Title: MML, statistically consistent invariant Bayesian probabilistic inference and the elusive model paradox Speaker: David L. Dowe - Clayton School of Information Technology, Monash University, Clayton (Melbourne), Australia [and Departmento de Sistemas Informatics y Computacion, Universidad Politecnica de Valencia (UPV), Valencia, Espan~a] (Brief?) speaker bio': David Dowe is Associate Professor in the Clayton School of Information Technology (formerly Department of Computer Science) at Monash University in Melbourne, Australia. He was the closest collaborator of Chris Wallace (1933-2004), the originator (Wallace and Boulton, Computer J, 1968) of Minimum Message Length (MML). In Wallace's (posthumous, 2005) book on MML, Dowe is the most cited and most discussed living person. Dowe was guest editor of the Christopher Stewart WALLACE (1933-2004) memorial special issue of the Computer J (Vol. 51, No. 5 [Sept. 2008]) and will be chair of the Ray Solomonoff (1926-2009) 85th memorial conference in late 2011. Dowe's many contributions and applications of MML to machine learning, statistics and philosophy, etc. include (e.g.) (i) his conjecture that only MML and close Bayesian approximations can - in general - guarantee both statistical invariance and statistical consistency (e.g., Dowe, Gardner & Oppy, Brit J Philos Sci, 2007), (ii) his 2010 book chapter on MML and philosophy of statistics in the Handbook of the Philosophy of Science - (HPS Volume 7) Philosophy of Statistics, Elsevier [ISBN: 978-0-444-51862], (iii) his work (Dowe & Hajek, 1998) (Hernandez Orallo & Dowe, AI journal, 2010) using MML as an response to Searle's Chinese room argument and showing how MML can be used to quantify intelligence (http://users.dsic.upv.es/proy/anynt), (iv) his uniqueness result about the invariance of log-loss probabilistic scoring, (v) his supervision of the world's longest running (since 1995) compression-based log-loss competition (at www.csse.monash.edu.au/~footy), (vi) the first work on MML Bayesian nets using both discrete and continuous variables, etc. Abstract: We outline the Minimum Message Length (MML) principle (from Bayesian information theory) (Wallace and Boulton, Computer J, 1968) of statistics, machine learning, econometrics, inductive inference and (so-called) data mining. We explain the result from elementary information theory that the information content (or code length) of an event is the negative logarithm of its probability, l = - log(p). We also mention the notion of statistical invariance (if analysing a cube, the estimate of the volume should be the cube of the estimate of the side length; if analysing a circle, the estimate of the area should be pi times the square of the estimate of the radius, etc.) and the notion of statistical consistency (as you get more and more data, your estimate converges as closely as is possible to the correct answer). As desiderata, statistical invariance seems more than aesthetic, and statistical consistency seems much more than aesthetic. We relate MML to algorithmic information theory (or Kolmogorov complexity) (Wallace & Dowe, Computer J, 1999a), essentially the amount of information required to program a (Universal) Turing machine. We then highlight MML's ability to deal with problems where the amount of data (per parameter) is scarce (such as, e.g., latent factor analysis of (e.g.) I.Q. or of octane rating, or the classic Neyman-Scott (1948) problem). It is this ability of MML which lead to the speaker's conjecture (Dowe et al., 1998; Dowe, 2010) about the uniqueness of MML in being able to be both statistically invariant and statistically consistent for problems where the amount of data per parameter is bounded above. We then relate MML to a few problems in the philosophy of science. Depending upon time and the wishes of the audience, etc., such problems might be (e.g.) (i) the elusive model paradox (Scriven, 1965; Lewis & Shelby Richardson, 1966; Dowe 2008a, 2008b, 2010), (ii) ``objective'' (Bayesian) inference, inference (and explanation) (Wallace & Boulton, 1968) versus prediction (Solomonoff, 1964), (iii) MML, Searle's Chinese room and ``intelligence'', (iv) Goodman's ``grue'' problem (paradox) of induction, (v) inevitability of financial market inefficiency, (vi) probabilities of conditionals, (vii) entropy not being the arrow of time, (viii) fictionalism, etc.