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In statistical hypothesis testing, the error-exponent of a hypothesis testing procedure is the rate at which the error probability of a test decays exponentially with the number of samples used in the test. For example, if the probability of error $$P_{\mathrm{error}}$$ of a test decays as $$e^{-n \beta}$$, where $$n$$ is the sample size, the error exponent is $$\beta$$.

Formally, the error-exponent of a test is defined as the limiting value of the ratio of the negative logarithm of the error probability to the sample size for large sample sizes: $$\lim_{n \to \infty}\frac{- \ln P_{\mathrm{error}}}{n}$$. Error-exponents for different hypothesis tests are computed using results from large deviations theory.

Error-exponents in binary hypothesis testing
Consider a binary hypothesis testing problem in which observations are modeled as independent and identically distributed random variables under each hypothesis. Let $$ Y_1, Y_2, \ldots, Y_n $$ denote the observations. Let $$ f_0 $$ denote the probability density function of each observation $$Y_i$$ under the null hypothesis $$H_0$$ and let $$ f_1 $$ denote the probability density function of each observation $$Y_i$$ under the alternate hypothesis $$H_1$$.

In this case there are two possible error events. Error of type 1 occurs when the null hypothesis is true and it is wrongly rejected. Error of type 2 occurs when the alternate hypothesis is true and null hypothesis is not rejected. The probability of type 1 error is denoted $$P (\mathrm{error}|H_0)$$ and the probability of type 2 error is denoted $$P (\mathrm{error}|H_1)$$.

Optimal error-exponent for Neyman-Pearson testing
In the Neyman-Pearson version of binary hypothesis testing, one is interested in minimizing the probability of type 2 error $$P (\mathrm{error}|H_1)$$ subject to the constraint that the the probability of type 1 error $$P (\mathrm{error}|H_0)$$ is less than or equal to a pre-specified level $$\alpha$$. In this setting, the optimal testing procedure is a likelihood-ratio test. Furthermore, the optimal test guarantees that the type 2 error probability decays exponentially in the sample size $$n$$ according to $$\lim_{n \to \infty} \frac{- \ln P (\mathrm{error}|H_1)}{n} = D(f_0\|f_1)$$. The error-exponent $$D(f_0\|f_1)$$ is the Kullback-Leibler divergence between the probability distributions of the observations under the two hypotheses. This exponent is also referred to as the Chernoff-Stein lemma exponent.

Optimal error-exponent for average error probability in Bayesian hypothesis testing
In the Bayesian version of binary hypothesis testing one is interested in minimizing the average error probability under both hypothesis, assuming a prior probability of occurrence on each hypothesis. Let $$ \pi_0 $$ denote the prior probability of hypothesis $$ H_0 $$. In this case the average error probability is given by $$ P_{\mathrm{ave}} = \pi_0 P (\mathrm{error}|H_0) + (1-\pi_0)P (\mathrm{error}|H_1)$$. In this setting again a likelihood ratio test is optimal and the optimal error decays as $$ \lim_{n \to \infty} \frac{- \ln P_{\mathrm{ave}} }{n} = C(f_0,f_1)$$ where $$C(f_0,f_1)$$ represents the Chernoff-information between the two distributions defined as $$ C(f_0,f_1) = \min_{\lambda \in [0,1]} \int (f_0(x))^\lambda (f_1(x))^{(1-\lambda)} dx $$.

New
1918 flu pandemic in India was the outbreak of an unusually deadly influenza pandemic in India between 1918-1920 as a part of the worldwide Spanish flu pandemic. Also referred to as the Bombay Influenza or the Bombay Fever in India, the pandemic is believed to have killed up to 12-17 million people died in the country, the most among all countries. Arnold (2019) estimates at least 12 million dead, about 5% of the population.

In India the pandemic broke out in Bombay in June 1918,  with one of the possible routes being via ships carrying troops returning from the First World War in Europe. The pandemic then spread across the country from west and south to east and north. It hit different parts of the country in three waves with the second wave being the highest in mortality rate. The pandemic peaked in the last week of September of 1918 in Bombay, in the middle of October in Madras and in the middle of November in Calcutta. According to the Sanitary Commisioner's report for 1918, the maximum death toll in a week exceeded 200 deaths in both Bombay and Madras. In his memoirs the Hindi poet, Suryakant Tripathi, wrote that "Ganga was swollen with dead bodies." In a report released by the sanitary commissioner in 1918 all rivers across India were clogged up with bodies.

Mahatma Gandhi, the chief leader of India's independence struggle, was also infected by the virus. The pandemic had a significant influence in the freedom movement in the country. The medical infrastructure in the country was unable to meet the sudden increase in demands for medical attention. The consequent toll of death and misery, and economic fallout brought about by the pandemic led to an increase in emotion against colonial rule.

R. Heli
R. Heli was a former Director of Agriculture of the state of Kerala and the first Principal Information Officer of the Farm Information Bureau (FIB) of Kerala.

After completing his studies at the agriculture university in Bangalore, Heli started his career as an agriculture officer with the Rubber Board in 1955, before moving to the Agriculture Department of Thiru-Kochi in 1956 and, in 1957, the State Agriculture Department of Kerala.

Heli was a pioneer of farm journalism in Kerala. He was instrumental in starting agriculture-related articles in Malayalam daily newspapers. He was among the early authors of articles in ‘Karshikarangam’, the column dedicated for agriculture in Mathrubhumi. He was also involved in promoting programs on agriculture in radio and television, including 'Vayalum Veedum' in Akashavani (All India Radio) and 'Noorumeniyude Koithukar' and 'Nattinpuram' in Doordarshan. He was also the first full-time editor of Kerala Karshakan, a monthly farm magazine published by the Government of Kerala since 1954. He also authored a reference book on agriculture in Malayalam titled 'Krishipadam'. His efforts helped in promoting the latest advancements in the field of agriculture among Kerala's farmers. He also played a role in opening Krishi Bhavans and popularising group farming in Kerala. He had also served as a consultant to the MS Swaminathan Research Foundation.

Heli was a recipient of the first Karshaka Bharathi Award for farm journalism and the Kerala Press Academy Award.

Heli was the son of P. M. Raman, the first municipal chairman of Attingal. He was also the brother of R. Prasannan, a former secretary of the Kerala Assembly and R. Prakasam, former MLA of Kerala.

K. V. Thikkurissi
K. V. Thikkurissi (born V. V Krishna Varman Nair) was a Malayalam author who wrote books in different genres including poetry, children's fiction, biography and travelogues. Born in Thikkurissi in Marthandam, he started his literary career in Thiruvananthapuram following the separation of Kanyakumari from Thiruvananthapuram. He won an award from the Kendra Sahitya Akademi for his poem Bhakranangal in 1960. His other noted works include biographies of R. Narayana Panickar and Chattambi Swamikal and children's stories about Vikramaditya. He was a member of Kerala Sahitya Akademi, Kerala Sangeetha Nadaka Academy and Kalamandalam. He also worked as a high school teacher in different schools in Thiruvananthapuram.

Shiriya River
Shiriya River is a West flowing river flowing through the states of Karnataka and Kerala. It is 67 km in length, making it the eighteenth longest river in Kerala, and the second longest river in the district of Kasaragod. It originates in Anegundi Reserve Forest in Karnataka at an elevation of 230 metres above sea level and empties into the Arabian sea near the town of Shiriya located about 11 km north of Kasaragod. At its mouth the river joins the backwaters between the towns of Shiriya and Kumbla forming the Kumbla-Shiriya estuary. The main tributaries of the river are Kallanje Thodu, Kanyana Thodu, Eramatti Hole and Kumbla.