# Forecasting the effective date of the TPNW

This article was created to share a statistical forecast of the date of effectiveness of the United Nations Treaty on the Prohibition of Nuclear Weapons and invite related commentary, encouraging contributors to “be bold but not reckless,” subject to the Wikimedia standards of writing from a neutral point of view, citing credible sources, and raising other questions and concerns on the associated '“Discuss”' page.
Figure 1. Date of the 50th ratification of the UN Treaty on the Prohibition of Nuclear Weapons (TPNW). Until the 50th ratification (or acceptance, approval, or accession), this will be a forecast, obtained as discussed in this article. The treaty becomes effective 90 days after the 50th ratification.

This article was created to share updates on a forecast for the effective date of the United Nations Treaty on the Prohibition of Nuclear Weapons (TPNW) and to invite related commentary. Figure 1 forecasts the date on which the 50th acceptance, approval, ratification, or accession will be filed with the United Nations Treaty Collection.[1] The time between acceptances, etc., has averaged just over 25 days. With this the date on which the 50th acceptance, etc., will be officially filed is the current date plus the product of the number of additional countries needed and the average time between acceptances, etc. The treaty becomes effective 90 days after the 50th ratification.

As of 2020-09-08 there have been 42 ratifications and 2 accessions.[2] For simplicity, in the rest of this article, we use the term “ratification” to mean acceptance, approval, ratification, or accession.

This changes every day. Each new ratification impacts this forecasted effective date in two ways. Most obviously, it reduces the number of additional countries needed. More subtly, it also reduces slightly the average time between ratifications. Conversely, each day that passes without an additional ratification increases very slightly the average time between ratifications.

This article provides space for news updates on efforts to convince the governments of different countries to ratify the TPNW. This is followed by a brief discussion of the statistical theory and the computational methodology supporting the creation and updating of Figure 1.

## News

Anyone with relevant news on an effort to get another country to ratify[3] the TPNW is invited to post a brief note here, with a reference where further information about that can be found. Substantive advances may also be cited in the companion Wikipedia article on the Treaty on the Prohibition of Nuclear Weapons.

## Methodology

We discuss here the statistical methodology used to compute and update Figure 1. We also discuss the information technology used.

### Statistical theory

The time between acceptances, etc., of the TPNW is an example of a renewal process. The simplest renewal process assumes that this renewal time is exponentially distributed, which we assume.

An obvious deficiency with the exponential distribution for this case is that it assumes it is essentially impossible for multiple nations to deposit their acceptances, etc., at the same time. In fact, 15 of the first 44 countries to accept, etc., the TPNW did so in 4 clusters:

Dates with multiple countries officially depositing acceptance, approval, ratification, or accession
date countries
2017-09-20 3: Guyana, Holy See, Thailand
2018-09-26 4: Gambia, Samoa, San Marino, Vanuatu
2019-09-26 5: Bangladesh, Kiribati, Lao People's Democratic Republic, Maldives, Trinidad and Tobago
2020-08-06 3: Ireland, Nigeria, Niue

However, it is commonly said that, “All models are wrong, but some are useful.” The exponential assumption seems more than adequate for present purposes.[4]

With these assumptions, standard theory for censored estimation of the mean of the exponential distribution with ${\displaystyle k}$ ratifications is that we've observed ${\displaystyle (k-1)}$ times between ratifications plus a censoring time for the ${\displaystyle (k+1)}$st ratification. With this the

mean time between ratifications (MTBR) = (time from the first ratification to today) / ${\displaystyle (k-1)}$

As of 2020-09-08, this MTBR is 25.21 days. If another day passes without another ratification, this average will increase by 1/43 = 0.023 days. If one more country officially deposits their ratification documents tomorrow, this average will decrease by roughly 0.6 days.

### Information technology

This methodology is documented in an RMarkdown vignette that will be added to the Ecfun[5] package for R (programming language). From there it will be accessible via the development version of Ecfun on GitHub and eventually via the Comprehensive R Archive Network.

This vignette reads the web page for the Treaty on the Prohibition of Nuclear Weapons[6] on the website of the United Nations, scrapes the table of signatories and ratifications from that, and recomputes Figure 1. That updated figure is then manually uploaded to Wikimedia Commons, replacing the previous version of Figure 1. After that is done, any refresh or new visit to this article will access the updated figure.

## Notes

1. United Nations Treaty CollectionWikidata Q443104.
2. The accessions are the Cook Islands and Niue.
3. In this article, the term “ratify” is to be interpreted as either accept, approve, ratify, or accede to the TPNW. The difference is important for some purposes but seemingly not for this.
4. Other assumptions might produce slightly more accurate predictions. However, the improvement apparent from considering an apparently better model is accompanied by a concomitant increase in the variance of parameter estimates. Even better models might be achieved by Bayesian model averaging (BMA). However, that hardly seems worth the effort for present purposes.
5. Spencer Graves (4 February 2020), Ecfun: Functions for EcdatWikidata Q56452538.