Reassembling the Novel. The English Novel, 1789–1919

Abstract

An inclusive history of the novel during the long 19th century, one involving the demography of novels and novelists, has been widely discussed. A precondition for this kind of historical research is an exhaustive list of novels published during the period. The contribution of this paper are estimates of yearly rates of new novel production between 1837 and 1919 in the British Isles.

1 Introduction

An inclusive history of the novel during the long 19th century, one involving the demography of novels and novelists, has been widely discussed. A precondition for this kind of historical research is an exhaustive list of novels published during the period. The contribution of this paper are estimates of yearly rates of new novel production between 1837 and 1919 in the British Isles.¹ James Raven, Antonia Forster,² Peter Garside, Rainer Schöwerling,³ Peter Garside et al.⁴ (hereafter ‘RFGS’) have already provided an exhaustive bibliography covering the years 1770 to 1836. The approach used to estimate novelistic production here is applicable to other geographic and linguistic contexts. Moreover, year-to-year changes in the rate of new novel publication in one region are likely to be informative about how quickly (or slowly) novelistic production is changing in neighboring regions. Yearly estimates of the rate of novelistic production are essential in a variety of projects associated with literary and publishing history. For example, these estimates facilitate bibliographic work as they permit literary historians to assess the completeness of existing bibliographies for a given year.

This contribution is usefully seen as participating in a broader project: a data-intensive, sociologically-inclined literary history seeking to addresses long-standing questions in the history of the novel using digital surrogates of surviving literary works.⁵ Although sociology of literature in the 1950s and 1960s foundered due to a lack of information about writers, works, and related documents—or representative samples thereof—contemporary library-scale digitization, inexpensive computational resources, and widespread sharing of machine-readable datasets permit resuming a variety of research projects on more secure footing.

Before presenting and discussing the new estimates of yearly novelistic production in the British Isles, this paper mentions existing research which stands to benefit from an exhaustive bibliography of the novel in the 19th century.

2 Related Work

Projects likely to benefit from the availability of an exhaustive bibliography of published novels tend to be affiliated with the sociology of literature or sociologically-inclined literary history. Sociologically-inclined literary history has long been associated with inclusionist demands as well as the use of new methods. To the extent that previous research agendas linked to sociology of literature failed or were abandoned due to the lack of reliable information about novelistic production, these agendas merit revisiting for reasons mentioned earlier—notably the relative abundance of book page images and book reviews as well as machine-readable bibliographic and biographical records. These agendas hold out the promise of studying literature at multiple scales and of enlarging the available vocabularies for discussing the history of literature.

A characteristic demand of sociologically-inclined literary history is the demand for an inclusive literary history. The most recent advocate for an inclusive history of the novel is Franco Moretti.⁶ Of the ca. 25,000 new novels published in the British Isles during the 19th century, Moretti estimates only about 200—less than 1%—figure in teaching and research.⁷ The demand for an inclusive approach to literary history and many research questions discussed under the heading of sociology of literature are present in earlier works as well, in particular Daniel Mornet’s work from the 1910s and in Robert Escarpit’s Sociologie de la littérature (1958).⁸ Mornet embraced an inclusive approach to the study of literary taste, explored patterns in reading broadly, and suggested attending to the potential influence of ‘minor’ authors. The research agendas of Escarpit, Mornet and sociologically-inclined literary history in general suffered due to the lack of accessible and trusted bibliographic data.⁹ The resources available to them did not include, needless to say, machine-readable bibliographic records of all surviving 19th-century books much less digital facsimiles of the pages of tens of thousands of surviving works.

The testimony of John Sutherland¹⁰ to the lack of available bibliographical and biographical details is informative. Sutherland mentions the “sheer unavailability of necessary empirical knowledge” as an obstruction to literary sociology, adding, “[O]ne of the things that makes literary sociology so easy to do at the moment is that we don’t know enough to make it difficult.”¹¹ These sentiments echo Eliot’s description of difficulties encountered in his work during the late 1990s.¹²

A second characteristic of sociologically-inclined literary history, tied to the demand for an inclusive literary history, is an openness to new methods. The demand for a diversification of methods—in particular, beyond close reading (“direct textual reading”)¹³—is familiar in Moretti’s work and one linked explicitly to the need to analyze the morphology of the hundreds of thousands of literary works.¹⁴ The openness to a mixture of methods in sociologically-inclined literary history is easy to distinguish from recent forms of interdisciplinarity in literary studies because, as observers have noted, the latter is sharply constrained: methods are allowed safe passage into literary studies only if they do not use numbers.¹⁵ Sociologically-inclined literary history, by contrast, entertains the borrowing of survey methods from the social sciences and a range of techniques from statistics, computational linguistics, complex systems, and biological systematics.¹⁶

3 The Rise of the Text Industry

Between 1840 and 1860 the rate at which new novels were published in the British Isles grew approximately twice as fast as the population of individuals able to read (‘readers’) (Fig. 1).¹⁷ (The method used to estimate the rate of growth during this period are described in the Methodological Appendix.) Such a development would have required a doubling of numerous processes of interest to literary historians, not least a doubling of the number of publishable manuscripts. Existing narratives of the period do not observe this growth or, to the extent that they do, attribute growth to factors such as changing tastes among readers and clever marketing strategies by publishers. This section argues that factors such as declining unit costs and changes in the industrial organization of publishing deserve to play a leading role in the narrative of the growth in novelistic production in the 19th century.

Fig. 1

New Novels Per Million Readers published in the British IslesFootnote

Cross marks indicate known data from RFGS. Points are median estimates and error bars indicate 80% credible intervals. The model used for estimating intervals is described in the Methodological Appendix. UK Population figures are from Angus Maddison (Statistics on World Population, GDP and Per Capita GDP, 1–2008 AD, n.p. 2009). Literacy figures are collected in Gregory Clark (A Farewell to Alms: A Brief Economic History of the World, Princeton 2007). Population figures prior to 1820 are only available for 1800 and 1810. Especially prior to 1820, population and literacy estimates are somewhat unreliable. Adjusting for population and literacy is, however, essential due to the pace and scale of change. Between 1800 and 1900 population likely increased by between 300 and 400%. Basic literacy in 1800 was likely around 61% for men and 42% for women. By 1900 literacy was approaching 100%.

The pace of growth in new novels outstripped that of book publishing in general which itself was growing faster than the reading population between 1840 and 1860.¹⁹ Cataloging the yearly production of new titles is an obvious first step towards addressing a range of unanswered questions concerning the material processes by which literature is produced, distributed, marketed, and consumed. As Sutherland²⁰ notes, the extent of scholarly ignorance on these matters is near total. For example, nobody knows how many people pursued careers as novelists in the British Isles in the 19th century.²¹ Narrow intervals containing the number of new titles published each year allow us to begin to answer these and related questions.²²

Between 1840 and 1860, the rate at which new titles appeared grew appreciably. After 1860 growth relative to the reading population is distinctly slower. It is something of a mystery, then, why the rate of new novel publication, adjusted for the reading population, would rise dramatically between 1840 and 1860. Such change involved a variety of other processes of interest: a doubling of manuscripts received, a doubling of paper consumed by publishing books, a doubling of the labor of compositors, and so forth. Given the fixed costs associated with writing or printing a novel, the increase in the number of new novels appearing in the literary market merits a thorough accounting. How was this extra demand (on the publisher’s side) for manuscripts met? Assuming that the demand could not be met entirely by the existing population of novelists, where did the new novelists come from? Did their recruitment diversify the socio-economic or regional background of the existing pool of writers? (Table 1)

Table 1 New Novels by DecadeFootnote

Sources: 1779–1836, RFGS; ‘Novels (model)’ shows the 80 percent credible interval predicted by the model; Nineteenth-Century Short Title Catalog (NSTC) is NSTC (LOCED) from Eliot (1997). The duplicate values in NSTC (LOCED) for the 1850s and 1860s are not typos; the number of titles associated with each decade are the same.

Two developments deserve to be part of any account of the increase in the rate at which new novels were being published. These developments have tended not to feature prominently in stories of the growth in new novels during the period or have tended to be equated with other factors such as changing tastes and clever advertising strategies. Both developments would have contributed to a decline in the unit cost associated with publishing a novel. This, in turn, would have led to a higher rate of new novel publication. After describing the two developments, we will discuss how declining unit costs would have likely led to an increased rate of new novel publication.

The first development is declining factor costs associated with the emergence of steam-powered printing and steam-powered paper production. It is clear that the cost of paper and the cost of printing declined tremendously over the 19th century, although precisely when and where the decline occurred needs to be determined.²⁴ Steam-power was introduced in the production of paper around 1807 and steam-powered printing was introduced around 1814.²⁵ By 1825 half of all paper in England was made by machine.²⁶ If paper and printing costs were not already declining by 1830, it seems likely there was at least the expectation of their doing so in the near future. This is consequential because paper and machining costs made up a considerable fraction of the cost of publishing a book.²⁷ estimates suggest that in 1850 paper and machining costs, taken together, exceeded the cost of compositing in print run of 1,000.²⁸

New and maturing forms of industrial organization are the second factor likely contributing to declining unit costs. Something which increasingly resembles the modern publishing industry emerges between 1840 and 1860.²⁹ Associated developments likely contributed to declining unit costs via economies of scale, declining overhead, accounting improvements, and declining cost of capital.

In 1844 regulation was introduced that required companies to post audited balance sheets with the Registrar of Companies, a requirement which did not directly affect publishers, which were typically organized as partnerships, but gives a sense of broader changes in the business environment. Weedon³⁰ considers 1844 a turning point, writing that “from this time [1844] on recognizable and systematic accounting systems began to take shape in many publishing houses.”³¹ (Capital was indeed difficult to raise in the 1830s and grew easier over time.³²) One piece of evidence which would be consistent with an account focused on economies of scale would be evidence suggesting that larger publishers were steadily increasing the number of new novels they published. Since we lack comprehensive bibliographies for the period of interest there is no way to demonstrate this directly. We can, however, show that there is no evidence of any significant decline in concentration among publishers before 1840 (Fig. 2 and 3). We should also recall that measuring the output of a publisher using new novels understates production—and, with it, economies of scale—as many publishers of novels began to reissue previously published novels. And reissuing novels was an activity which grew in significance only after 1830. For example, Richard Bentley, who is among the top four publishers for 1835–1836, published 126 reissued works in the Standard Novels series between 1831 and 1855, 19 of which were published (with Henry Colburn) before 1833.³³

Fig. 2

New novels published by largest four publishersFootnote

Calculations rely on manually identifying the publisher using the ‘publication’ field in a random sample of 360 titles published between 1810 and 1836 appearing in RFGS. Error bars (80% credible intervals) reflect uncertainty due to sampling. Yearly rate is calculated by dividing the number of novels published in each period by the number of years in the period.

Fig. 3

Proportion of new novels published by largest four publishersFootnote

Calculations rely on manually identifying the publisher using the ‘publication’ field in a random sample of 360 titles published between 1810 and 1836 appearing in RFGS. Error bars (80% credible intervals) reflect uncertainty due to sampling.

One well-known anecdote suggests the potential magnitude of efficiency gains between 1840 and 1860. Dickens’ Dombey and Son (1846) and Our Mutual Friend (1865) were printed in similar quantities (30,000 and 32,000 respectively). Adjusting for deflation, the unit cost of Our Mutual Friend was roughly half (58%) of that of Dombey and Son.³⁶ If this example is typical, there is little need to search for additional factors contributing to the acceleration observed between 1840 and 1860. Publishing a book simply becomes less expensive.

We should expect to see individual publishers publishing more books if per unit costs fall. Why this should be is not immediately obvious because nothing forces a publisher, given positive expected returns and the opportunity to publish more books at the same cost, to take advantage of the opportunity. In a competitive environment, however, a variety of pressures would favor the publisher which prints the greater number of titles. Since publishing more books would bring with it increased revenue, lower variability in revenue, and economies of scale, firms printing more books would tend to accrue more financial resources, something which tends to be a competitive advantage. Moreover, bringing a greater number of books to market is, by itself, a costly and advantageous signal of quality to readers and to potential writers. Although there’s considerable uncertainty about when and by how much unit costs declined during the period, we should be more confident that publishers who elected to print more rather than fewer titles would be more likely to survive in a competitive environment. In light of this, we should anticipate observing a greater number of novels being published when unit costs decline.

Competing narratives which attribute the increase in the per-reader rate of new novel appearance between 1840 and 1860 to growing demand for novels in the population deserve to be viewed with scepticism. Such accounts suggest that the increase is due to one or both of the following: 1) an increase in the number of novel readers (in excess of what would be expected from a growing reading population) and 2) an intensification of reading among existing novel readers. The precise mechanism proposed varies but can include, for example, publishers’ ‘stimulating demand’ with clever advertisements or typography. It would also include the suggestion that publishers, individually or collectively, managed to appeal to “public taste” in a previously unknown manner which bolstered demand.³⁷ An expanding market for books is often simply assumed, although typically without clarifying how fast the expansion is occurring—in particular, if it is expanding faster than the reading population:³⁸ is not exceptional in mentioning “[t]he burgeoning mass market of the first half of the nineteenth century.”³⁹

One straightforward accounting of the increase in new titles would look to an increase in the number of readers of new novels among the existing population of readers. Such an increase is easy to imagine if we are persuaded that not everyone who can read and afford access to novels does indeed spend time reading novels. The strongest reason to discount this narrative, however, is that time spent on reading is inelastic. Given a finite number of hours in each day, time spent on reading is constrained and, with it, the number of books one is able to read in a given year. That the population of readers might, collectively, increase time spent reading new novels by as much as ten percent between 1840 and 1860 is difficult to credit. And a lateral shift away from non-novel reading to novel reading is incompatible with the evidence: the rate at which all books (non-novels and novels) is also accelerating over much of the period 1840–1860.⁴⁰

Another accounting of the growth in new novels focuses on the improving economic fortunes of the population. Given the considerable expense of a new novel (ca. 21 s 6d) or an annual subscription to a circulating library (ca. 20s)—roughly a week’s wages for an unskilled worker worker in 1850—it is certain that a large fraction of the reading population could not afford access to new novels before 1840. This narrative, however, is implausible because there is no evidence of rising wages until well after the acceleration in the rate of new novel publication. Contrary to expectations about a period firmly within the industrial revolution, typical incomes did not start to rise until after 1830 and then only at a relatively slow pace: an average yearly rate of growth of 0.86% between 1830 and 1860.⁴¹

The theory that the population of existing novel readers intensified their reading of new novels after 1840 and that this new demand influenced the rate of publication of new novels is difficult to credit for reasons already mentioned. Time available for reading sharply constrains the scope for intensification of novel reading among those who were already avid novel readers in 1840. For those who did not read many novels, increasing the rate at which they read novels more than even ten percent would encounter considerable friction. New novels remained luxury goods and circulating libraries’ subscriptions limited the number of novels which could be borrowed at any given time.

What about the export market for novels? Total book exports do increase during the 19th century but there does not appear to be any particular departure or development of interest prior to or during the 1830s and 1840s.⁴²

The rapid growth between 1840 and 1860 in the per-reader rate of new novel publication deserves greater attention than it has received. This period of growth is surprising because it occurs before mass literacy and the general growth in incomes associated with the industrial revolution. It also deserves attention from literary historians because the sustained rate of growth is high enough that it could not have occurred without widely-felt changes in a variety of processes at the heart of the literary market.

Novel writers, in particular, must have felt the consequences of a doubling in the rate of new novel publication. For example, a doubling of the rate of new novels published would require either an intensification of labor by existing writers, a broadening of the population of writers, or some combination of the two. Any of these would likely be associated with substantial and durable changes in the relationship between writers and publishers. For example, an intensification of work or a broadening of the population of writers might have favored certain kinds of writers or the production of certain kinds of novels (e.g., novels in certain genres or with certain formal features) if these novels were easier (in some sense) to produce.

4 Conclusion

The digitization of bibliographic data and surviving novels makes a variety of tasks involved in the study of literary history less time-consuming and less resource intensive. In many cases this development enables research that would otherwise be abandoned as impractical.

With distance from the arrival of—and optimism surrounding—large-scale library digitization projects in the late 2000s, it is perhaps easier to reflect soberly on the necessary supports for doing data-intensive literary history at scale. Without some knowledge of how many novels were published each year—along with related information such as publisher concentration and the demography of novelists—is difficult to make use of digital facsimiles. This paper contributes a description of the growth of novelistic production during the long 19th century, and, in particular, new estimates of the number of novels published each year between 1837 and 1919. These estimates will facilitate current bibliographic work and support future research in sociologically-inclined literary history.

Methodological Appendix: Inferring the Rate of New Novel Publication, 1800–1919

The quantities which will be estimated are the underlying yearly rates at which new novels (i.e., previously unpublished novels) appeared between 1800 and 1919. The number of novels published between 1800 and 1836 (inclusive) are known and can be used to check the predictions of the model.

1.1 1. Data

New Titles 1800–1836: Garside/Schöwerling and Garside et al. (‘RFGS’).

Thanks to an exhaustive survey we know the number of new novels appearing between 1770 and 1836 (inclusive).⁴³ (Only the numbers associated with the years 1800–1836 are used by the model.) The bibliography by RFGS both provides the most important time series used by the model and anchors the effort more generally by providing a particular definition of the novel. The counts of new novel publications during these years will be denoted with the variable $y_{i}$ where $i$ indexes the year. For example, the first year, 1800, is associated with the index 1. A sequence of counts will be indicated by joining the starting index and ending index with a colon, e.g., $y_{1:120}$.

NSTC Titles 1800–1870 with London, Oxford, Cambridge, Edinburgh, and Dublin Imprint Locations (NSTC (LOCED))

Simon Eliot⁴⁴ extracted yearly totals of titles listed in the Nineteenth-Century Short Title Catalog (NSTC) whose publication information indicates the place of publication was either London, Oxford, Cambridge, Edinburgh, or Dublin (LOCED). The difficulty encountered in using these figures is that for years after 1836 we do not know what percentage of NSTC (LOCED) titles are new novels. These percentages must be inferred. The NSTC (LOCED) counts are recorded in the sequence $n_{1:71}$, where the index indicates the year.

The NSTC assigns undated material to the nearest half-decade (to a year ending with a ‘0’ or a ‘5’).⁴⁵ Rather than modify the model to accommodate this idiosyncrasy, years which end in a ‘0’ or a ‘5’ are not used in the model.

Publishers’ Circular Yearly Totals for 1843 to 1919 (PC)

Publishers’ Circular yearly totals are counts of the number of new editions reported in Publishers’ Circular between 1843 and 1919. These totals are reported in Simon Eliot.⁴⁶ These counts are recorded in the sequence $p_{1:120}$, where the index indicates the year. No reliable counts are available before 1843, so the only the subsequence $p_{44:120}$ is used.

The difficulty with using the PC data is the same difficulty encountered with the NSTC (LOCED) titles. The percentage of PC editions which are new novels is unknown. Although the specific percentage is unknown, we do have a considerable amount of prior information. From one year to the next, for example, it seems a safe assumption that the percentage is unlikely to change dramatically. Even over a longer period, we can be confident that wild swings are highly unlikely. We do not anticipate that the percentage of all editions which are new novels would swing from 2% between 1820 and 1824 to 20% between 1845 and 1849.

Elicited Quartiles for 1886, 1891, and 1894

Following the procedure described in Paul H. Garthwaite, Joseph B. Kadane, Anthony O’Hagan,⁴⁷ we elicited from Troy Bassett information about the number of new novels published during three years 1886, 1891, and 1894. For each year, quartiles of the distribution matching Bassett’s beliefs about the total number of new novels published in that year were elicited. As editor of At the Circulating Library: A Database of Victorian Fiction, 1837–1901,⁴⁸ Bassett has a range of information valuable in making accurate estimates. For example, Bassett has precise information about lower bounds for the number of novels published during these years (i.e., the number of novels already recorded for these years in the database) and the rate at which new novels are currently being identified.

The elicited quartiles used are the following:

• 1886: 393.75, 481.25, 612.5

• 1891: 481.25, 525.0, 612.5

• 1894: 656.25, 787.5, 962.5

Because At the Circulating Library uses a broader definition of the novel than, the quartiles shown above reflect a discount of 12.5% from the original elicited quartiles. This number was chosen as an approximation of the discount reported by Bassett. Bassett states that between 10 and 15% of the novels recorded in At the Circulating Library would be excluded from RFGS.

Given the quartiles of a distribution, a probability distribution which has approximately the same quartiles can be found. In this case, Gamma distributions are used as the approximating distributions.

Athenaeum Reviews of Novels: 1860, 1865, …, 1900: Ellen Miller Casey

Ellen Miller Casey provides counts for the number of novels reviewed in The Athenaeum during nine years: 1860, 1865, 1870, 1875, 1880, 1885, 1890, 1895, 1900. (The Athenaeum was a London literary magazine published from 1828 to 1921.) This series shows a steep increase in the number of titles reviewed. Like every source of book reviews published at the time, these counts underestimate the total number of new novels published as not all new novels are reviewed. These nine counts are recorded in the sequence $a_{1:120}$ where the index indicates the year. Only values associated with the nine years are used.

1.2 2. Model

The model offers a narrative of novelistic production in terms of the yearly rate of new novel publication. This narrative can be broken down into two main pieces: an underlying trend and periodic deviations from the trend.

The model assumes that the rate of new novel publication tends to grow at a fixed percentage each year during the period. The model also makes assumptions about deviations from this growth trend. Accomodating deviations is essential because there is no doubt that a variety of events affected the rate of (new) novel publications during the period–e.g., a cholera epidemic in the 1840s, a recession in the 1850s, and World War I. In order to make accurate yearly predictions of the number of novels, the model must be flexible enough to accommodate significant deviations from trend.

The growth trend and deviations are modeled using a Gaussian process.⁴⁹ Instead of having year-specific deviations be independently distributed (as in conventional linear models), deviations are assumed to be correlated with each other in a manner specified by a Gaussian process. The Gaussian process is characterized by a mean function $m$ and a covariance function $k$ (sometimes called a kernel). The covariance function used in the model is the squared exponential covariance function. An important parameter in the covariance function is the characteristic length-scale $l$, which governs to what extent deviations in nearby years are correlated with each other.

In symbols, the yearly rates of new novel publication are modeled on a log-scale as follows:

$$ \begin{array}{*{20}c} {\lambda_{1:120} } & { \sim MultivariateNormal\left( {\alpha_{\lambda } + \beta_{\lambda } t_{1:120} ,K\left( {t_{1:120} } \right)} \right)} \\ {k\left( {x_{i} ,x_{j} } \right)} & {} \\ \end{array} $$

$K$ is an $n \times n$ covariance matrix whose elements are specified by the covariance function $k$. An element $\left( {i,j} \right)$ of $K$ corresponds to $k\left( {x_{i} ,x_{j} } \right)$. $t_{1:120}$ is a column vector of integers associated with the years (1 for 1800, 2 for 1801, …, 120 for 1919). The rate of new novel publication in year $i$ is $exp\left( {\lambda_{i} } \right)$. Generic weakly informative priors are placed on all the parameters not explicitly mentioned above. The characteristic length-scale $l_{\lambda }$ is modeled with a Gamma distribution placing 90% of its mass on values between 1 and 10. This prior distribution expresses the belief that deviations will tend to persist for between 1 and 10 years. Such a prior is, for example, consistent with the belief that a financial crisis might affect the rate of publication in the short term but would cease to influence publication rates in years which are more than ten years distant from the crisis.

The yearly rates of new novel publication $exp\left( {\lambda_{1} } \right),exp\left( {\lambda_{2} } \right), \ldots exp\left( {\lambda_{120} } \right)$ are connected to observations of the number of new novels published with a Negative Binomial sampling distribution. The total number of new novels published is known for years between 1800 and 1836 (inclusive). In symbols, this sampling model reads:

$$ y_{i} \sim NegativeBinomial_{2} \left( {exp\left( {\lambda_{i} } \right),\phi_{y} } \right)i \in \left\{ {1, \ldots ,37} \right\} $$

The negative binomial distribution has a variety of parameterizations. $NegativeBinomial_{2}$ is parameterized by a mean (i.e., location) parameter and a parameter controlling dispersion.⁵⁰

A second Gaussian process models the yearly proportion of PC titles which are new novels. In order to use the Gaussian process, these proportions must be expressed on the log odds scale. (The log odds is the logarithm of the odds, $log\left( {\frac{p}{1 - p}} \right)$, where $p$ is a proportion between 0 and 1.) In contrast to changes in the yearly rate of new novel publication, the proportion of PC titles which are new novels is expected to change slowly. Whereas an economic depression might affect the rate of new novel publication over a period of several years, it would be far less likely to affect the proportion of PC titles which are novels. In symbols, the yearly proportions are modeled as follows:

$$ \begin{array}{*{20}c} {\nu_{1:120} } & { \sim MultivariateNormal\left( {\alpha_{\nu } + \beta_{\nu } t_{1:120} ,K\left( {t_{1:120} } \right)} \right)} \\ {k\left( {x_{i} ,x_{j} } \right)} & {} \\ \end{array} $$

The proportion of PC titles which are novels in the year with index $i$ is $logit^{ - 1} \left( {\nu_{i} } \right)$. ($logit^{ - 1} \left( x \right)$, the inverse logistic function, inverts the transformation of a proportion to the log odds scale.) The characteristic length-scale $l_{\nu }$ is modeled with a Gamma distribution placing 90% of its mass on values between 8 and 36. This prior distribution expresses the belief that deviations will tend to persist for between 8 and 36 years.

In symbols, the sampling model for the observed yearly counts of PC titles is the following:

$$ p_{i} \sim NegativeBinomial_{2} \left( {\frac{{exp\left( {\lambda_{i} } \right)}}{{logit^{ - 1} \left( {\nu_{i} } \right)}},\phi_{p} } \right),i \in \left\{ {44, \ldots ,120} \right\} $$

Similarly, the sampling model for the observed yearly counts of NSTC (LOCED) titles is as follows:

$$ n_{i} \sim NegativeBinomial_{2} \left( {\frac{{\pi_{n} exp\left( {\lambda_{i} } \right)}}{{logit^{ - 1} \left( {\nu_{i} } \right)}},\phi_{n} } \right),i \in \left\{ {x \vee x \in \left\{ {1,2, \ldots ,71} \right\} \wedge \left( {x - 1} \right)mod5 \ne 0} \right\} $$

The NSTC (LOCED) counts are always higher than the PC title counts. We make the assumption that the yearly rate for NSTC (LOCED) counts is equal to the yearly rate for PC title counts multiplied by a constant factor, $\pi_{n}$.

The distributions elicited from Bassett are incorporated as follows:

$$ \begin{array}{*{20}c} {\lambda_{87} } & { \sim Gamma\left( {278.36,46.3} \right)} \\ {\lambda_{92} } & { \sim Gamma\left( {1530.73,245.4} \right)} \\ {\lambda_{95} } & { \sim Gamma\left( {667.9,101.8} \right)} \\ \end{array} $$

These distributions approximate the elicited quartiles described above. Note that $\lambda_{i}$ is the logarithm of the yearly rate of publication. The approximating distributions therefore also use the log scale.

Finally, the counts of new novels reviewed in The Antheneum are incorporated as follows:

$$ \begin{array}{*{20}c} {a_{i} } & { \sim NegativeBinomial_{2} \left( {\pi_{a} exp\left( {\lambda_{i} } \right),\phi_{n} } \right),i \in \left\{ {61,66, \ldots ,101} \right\}} \\ {\pi_{a} } & { \sim Gamma\left( {15.5,32} \right)} \\ \end{array} $$

Because The Antheneum does not review all new novels published, the rate of new novel publication is discounted by a factor $\pi_{a}$. An informative Gamma prior placing 90% of mass on a value between 30 and 70% is used as it seems very likely that The Antheneum reviews a fraction of new novels each year lying in this range.

1.3 3. Inference

Posterior inference is performed using Stan.⁵¹