required to decide on the prior distribution. Previously available census information would be reasonable data to include when constructing the prior distribution.

Collecting and analyzing the (new) data leads to the “posterior” inferences, including the predicted results and the degree of confidence.

Students of probability theory and statistics will be familiar with Bayes’ Theorem. On the left side of this equation, “P[E](H)” is the probability of the hypothesis, ‘H’, after taking into account the data from experiement ‘E’.

On the right side of the equation, “P(H)” is the unconditional probability of the basic hypothesis. “P[H](E)” is the prior probability that the Experimental data would fit the Hypothesis. “P(E)” is the basic probability of the Experimental data.

## China and India: A Steeper Decline?

Decoded Science asked why China and India are predicted to have a more steep decline in the working ratio than others, and Professor Raftery responded that it was due to, “[t]*wo reasons, fertility and migration. First, China’s fertility is lower than that of the US… India’s fertility is quite likely to go lower than that of the US in the future. Second, the US has more immigration than China or India, leading to continuing increases in the numbers of working age people.*”

## Further Notes on the New Methodology for this Population Study

Previous studies would project population change using a standard approach that predicts one estimate, but does not quantify the uncertainty of the prediction. In contrast, political polls tend to say “N% responded ‘yes’; this result has an accuracy of 95%, 19 times out of 20.”

This new model produces a low versus high estimate for a country’s population, along with the likelihood that the actual number will be in that range, taking a Bayesian statistical approach, using rates of fertility (births), mortality (deaths) and immigration or emigration.

## Implications of this Population Study

In the light of this population study, politicians and planners need to consider how to deliver health and housing services to the increasing numbers of retired seniors and the elderly; particularly as the working population is growing proportionately smaller.

**References**:

Raftery, A., Li, Sevcikova, H., Gerland, P., Heilig, G. *Bayesian probabilistic population projections for all countries*. (2012). PNAS. Accessed August 20, 2012.

Joyce, J. *Bayes’ Theorem*. The Stanford Encyclopedia of Philosophy (2008). Accessed August 20, 2012.

SAS/STAT(R).* Prior Distributions*. 9.2 User’s Guide, 2nd Edition. (2012). Accessed August 20, 2012.

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