http://www.math.umass.edu/Calendar/calendar.html <em style="font-style:normal;font-variant:small-caps;color:#881C1C">Statistics and Probability Seminar</em><br><b>Forecasting with Hidden Markov Models </b><br>Daniel W. Chambers , Mathematics Department, Boston College <br><br>A hidden Markov model (HMM) consists of two random processes: a state sequence X_1, X_2, . . . and an observation sequence Y_1, Y_2 , . . . The state sequence is unknown (hidden), while the observation sequence is seen. The state sequence is a Markov chain and, at each time t, the observation Y_t depends on the state of the system- that is, the value of X_t . Hidden Markov models saw early use in speech recognition, but have seen applications in many other settings, including modeling ion channels, genetic sequences, and seismological activity. We will review HMM’s, including parameter estimation algorithms, and then give a straightforward extension that allows us to forecast future observations, given past observations. That is, we will give the (calculable) density of Y_t+k, conditional on the values of Y_1 , . . . , Y_t for any k ≥ 1. We will give two examples: (1) the “occasionally dishonest casino” of Durbin et al. (Biological Sequence Analysis), and (2) forecasting mainshock earthquake activity in southern California (joint work with John Ebel, Alan Kafka, and Jenny Baglivo). <br><br>Refreshments at 3:45<br><br>4:00pm-5:00pm, Monday, November 23, 2009 in LGRT 1634<br> http://www.math.umass.edu/Calendar/abstract.html?seminar=Statistics and Probability Seminar&date=2009-11-23&time=16:00:00&loc=LGRT 1634&refer=/Calendar/calendar.html <em style="font-style:normal;font-variant:small-caps;color:#881C1C">Representation Theory</em><br><b>Twisted geometric Satake correspondence</b><br>Ryan Reich, Harvard<br><br>Geometric Satake correspondence is a way to construct from a reductive group G its Langlands dual group G*. (One can think of it as a deep generalization of duality of vector spaces.) This is a bases of the geometric approach to ``Langlands program'' which is a unifying view on much of Number Theory, Representation Theory, Algebraic Geometry and more recently also some Quantum Field Theory. The ``twisted'' version is a recent development which extends the scope of Langlands program.<br><br>4:00pm-5:00pm, Monday, November 23, 2009 in LGRT 1234<br>Note special room<br> http://www.math.umass.edu/Calendar/abstract.html?seminar=Representation Theory&date=2009-11-23&time=16:00:00&loc=LGRT 1234&refer=/Calendar/calendar.html