November 2022

Loss and Damage and COP27

The 27th session of the Conference of the Parties (COP27) has just concluded this morning at the Sharm El-Sheikh (Egypt) Climate Change Conference with the signing of what’s proclaimed a landmark deal, the endorsement of the “loss and damage” fund.

Governments took the ground-breaking decision to establish new funding arrangements, as well as a dedicated fund, to assist developing countries in responding to loss and damage. Governments also agreed to establish a ‘transitional committee’ to make recommendations on how to operationalize both the new funding arrangements and the fund at COP28 next year. The first meeting of the transitional committee is expected to take place before the end of March 2023.

UN Climate Press Release:

From COP 19

“Acknowledging the contribution of adaptation and risk management strategies towards addressing loss and damage associated with climate change impacts”

FCCC/CP/2013/10/Add.1: Decision 2/CP.19

Although the term, loss and damage, came inside COP books in 2013 at the COP17 in Warsaw, Poland, the push for a suitable compensation mechanism supporting vulnerable countries to endure the cost of climate change, which is predominantly inflicted by a few industrialised countries, has a long history. As per Wiki, AOSIS proposed an insurance pool as early as 1991 when United Nations Framework Convention on Climate Change (UNFCCC) was in the process of setting up.

Reference

COP27: UNFCCC

COP19 Reports: UNFCCC

Loss and damage: Wiki

Loss and Damage and COP27 Read More »

The goodness of Fit Continued

After fitting the data with the linear regression model, you determine the R-squared, which tells how good the fit is. R-squared represents how good the relationship between the model and the dependent variable is on a 0 to 1 scale.

Let’s take the previous example,

The question is: How good is the red line (model) compared to the mean?

That gives you the R-squared.
R2 = [Var(mean) – Var(line)] / Var (mean) = 1 – [ Var(line) / Var (mean)]

In the best fitting case, there is no variation around the model line and in the worst case, it is as bad as that around the mean.

The variation around the mean = sum of squares of differences between the mean and the actual data = 41.27269.

The variation around the line = sum of squares of differences between the line and the actual data = 13.7627.

Therefore, R2 = (41.27269 – 13.7627) / 41.27269 = 0.6665

Q1 <- data.frame("x" = c(10, 8, 13, 9.0, 11.0, 14.0, 6.0, 4.0, 12.0, 7.0, 5.0), "y" = c(8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68))

V_mean <- sum((Q1$y-mean(Q1$y))^2) 

V_line <- sum((Q1$y - 3 - 0.5*Q1$x)^2)

R_squared <- (V_mean - V_line) / V_mean

Not to forget: 3 + 0.5*Q1$x (Y = 3.0 + 0.5 X) is the equation of the line.

The goodness of Fit Continued Read More »

The goodness of Fit of Linear Regression

Regression models are a potential pathway to finding the relationship between dependent variables (response variable) and independent variables (predictor variables). And we have seen linear regression in the previous post. We will continue from there, focussing on a measure of the goodness of fit – the R-squared. Start with a scatter plot of an X vs Y.

The most convenient way to think about linear regression is the broken red line – which represents the best fit – on the plot. The equation of that line is the model for predicting Y from X.

In our case, we shall see soon; the formula is Y = 3 + 0.5 x X.

For the time being, you may consider that that line is drawn to balance between the dots of the scatter.

Residuals – the distances from the fit

The lengths of the lines are the residuals of each data from the regression line. Remember, if the data are purely random and independent, the histogram of the residual forms a normal distribution with a mean equal to zero.

While the line is a result of a balancing act between the residuals, it is not by minimising the distances (as in the figure above) but by minimising the sum of squares of them (the figure below).

Squares of residuals

So, the line is drawn at which the sum of the squares of the errors is minimum.

The goodness of Fit of Linear Regression Read More »

Linear Regression

Regression is a tool that enables us to find the relationship between two variables. The most commonly used one among them is linear regression, where we find the dependant variation (y) as a function of the independent variable (x) in the form of a line, y = m*x + c; m and c are constants.

A feature of regression is the term residual. A residual is a difference between the actual and predicted values (as per the equation).

Let’s use the human height vs weight dataset to understand the concept of regression. The dataset has 25,000 synthetic records of human heights and weights of 18-year-old children. These were simulated from a 1993 Growth Survey of 25,000 children from birth to 18 years of age recruited from Maternal and Child Health Centres and schools.

Now, build a linear regression between the height and the weight by running the following R code.

lm(hw_data$Weight.Pounds. ~ hw_data$Height.Inches.)

It gives the following output.


Call:
lm(formula = hw_data$Weight.Pounds. ~ hw_data$Height.Inches.)

Coefficients:
           (Intercept)  hw_data$Height.Inches.  
               -82.576                   3.083

So the equation becomes weight = 3.083 x height – 82.576. You can add the line (the regression line) to the plot by typing,

abline(lm(hw_data$Weight.Pounds. ~ hw_data$Height.Inches.))

The residuals must follow a Gaussian if the data is random and independent. Let’s get the residual and make a histogram.

hist(hw_data$Weight.Pounds. - ( -82.576  +  3.083  * hw_data$Height.Inches.), main = "", xlab = "Residual", ylab = "Frequency")

UCLA Statistics

Linear Regression Read More »

Jevons Paradox

Jevons paradox is a term associated with behavioural economics in which one, often a policymaker, expects a substantial decrease in energy consumption by replacing a lower efficiency unit with a higher one, instead finding only a marginal drop, or worse, an increase. It is also sometimes called the rebound effect.

Mexico’s C4C program

An example is a study by Davis et al. on the Cash for Coolers (C4C) program that ran in Mexico. C4C was a large-scale replacement program started in 2009 that helped ca. 1.5 million households to replace old refrigerators and air coolers with new energy-efficient (> 5% from the 2002 standard) ones. In return, the household can get up to $185 in subsidies.

A World Bank study, for example, estimated a savings of 481 kWh/y from the change out of refrigerators. In reality, Davis’ study found that the real benefit was about 11 kWh per month which translated to 11 x 12 = 132 kW/y, just over a quarter of what was originally envisaged.

Increased consumption from coolers

The air conditioner story was even more dramatic. After the substitution with the more energy-efficient ones, the overall energy consumption increased!

There can be different explanations for what happened. But one thing is clear – the implementor had made inaccurate assumptions about consumer behaviour. It is possible that in the process, the household got a chance to turn in some of the old, unused appliances in return for a subsidised new one.

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Population but No Explosion

We have covered the topic of the population a few times already. Parameters such as fertility per woman and population growth rates started their downward journey for most countries some time ago. Take the top four populous countries in the world, China, India, the US and Indonesia.

ChinaIndiaUSIndonesia
Population
growth rate (%)
(1963)		2.462.061.442.66
Population
growth rate (%)
(2019)		0.3551.010.4551.1
Child per woman
(1963)		~65.883.355.63
Child per woman
(2021)		1.662.221.892.24

8 Billionth Child

But today is a special day. The United Nations considers 15th November 2022 as the official day of the birth of the 8th billionth child. It took 11 years for the number to go from seventh billion to eighth. And it will take another 15 years to reach ninth. Based on the UN estimates, the global population will peak somewhere between 10 and 11 billion.

The question is: how reliable is this UN estimate? The answer comes from a study published in 2001 by Nico Keilman. The publication explored 16 sets of population projections by the UN between 1951 and 1998 and concluded that they did a decent job of predicting population. Following are the Mean absolute percentage error (MAPE) of those studies.

Base YearMAPE
1950I12.6
1950II11.2
1950III3.5
19601.8
19652.2
19701.5
1975I0.6
1975II0.2
1980I0.2
1980II0.2
1985I0.9
1985II0.9
1990I1.1
1990II0.6
1995I0.4
Mean absolute percentage error (MAPE) in projected total population size

References

Population forecast: Gapminder
8 billionth child: BBC
The world’s population has reached 8 B. Don’t panic: The Economist
Keilman, N., Population Studies, 2001, 55, 149

Population but No Explosion Read More »

The Happiness Formula – Experience vs Memory

We started this blog stating that the “Thoughtful Examinations” was about life, knowledge, and happiness, yet we have spent the least amount of time, so far, on the topic of happiness, but not today. Let us start with a question: what causes happiness?

Before answering the question, we will briefly consider the two kinds of experiences of happiness. As per Nobel laureate Daniel Kahneman, they are the experiencing self and remembering self. The former is about joy, or the pain someone undergoes at a given moment, and the latter is about how she remembers it later.

Kahneman’s team conducted an experiment in which he collected data from 682 patients undergoing the colonoscopy process. As you may know, a colonoscopy is not a pleasant experience. It was a randomised control test (RCT) in which the group was divided into two – the first group was called the normal, and the second was the modified.

Adding a minute of happiness

For the normal group, it was the standard colonoscopic procedure, whereas, for the modified group, the researchers added a few minutes of a non-pharmacologic intervention by extending the duration with lessened pain to the patient. The tip of the colonoscope was allowed to rest in the rectum for about 3 minutes without any suction or inflation.

The assessment used the so-called Gottman–Levenson approach: the participants (patients who authorised the researchers to collect data) got a handheld device through which one can mark the extent of pain at regular intervals, from no pain (score = 0) to extreme pain (score = 10).

The end makes a difference

The study results were evaluated on two parameters – the patient’s feedback to a questionnaire and the rate of return for a follow-up colonoscopy. The questionnaire was a retrospective evaluation of how a participant felt about the procedure. The results were significantly different from each other. The patients who received the modified treatment remembered the whole event as less painful, although the beginning, the middle part and the peak pains were comparable to both groups.

The Happiness Formula – Experience vs Memory Read More »

The Myside Bias

The last few posts covered one important aspect of our irrationality. That it is beyond the education level or other types of cognitive deficiencies, but purely ideological. The author Steven Pinker calls it the myside bias.

The Myside Bias Read More »

Partisan Bias

Who is more biased in US politics – democrats or republicans? The answer is – democrats think it’s the republicans, and the republicans think it’s the Democrats! This is what is known as partisan bias, in which the person or group of a particular political view act, interpret or promotes ideas that align with their ideological background.

There is a notion in political psychology which proposes that it is the conservatives that possess more bias in their view owing to their inability to update with changes that go around in the world. It led to the school of asymmetric partisan bias theory.

Ditto and coworkers (2019) did a meta-analysis of 51 experimental studies on the partisan bias. The studies included topics ranging from environmental to gun control, welfare to abortion. Interestingly, most of the study results showed overall biases with r values in the range of 0.2 – 0.3, which we know from an earlier post, is close to randomness. Naturally, the difference of r values between liberals and conservatives was also close to zero.

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Motivated Reasoning – Climate Change

The irrationality of the public on subjects of global impacts, such as climate change, has been explained using three dominant theories. They are 1) the scientific illiteracy theory, 2) the bounded rationality theory, and 3) the cultural cognition theory. The first assumes that most people lack the science education to understand the complex nature of global warming. The second one goes hand in hand with Kahneman’s definition of system 1 (fast) and system 2 (slow) thinking. The third one concerns the perception of risks and how they fit with an individual’s value systems.

To apply this to climate change: a familiar narrative is that the average public lacks the capacity to comprehend the science behind it and therefore resorts to some form of heuristics to understand, which is often governed by her beliefs. The name associated with this portrayal is the public irrationality thesis (PIT).

Application to climate change

Kahan et al. have applied the theory to testing. Contrary to the expectation, in his first test (N = 1540), he found that increased science literacy and numeracy did not increase the risk perception of climate change; in fact, it slightly decreased!

On the other hand, the study found that an egalitarian individual (communitarian) is more likely to have a higher risk perception of climate than a hierarchical person (individualist). It remained the same or slightly increased with her numeracy. It was striking that the hierarchical individualist did not progress her risk perception as a function of numeracy; instead, it slightly reduced!

Nuclear risk

On the other hand, to answer the question about the impact of nuclear power on human health and safety, both types of individuals showed reduced perceived risks as a function of their literacy.

Beliefs over rationality

Both these data suggest that increasing science education and numeracy is not necessarily to help detach oneself from her beliefs.

Motivated Reasoning – Climate Change Read More »